gcmsiv.xml

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<rfc category="info" ipr="trust200902" number="8452" submissionType="IRTF"
     consensus="yes">
  <front>
    <title abbrev="AES-GCM-SIV">AES-GCM-SIV: Nonce Misuse-Resistant Authenticated Encryption</title>

    <author fullname="Shay Gueron" initials="S." surname="Gueron">
      <organization abbrev="University of Haifa &amp; AWS">University of Haifa and Amazon</organization>
      <address>
        <postal>
          <street>Abba Khoushy Ave 199</street>
          <city>Haifa</city>
          <code>3498838</code>
          <country>Israel</country>
        </postal>
        <email>shay@math.haifa.ac.il</email>
      </address>
    </author>

    <author fullname="Adam Langley" initials="A." surname="Langley">
      <organization>Google LLC</organization>
      <address>
        <postal>
          <street>345 Spear St</street>
          <city>San Francisco</city>
          <region>CA</region>
          <code>94105</code>
          <country>United States of America</country>
        </postal>
        <email>agl@google.com</email>
      </address>
    </author>

    <author fullname="Yehuda Lindell" initials="Y." surname="Lindell">
      <organization>Bar-Ilan University and Unbound Tech</organization>
      <address>
        <postal>
          <street>Ramat Gan</street>
          <code>5290002</code>
          <country>Israel</country>
        </postal>
        <email>Yehuda.Lindell@biu.ac.il</email>
      </address>
    </author>

    <date month="April" year="2019" />

    <workgroup>Crypto Forum</workgroup>

    <keyword>authenticated encryption</keyword>
    <keyword>aead</keyword>
    <keyword>aes</keyword>
    <keyword>gcm</keyword>
    <keyword>siv</keyword>

    <abstract>
      <t>This memo specifies two authenticated encryption algorithms that are
      nonce misuse resistant -- that is, they do not fail catastrophically
      if a nonce is repeated.</t>

      <t>This document is the product of the Crypto Forum Research Group.</t>
    </abstract>
  </front>

  <middle>
    <section title="Introduction">
      <t>The concept of Authenticated Encryption with Additional Data (AEAD)
      <xref target="RFC5116"/> couples confidentiality and integrity in a
      single operation, avoiding the risks of the previously common practice
      of using ad hoc constructions of block-cipher and hash primitives. The
      most popular AEAD, AES-GCM <xref target="GCM"/>, is seeing widespread
      use due to its attractive performance.</t>

      <t>However, some AEADs (including AES-GCM) suffer catastrophic failures
      of confidentiality and/or integrity when two distinct messages are
      encrypted with the same key and nonce. While the requirements for AEADs
      specify that the pair of (key, nonce) shall only ever be used once, and
      thus prohibit this, this is a worry in practice.</t>

      <t>Nonce misuse-resistant AEADs do not suffer from this problem. For this class of AEADs, encrypting two messages with the same nonce only discloses whether the messages were equal or not. This is the minimum amount of information that a deterministic algorithm can leak in this situation.</t>

      <t>This memo specifies two nonce misuse-resistant AEADs:
      AEAD_AES_128_GCM_SIV and AEAD_AES_256_GCM_SIV. These AEADs are designed
      to be able to take advantage of existing hardware support for AES-GCM
      and can decrypt within 5% of the speed of AES-GCM (for multikilobyte
      messages). Encryption is, perforce, slower than AES&#8209;GCM, because two
      passes are required in order to achieve that nonce misuse-resistance
      property. However, measurements suggest that it can still run at
      two-thirds of the speed of AES-GCM.</t>

      <t>We suggest that these AEADs be considered in any situation where
      nonce uniqueness cannot be guaranteed. This includes situations where
      there is no stateful counter or where such state cannot be guaranteed,
      as when multiple encryptors use the same key. As discussed in <xref
      target="seccon"></xref>, it is RECOMMENDED to use this scheme with
      randomly chosen nonces.</t>

      <t>This document represents the consensus of the Crypto Forum Research Group (CFRG).</t>
    </section>

    <section title="Requirements Language">
        <t>
    The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL
    NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED",
    "MAY", and "OPTIONAL" in this document are to be interpreted as
    described in BCP&nbsp;14 <xref target="RFC2119"/> <xref target="RFC8174"/> 
    when, and only when, they appear in all capitals, as shown here.
        </t>
    </section>

    <section title="POLYVAL">
      <t>The GCM-SIV construction is similar to GCM: the block cipher is used
      in counter mode to encrypt the plaintext, and a polynomial authenticator
      is used to provide integrity. The authenticator in GCM-SIV is called
      POLYVAL.</t>

      <t>POLYVAL, like GHASH (the authenticator in AES-GCM; see <xref
      target="GCM"/>, Section 6.4), operates in a binary field of size
      2^128. The field is defined by the irreducible polynomial x^128 + x^127
      + x^126 + x^121 + 1. The sum of any two elements in the field is the
      result of XORing them. The product of any two elements is calculated
      using standard (binary) polynomial multiplication followed by reduction
      modulo the irreducible polynomial.</t>

      <t>We define another binary operation on elements of the field: 
<vspace />
dot(a, b), where dot(a, b) = a * b * x^-128. The value of the field element
      x^-128 is equal to x^127 + x^124 + x^121 + x^114 + 1. The result of this
      multiplication, dot(a, b), is another field element.</t>

      <t>Polynomials in this field are converted to and from 128-bit strings
      by taking the least significant bit of the first byte to be the
      coefficient of x^0, the most significant bit of the first byte to be the
      coefficient of x^7, and so on, until the most significant bit of the
      last byte is the coefficient of x^127.</t>

      <t>POLYVAL takes a field element, H, and a series of field elements
<vspace />
X_1, ..., X_s. Its result is S_s, where S is defined by the iteration S_0 =
      0; S_j = dot(S_{j-1} + X_j, H), for j = 1..s.</t>

      <t>We note that POLYVAL(H, X_1, X_2, ...) is equal to
      ByteReverse(GHASH(ByteReverse(H) * x, ByteReverse(X_1),
      ByteReverse(X_2), ...)), where ByteReverse is a function that reverses
      the order of 16 bytes. See <xref target="ghash"></xref> for a more
      detailed explanation.</t>
    </section>

    <section title="Encryption">
      <t>AES-GCM-SIV encryption takes a 16- or 32-byte key-generating key, a
      96-bit nonce, and plaintext and additional data
      byte strings of variable length. It outputs an authenticated ciphertext that will be 16
      bytes longer than the plaintext. Both encryption and decryption are only
      defined on inputs that are a whole number of bytes.</t>

      <t>If the key-generating key is 16 bytes long, then AES-128 is used
      throughout. Otherwise, AES-256 is used throughout.</t>

      <t>The first step of encryption is to generate per-nonce,
      message-authentication and message-encryption keys. The
      message-authentication key is 128 bit, and the message-encryption key is
      either 128 (for AES-128) or 256 bit (for AES-256).</t>

      <t>These keys are generated by encrypting a series of plaintext blocks
      that contain a 32-bit, little-endian counter followed by the nonce, and
      then discarding the second half of the resulting ciphertext. In the
      AES-128 case, 128 + 128 = 256 bits of key material need to be generated,
      and, since encrypting each block yields 64 bits after discarding half,
      four blocks need to be encrypted. The counter values for these blocks
      are 0, 1, 2, and 3. For AES-256, six blocks are needed in total, with
      counter values 0 through 5 (inclusive).</t>

      <t>In pseudocode form, where "++" indicates concatenation and "x[:8]" indicates taking only the first eight bytes from x:</t>
      <figure align="center">
        <artwork align="left"><![CDATA[
func derive_keys(key_generating_key, nonce) {
  message_authentication_key =
      AES(key = key_generating_key,
          block = little_endian_uint32(0) ++ nonce)[:8] ++
      AES(key = key_generating_key,
          block = little_endian_uint32(1) ++ nonce)[:8]
  message_encryption_key =
      AES(key = key_generating_key,
          block = little_endian_uint32(2) ++ nonce)[:8] ++
      AES(key = key_generating_key,
          block = little_endian_uint32(3) ++ nonce)[:8]

  if bytelen(key_generating_key) == 32 {
    message_encryption_key ++=
        AES(key = key_generating_key,
            block = little_endian_uint32(4) ++ nonce)[:8] ++
        AES(key = key_generating_key,
            block = little_endian_uint32(5) ++ nonce)[:8]
  }

  return message_authentication_key, message_encryption_key
}
]]></artwork>
      </figure>

      <t>Define the "length block" as a 16-byte value that is the concatenation of the 64-bit, little-endian encodings of bytelen(additional_data) * 8 and bytelen(plaintext) * 8. Pad the plaintext and additional data with zeros until they are each a multiple of 16 bytes, the AES block size. Then X_1, X_2, ... (the series of field elements that are inputs to POLYVAL) are the concatenation of the padded additional data, the padded plaintext, and the length block.</t>

      <t>Calculate S_s = POLYVAL(message-authentication-key, X_1, X_2,
      ...). XOR the first twelve bytes of S_s with the nonce and clear the
      most significant bit of the last byte. Encrypt the result with AES using the message-encryption key to produce the tag.</t>

<!--[rfced] Are the underscores around the word "plaintext" 
being used for emphasis or another purpose, or may we remove them?

Original:
   (It's worth highlighting a contrast with AES-GCM here: AES-GCM
   authenticates the encoded additional data and ciphertext, while AES-
   GCM-SIV authenticates the encoded additional data and _plaintext_.)
--> 
      <t>(It's worth highlighting a contrast with AES-GCM here: AES-GCM
      authenticates the encoded additional data and ciphertext, while
      AES&#8209;GCM-SIV authenticates the encoded additional data and <spanx
      style="emph">plaintext</spanx>.)</t>

      <t>The encrypted plaintext is produced by using AES, with the
      message-encryption key, in counter mode (see <xref target="SP800-38A"/>,
      Section 6.5) on the unpadded plaintext. The initial counter block is the
      tag with the most significant bit of the last byte set to one. The
      counter advances by incrementing the first 32 bits interpreted as an
      unsigned, little-endian integer, wrapping at 2^32. The result of the
      encryption is the encrypted plaintext (truncated to the length of the
      plaintext), followed by the tag.</t>

      <t>In pseudocode form, the encryption process can be expressed as:</t>
      <figure align="center">
        <artwork align="left"><![CDATA[
func right_pad_to_multiple_of_16_bytes(input) {
  while (bytelen(input) % 16 != 0) {
    input = input ++ "\x00"
  }
  return input
}

func AES_CTR(key, initial_counter_block, in) {
  block = initial_counter_block

  output = ""
  while bytelen(in) > 0 {
    keystream_block = AES(key = key, block = block)
    block[0:4] = little_endian_uint32(
        read_little_endian_uint32(block[0:4]) + 1)

    todo = min(bytelen(in), bytelen(keystream_block)
    for j = 0; j < todo; j++ {
      output = output ++ (keystream_block[j] ^ in[j])
    }

    in = in[todo:]
  }

  return output
}

func encrypt(key_generating_key,
             nonce,
             plaintext,
             additional_data) {
  if bytelen(plaintext) > 2^36 {
    fail()
  }
  if bytelen(additional_data) > 2^36 {
    fail()
  }

  message_encryption_key, message_authentication_key =
      derive_keys(key_generating_key, nonce)

  length_block =
      little_endian_uint64(bytelen(additional_data) * 8) ++
      little_endian_uint64(bytelen(plaintext) * 8)
  padded_plaintext = right_pad_to_multiple_of_16_bytes(plaintext)
  padded_ad = right_pad_to_multiple_of_16_bytes(additional_data)
  S_s = POLYVAL(key = message_authentication_key,
                input = padded_ad ++ padded_plaintext ++
                        length_block)
  for i = 0; i < 12; i++ {
    S_s[i] ^= nonce[i]
  }
  S_s[15] &= 0x7f
  tag = AES(key = message_encryption_key, block = S_s)

  counter_block = tag
  counter_block[15] |= 0x80
  return AES_CTR(key = message_encryption_key,
                 initial_counter_block = counter_block,
                 in = plaintext) ++
         tag
}
]]></artwork>
      </figure>
    </section>

    <section title="Decryption">
      <t>Decryption takes a 16- or 32-byte key-generating key, a 96-bit nonce,
      and ciphertext and additional data byte strings of variable length. It
      either fails or outputs a plaintext that is 16 bytes shorter than the
      ciphertext.</t>

      <t>To decrypt an AES-GCM-SIV ciphertext, first derive the message-encryption and message-authentication keys in the same manner as when encrypting.</t>

      <t>If the ciphertext is less than 16 bytes or more than 2^36 + 16 bytes,
      then fail. Otherwise, split the input into the encrypted plaintext and a
      16-byte tag. Decrypt the encrypted plaintext with the message-encryption
      key in counter mode, where the initial counter block is the tag with the
      most significant bit of the last byte set to one. Advance the counter
      for each block in the same way as when encrypting. At this point, the
      plaintext is unauthenticated and MUST NOT be output until the following
      tag confirmation is complete:</t>

      <t>Pad the additional data and plaintext with zeros until they are each
      a multiple of 16 bytes, the AES block size. Calculate the length block
      and X_1, X_2, ... as above and compute
      <vspace />
   S_s = POLYVAL(message-authentication-key, X_1, X_2, ...) 
      </t>

<t>
Compute the expected
      tag by XORing S_s and the nonce, clearing the most significant bit of
      the last byte and encrypting with the message-encryption key. Compare
      the provided and expected tag values in constant time. Fail the
      decryption if they do not match (and do not release the plaintext);
      otherwise, return the plaintext.</t>


      <t>In pseudocode form, the decryption process can be expressed as:</t>
      <figure align="center">
        <artwork align="left"><![CDATA[
func decrypt(key_generating_key,
             nonce,
             ciphertext,
             additional_data) {
  if bytelen(ciphertext) < 16 || bytelen(ciphertext) > 2^36 + 16 {
    fail()
  }
  if bytelen(additional_data) > 2^36 {
    fail()
  }

  message_encryption_key, message_authentication_key =
      derive_keys(key_generating_key, nonce)

  tag = ciphertext[bytelen(ciphertext)-16:]

  counter_block = tag
  counter_block[15] |= 0x80
  plaintext = AES_CTR(key = message_encryption_key,
                      initial_counter_block = counter_block,
                      in = ciphertext[:bytelen(ciphertext)-16])

  length_block =
      little_endian_uint64(bytelen(additional_data) * 8) ++
      little_endian_uint64(bytelen(plaintext) * 8)
  padded_plaintext = right_pad_to_multiple_of_16_bytes(plaintext)
  padded_ad = right_pad_to_multiple_of_16_bytes(additional_data)
  S_s = POLYVAL(key = message_authentication_key,
                input = padded_ad ++ padded_plaintext ++
                        length_block)
  for i = 0; i < 12; i++ {
    S_s[i] ^= nonce[i]
  }
  S_s[15] &= 0x7f
  expected_tag = AES(key = message_encryption_key, block = S_s)

  xor_sum = 0
  for i := 0; i < bytelen(expected_tag); i++ {
    xor_sum |= expected_tag[i] ^ tag[i]
  }

  if xor_sum != 0 {
    fail()
  }

  return plaintext
}
]]></artwork>
      </figure>
    </section>

    <section title="AEADs">
      <t>We define two AEADs, in the format of RFC 5116, that use AES-GCM-SIV:
      AEAD_AES_128_GCM_SIV and AEAD_AES_256_GCM_SIV. They differ only in the
      size of the AES key used.</t>

      <t>The key input to these AEADs becomes the key-generating key. Thus,
      AEAD_AES_128_GCM_SIV takes a 16-byte key and AEAD_AES_256_GCM_SIV takes
      a 32-byte key.</t>

      <t>The parameters for AEAD_AES_128_GCM_SIV are then as follows:
<vspace />
K_LEN is
      16, P_MAX is 2^36, A_MAX is 2^36, N_MIN and N_MAX are 12, and C_MAX is
      2^36 + 16.</t>

      <t>The parameters for AEAD_AES_256_GCM_SIV differ only in the key size:
<vspace />
K_LEN is 32, P_MAX is 2^36, A_MAX is 2^36, N_MIN and N_MAX are 12, and C_MAX is 2^36 + 16.</t>
    </section>

    <section title="Field Operation Examples">
      <t>Polynomials in this document will be written as 16-byte values. For example, the sixteen bytes 01000000000000000000000000000492 would represent the polynomial x^127 + x^124 + x^121 + x^114 + 1, which is also the value of x^-128 in this field.</t>

<!--[rfced] FYI, some line breaks and blank lines have been added to
make equations easier to read in Sections 5 and 7 and Appendixes
A and B. Please let us know if prefer other formatting. For example:

Original:
   If a = 66e94bd4ef8a2c3b884cfa59ca342b2e and b =
   ff000000000000000000000000000000 then a + b =
   99e94bd4ef8a2c3b884cfa59ca342b2e, a * b =
   37856175e9dc9df26ebc6d6171aa0ae9 and dot(a, b) =
   ebe563401e7e91ea3ad6426b8140c394.

Current:
      If a = 66e94bd4ef8a2c3b884cfa59ca342b2e and
         b = ff000000000000000000000000000000,
    then a + b = 99e94bd4ef8a2c3b884cfa59ca342b2e,
         a * b = 37856175e9dc9df26ebc6d6171aa0ae9, and
         dot(a, b) = ebe563401e7e91ea3ad6426b8140c394.
-->

<figure><artwork>
   If a = 66e94bd4ef8a2c3b884cfa59ca342b2e and
      b = ff000000000000000000000000000000,
 then a + b = 99e94bd4ef8a2c3b884cfa59ca342b2e,
      a * b = 37856175e9dc9df26ebc6d6171aa0ae9, and
      dot(a, b) = ebe563401e7e91ea3ad6426b8140c394.
</artwork></figure>
    </section>

    <section title="Worked Example">
      <t>Consider the encryption of the plaintext "Hello world" with the additional data "example" under key ee8e1ed9ff2540ae8f2ba9f50bc2f27c using AEAD_AES_128_GCM_SIV. The random nonce that we'll use for this example is 752abad3e0afb5f434dc4310.</t>

      <t>In order to generate the message-authentication and
      message-encryption keys, a counter is combined with the nonce to form
      four blocks. These blocks are encrypted with the key given above:</t>

      <figure align="center">
        <artwork align="left"><![CDATA[
Counter |       Nonce                         Ciphertext
00000000752abad3e0afb5f434dc4310 -> 310728d9911f1f38c40e952ca83d093e
01000000752abad3e0afb5f434dc4310 -> 37b24316c3fab9a046ae90952daa0450
02000000752abad3e0afb5f434dc4310 -> a4c5ae624996327947920b2d2412474b
03000000752abad3e0afb5f434dc4310 -> c100be4d7e2c6edd1efef004305ab1e7
]]></artwork>
      </figure>

      <t>The latter halves of the ciphertext blocks are discarded and the
      remaining bytes are concatenated to form the per-message keys. Thus, the
      message-authentication key is 310728d9911f1f3837b24316c3fab9a0, and the
      message-encryption key is a4c5ae6249963279c100be4d7e2c6edd.</t>

      <t>The length block contains the encoding of the bit lengths of the additional data and plaintext, respectively. The string "example" is seven characters, thus 56 bits (or 0x38 in hex). The string "Hello world" is 11 characters, or 88 = 0x58 bits. Thus, the length block is 38000000000000005800000000000000.</t>

      <t>The input to POLYVAL is the padded additional data, padded plaintext,
      and then the length block. This is
      6578616d706c6500000000000000000048656c6c6f20776f726c64000000000038000000000000005800000000000000,
      based on the ASCII encoding of "example" (6578616d706c65) and "Hello
      world" (48656c6c6f20776f726c64).</t>

      <t>Calling POLYVAL with the message-authentication key and the input above results in S_s = ad7fcf0b5169851662672f3c5f95138f.</t>

      <t>Before encrypting, the nonce is XORed in and the most significant bit of the last byte is cleared. This gives d85575d8b1c630e256bb6c2c5f95130f, because that bit happened to be one previously. Encrypting with the message-encryption key (using AES&#8209;128) gives the tag, which is 4fbcdeb7e4793f4a1d7e4faa70100af1.</t>

      <t>In order to form the initial counter block, the most significant bit of the last byte of the tag is set to one. That doesn't result in a change in this example. Encrypting this with the message key (using AES-128) gives the first block of the keystream: 1551f2c1787e81deac9a99f139540ab5.</t>

      <t>The final ciphertext is the result of XORing the plaintext with the keystream and appending the tag. That gives 5d349ead175ef6b1def6fd4fbcdeb7e4793f4a1d7e4faa70100af1.</t>
    </section>

    <section title="Security Considerations" anchor="seccon">
      <t>AES-GCM-SIV decryption involves first producing an unauthenticated
      plaintext. This plaintext is vulnerable to manipulation by an attacker;
      thus, if an implementation released some or all of the plaintext before
      authenticating it, other parts of a system may process malicious data as
      if it were authentic. AES-GCM might be less likely to lead
      implementations to do this because there the ciphertext is generally
      authenticated before, or concurrently with, the plaintext
      calculation. Therefore, this text requires that implementations MUST NOT
      release unauthenticated plaintext. Thus, system designers should consider
      memory limitations when picking the size of AES-GCM-SIV plaintexts:
      large plaintexts may not fit in the available memory of some machines,
      tempting implementations to release unverified plaintext.</t>

      <t>A detailed cryptographic analysis of AES-GCM-SIV appears in <xref
      target="AES-GCM-SIV"/>, and the remainder of this section is a summary of
      that paper.</t>

      <t>The AEADs defined in this document calculate fresh AES keys for each
      nonce. This allows a larger number of plaintexts to be encrypted under a
      given key. Without this step, AES-GCM-SIV encryption would be limited by
      the birthday bound like other standard modes (e.g., AES-GCM, AES-CCM
      <xref target="RFC3610"/>, and AES-SIV <xref target="RFC5297"/>). This
      means that when 2^64 blocks have been encrypted overall, a
      distinguishing adversary who is trying to break the confidentiality of
      the scheme has an advantage of 1/2. Thus, in order to limit the
      adversary's advantage to 2^-32, at most 2^48 blocks can be encrypted
      overall. In contrast, by deriving fresh keys from each nonce, it is
      possible to encrypt a far larger number of messages and blocks with
      AES-GCM-SIV.</t>

      <t>We stress that nonce misuse-resistant schemes guarantee that if a
      nonce repeats, then the only security loss is that identical plaintexts
      will produce identical ciphertexts. Since this can also be a concern (as
      the fact that the same plaintext has been encrypted twice is revealed),
      we do not recommend using a fixed nonce as a policy. In addition, as we
      show below, better-than-birthday bounds are achieved by AES-GCM-SIV when
      the nonce repetition rate is low. Finally, as shown in <xref
      target="BHT18"/>, there is a great security benefit in the
      multiuser/multikey setting when each particular nonce is reused by a
      small number of users only. We stress that the nonce misuse-resistance
      property is not intended to be coupled with intentional nonce reuse;
      rather, such schemes provide the best possible security in the event of
      nonce reuse. Due to all of the above, it is RECOMMENDED that AES-GCM-SIV
      nonces be randomly generated.</t>

      <t>Some example usage bounds for AES-GCM-SIV are given below. The
      adversary's advantage is the "AdvEnc" from <xref target="key-derive"/>
      and is colloquially the ability of an attacker to distinguish
      ciphertexts from random bit strings. The bounds below limit this
      advantage to 2^-32. For up to 256 uses of the same nonce and key (i.e.,
      where one can assume that nonce misuse is no more than this bound), the
<!--[rfced] Is the correct expansion for AAD "additional authenticated data"?
Please advise how best to expand in this sentence.

Original:
   For up to 256 uses of the same nonce and key (i.e., where one
   can assume that nonce misuse is no more than this bound), the
   following message limits should be respected (this assumes a short
   AAD, i.e. less than 64 bytes):
-->
      following message limits should be respected (this assumes a short AAD,
      i.e. less than 64 bytes):</t>

      <t><list>
          <t>2^29 messages, where each plaintext is at most 1 GiB</t>
          <t>2^35 messages, where each plaintext is at most 128 MiB</t>
          <t>2^49 messages, where each plaintext is at most 1 MiB</t>
          <t>2^61 messages, where each plaintext is at most 16 KiB</t>
      </list></t>

      <t>Suzuki et al. <xref target="multi-birthday"/> show that even if
      nonces are selected uniformly at random, the probability that one or
      more values would be repeated 256 or more times is negligible until the
      number of nonces reaches 2^102. (Specifically, the probability is
      1/((2^96)^(255)) * Binomial(q, 256), where q is the number of nonces.)
      Since 2^102 is vastly greater than the limit on the number of plaintexts
      per key given above, we don't feel that this limit on the number of
      repeated nonces will be a problem. This also means that selecting nonces
      at random is a safe practice with AES-GCM-SIV. The bounds obtained for
      random nonces are as follows (as above, for these bounds, the
      adversary's advantage is at most 2^-32):</t>

      <t><list>
          <t>2^32 messages, where each plaintext is at most 8 GiB</t>
          <t>2^48 messages, where each plaintext is at most 32 MiB</t>
          <t>2^64 messages, where each plaintext is at most 128 KiB</t>
      </list></t>

      <t>For situations where, for some reason, an even higher number of nonce
      repeats is possible (e.g., in devices with very poor randomness), the
      message limits need to be reconsidered. Theorem 7 in <xref
      target="AES-GCM-SIV"/> contains more details, but for up to 1,024
      repeats of each nonce, the limits would be (again assuming a short AAD,
      i.e. less than 64 bytes):</t>

      <t><list>
          <t>2^25 messages, where each plaintext is at most 1 GiB</t>
          <t>2^31 messages, where each plaintext is at most 128 MiB</t>
          <t>2^45 messages, where each plaintext is at most 1 MiB</t>
          <t>2^57 messages, where each plaintext is at most 16 KiB</t>
      </list></t>

      <t>In addition to calculating fresh AES keys for each nonce, these AEADs
      also calculate fresh POLYVAL keys. Previous versions of GCM-SIV did not
      do this and instead used part of the AEAD's key as the POLYVAL
      key. Bleichenbacher pointed out <xref target="Bleichenbacher16"/> that this allowed an attacker who
      controlled the AEAD key to force the POLYVAL key to be zero. If a user
      of this AEAD authenticated messages with a secret additional-data value,
      then this would be insecure as the attacker could calculate a valid
      authenticator without knowing the input. This does not violate the
      standard properties of an AEAD as the additional data is not assumed to
      be confidential. However, we want these AEADs to be robust against plausible
      misuse and also to be drop-in replacements for AES-GCM and so derive
      nonce-specific POLYVAL keys to avoid this issue.</t>

      <t>We also wish to note that the probability of successful forgery
      increases with the number of attempts that an attacker is permitted. The
      advantage defined in <xref target="key-derive"/> and used above is
      specified in terms of the ability of an attacker to distinguish
      ciphertexts from random bit strings. It thus covers both confidentiality
      and integrity, and Theorem 6.2 in <xref target="key-derive"/> shows that
      the advantage increases with the number of decryption
      attempts, although much more slowly than with
      the number of encryptions; the dependence on the number of decryption
      queries for forgery is actually only linear, not quadratic. The latter is an
      artifact of the bound in the paper not being tight. If an attacker is
      permitted extremely large numbers of attempts, then the tiny probability
      that any given attempt succeeds may sum to a non-trivial chance.</t>

      <t>A security analysis of a similar scheme without nonce-based key
      derivation appears in <xref target="GCM-SIV"/>, and a full analysis of
      the bounds when applying nonce-based key derivation appears in <xref
      target="key-derive"/>. A larger table of bounds and other information
      appears at <xref target="aes-gcm-siv-homepage"/>.</t>

      <t>The multiuser/multikey security of AES-GCM-SIV was studied by <xref
      target="BHT18"/>, which showed that security is almost the same as in
      the single-user setting, as long as nonces do not repeat many times
      across many
      users. This is the case when nonces are chosen randomly.</t>
    </section>

    <section title="IANA Considerations">
      <t>IANA has added two entries to the "AEAD Algorithms" registry:
      AEAD_AES_128_GCM_SIV (Numeric ID 30) and AEAD_AES_256_GCM_SIV (Numeric
      ID 31), both referencing this document as their specification.</t>
    </section>

  </middle>

  <back>
    <references title="Normative References">
      &RFC2119;
      &RFC8174;

      <reference anchor="SP800-38A"
		 target="https://csrc.nist.gov/publications/detail/sp/800-38a/final">
        <front>
          <title>
            Recommendation for Block Cipher Modes of Operation: Methods and Techniques
          </title>
          <author initials="M." surname="Dworkin" fullname="M. Dworkin">
            <organization/>
          </author>
          <date year="2001" month="December"/>
        </front>
        <seriesInfo name="NIST SP" value="800-38A"/>
	<seriesInfo name="DOI" value="10.6028/NIST.SP.800-38A"/>
      </reference>
    </references>

    <references title="Informative References">
      &RFC3610;
      &RFC5116;
      &RFC5297;

      <reference anchor="GCM" target="https://csrc.nist.gov/publications/detail/sp/800-38d/final">
        <front>
          <title>
            Recommendation for Block Cipher Modes of Operation: Galois/Counter
	    Mode (GCM) and GMAC
          </title>
          <author initials="M." surname="Dworkin" fullname="M. Dworkin">
            <organization/>
          </author>
          <date year="2007" month="November"/>
        </front>
        <seriesInfo name="NIST SP" value="800-38D"/>
<seriesInfo name="DOI" value="10.6028/NIST.SP.800-38D"/>
      </reference>

      <reference anchor="AES-GCM-SIV" target="https://eprint.iacr.org/2017/168">
        <front>
          <title>
            AES-GCM-SIV: Specification and Analysis
          </title>
          <author initials="S." surname="Gueron" fullname="Shay Gueron">
            <organization/>
          </author>
          <author initials="A." surname="Langley" fullname="Adam Langley">
            <organization/>
          </author>
          <author initials="Y." surname="Lindell" fullname="Yehuda Lindell">
            <organization/>
          </author>
          <date year="2017" month="July"/>
        </front>
      </reference>

      <reference anchor="BHT18" target="https://eprint.iacr.org/2018/136.pdf">
        <front>
          <title>
            Revisiting AES-GCM-SIV: Multi-user Security, Faster Key Derivation, and Better Bounds
          </title>
          <author initials="P." surname="Bose" fullname="Priyanka Bose">
            <organization/>
          </author>
          <author initials="V.T." surname="Hoang" fullname="Viet Tung Hoang">
            <organization/>
          </author>
          <author initials="S." surname="Tessaro" fullname="Stefano Tessaro">
            <organization/>
          </author>
          <date year="2018" month="May"/>
        </front>
        <seriesInfo name="Advances in Cryptology - EUROCRYPT" value="2018"/>
<seriesInfo name="DOI" value="10.1007/978-3-319-78381-9_18"/>
      </reference>

      <reference anchor="GCM-SIV" target="http://doi.acm.org/10.1145/2810103.2813613">
        <front>
          <title>
            GCM-SIV: Full Nonce Misuse-Resistant Authenticated Encryption at Under One Cycle Per Byte
          </title>
          <author initials="S." surname="Gueron" fullname="Shay Gueron">
            <organization/>
          </author>
          <author initials="Y." surname="Lindell" fullname="Yehuda Lindell">
            <organization/>
          </author>
          <date month="October" year="2015"/>
        </front>
        <seriesInfo name="Proceedings of the 22nd ACM SIGSAC Conference on
			  Computer and Communications" value="Security"/>
<seriesInfo name="DOI" value="10.1145/2810103.2813613"/>
      </reference>

      <reference anchor="key-derive" target="https://doi.org/10.1145/3133956.3133992">
        <front>
          <title>
            Better Bounds for Block Cipher Modes of Operation via Nonce-Based Key Derivation
          </title>
          <author initials="S." surname="Gueron" fullname="Shay Gueron">
            <organization/>
          </author>
          <author initials="Y." surname="Lindell" fullname="Yehuda Lindell">
            <organization/>
          </author>
          <date year="2017"/>
        </front>
        <seriesInfo name="Proceedings of the 2017 ACM SIGSAC Conference on
			  Computer and Communications" value="Security"/>
<seriesInfo name="DOI" value="10.1145/3133956.3133992"/>
      </reference>

      <reference anchor="aes-gcm-siv-homepage" target="https://cyber.biu.ac.il/aes-gcm-siv/">
        <front>
          <title>
            Webpage for the AES-GCM-SIV Mode of Operation
          </title>
          <author initials="S." surname="Gueron" fullname="Shay Gueron">
            <organization/>
          </author>
          <author initials="A." surname="Langley" fullname="Adam Langley">
            <organization/>
          </author>
          <author initials="Y." surname="Lindell" fullname="Yehuda Lindell">
            <organization/>
          </author>
          <date/>
        </front>
      </reference>

      <reference anchor="multi-birthday" target="http://dx.doi.org/10.1007/11927587_5">
        <front>
          <title>
            Birthday Paradox for Multi-collisions
          </title>
          <author initials="K." surname="Suzuki" fullname="Suzuki Kazuhiro">
            <organization/>
          </author>
          <author initials="D." surname="Tonien" fullname="Tonien Dongvu">
            <organization/>
          </author>
          <author initials="K." surname="Kurosawa" fullname="Kurosawa Kaoru">
            <organization/>
          </author>
          <author initials="K." surname="Toyota" fullname="Toyota Koji">
            <organization/>
          </author>
          <date year="2006"/>
        </front>
        <seriesInfo name="Information Security and Cryptology - ICISC 2006, Lecture Notes in Computer Science,"
		    value="Volume 4296"/>
<seriesInfo name="DOI" value="10.1007/11927587_5"/>
      </reference>

      <reference anchor="Bleichenbacher16" target="https://mailarchive.ietf.org/arch/msg/cfrg/qgh-Yxmj7CC7cq2YZLpmfGA3x-o">
        <front>
          <title>Subject: AES-GCM-SIV security of the additional data</title>
          <author initials="D" surname="Bleichenbacher" />
          <date month="24 June" year="2016" />
        </front>
        <seriesInfo name="message to the" value="cfrg mailing list"/>
      </reference>
    </references>

    <section anchor="ghash" title="The Relationship between POLYVAL and GHASH">
      <t>GHASH and POLYVAL both operate in GF(2^128), although with different irreducible polynomials: POLYVAL works modulo x^128 + x^127 + x^126 + x^121 + 1 and GHASH works modulo x^128 + x^7 + x^2 + x + 1. Note that these irreducible polynomials are the "reverse" of each other.</t>

      <t>GHASH also has a different mapping between 128-bit strings and field
      elements. Whereas POLYVAL takes the least significant to
      most significant bits of the first byte to be the coefficients of x^0 to
      x^7, GHASH takes them to be the coefficients of x^7 to x^0. This
      continues until, for the last byte, POLYVAL takes the least significant
      to most significant bits to be the coefficients of x^120 to x^127, while
      GHASH takes them to be the coefficients of x^127 to x^120.</t>

      <t>The combination of these facts means that it's possible to "convert" values between the two by reversing the order of the bytes in a 16-byte string. The differing interpretations of bit order takes care of reversing the bits within each byte, and then reversing the bytes does the rest. This may have a practical benefit for implementations that wish to implement both GHASH and POLYVAL.</t>

      <t>In order to be clear which field a given operation is performed in,
      let mulX_GHASH be a function that takes a 16-byte string, converts it to
      an element of GHASH's field using GHASH's convention, multiplies it by x,
      and converts it back to a string. Likewise, let mulX_POLYVAL be a function
      that converts a 16-byte string to an element of POLYVAL's field using
      POLYVAL's convention, multiplies it by x, and converts it back.</t>

      <t>Given the 16-byte string 01000000000000000000000000000000, mulX_GHASH of that string is 00800000000000000000000000000000 and mulX_POLYVAL of that string is 02000000000000000000000000000000. As a more general example, given 9c98c04df9387ded828175a92ba652d8, mulX_GHASH of that string is 4e4c6026fc9c3ef6c140bad495d3296c and mulX_POLYVAL of it is 3931819bf271fada0503eb52574ca5f2.</t>

      <t>Lastly, let ByteReverse be the function that takes a 16-byte string and returns a copy where the order of the bytes has been reversed.</t>

      <t>Now GHASH and POLYVAL can be defined in terms of one another:</t>

      <t>POLYVAL(H, X_1, ..., X_n) = ByteReverse(GHASH(mulX_GHASH(ByteReverse(H)), ByteReverse(X_1), ..., ByteReverse(X_n)))</t>

      <t>GHASH(H, X_1, ..., X_n) = ByteReverse(POLYVAL(mulX_POLYVAL(ByteReverse(H)), ByteReverse(X_1), ..., ByteReverse(X_n)))</t>

<figure><artwork>
As a worked example: 
   let H = 25629347589242761d31f826ba4b757b, 
       X_1 = 4f4f95668c83dfb6401762bb2d01a262, and 
       X_2 = d1a24ddd2721d006bbe45f20d3c9f362. 
   POLYVAL(H, X_1, X_2) = f7a3b47b846119fae5b7866cf5e5b77e. 
</artwork></figure>
<t>
If we wished to calculate this given only an implementation of GHASH, then the
key for GHASH would be 
</t>

<figure><artwork>
mulX_GHASH(ByteReverse(H)) = dcbaa5dd137c188ebb21492c23c9b112. 

Then ByteReverse(GHASH(dcba..., ByteReverse(X_1), ByteReverse(X_2))) 
     = f7a3b47b846119fae5b7866cf5e5b77e, as required.
</artwork></figure>

      <t>In the other direction, GHASH(H, X_1, X_2) =
      bd9b3997046731fb96251b91f9c99d7a. If we wished to calculate this given
      only an implementation of POLYVAL, then we would first calculate the key
      for POLYVAL: </t>

<figure><artwork>
mulX_POLYVAL(ByteReverse(H)) = f6ea96744df0633aec8424b18e26c54a.

Then ByteReverse(POLYVAL(f6ea..., ByteReverse(X_1), ByteReverse(X_2)))
     = bd9b3997046731fb96251b91f9c99d7a.
</artwork></figure>
    </section>

    <section anchor="aesgcm" title="Additional Comparisons with AES-GCM">
      <t>Some functional properties that differ between AES-GCM and
      AES-GCM-SIV that are also worth noting:</t>

      <t>AES-GCM allows plaintexts to be encrypted in a streaming fashion -- i.e., the beginning of the plaintext can be encrypted and transmitted before the entire message has been processed. AES-GCM-SIV requires two passes for encryption and so cannot do this.</t>

      <t>AES-GCM allows a constant additional-data input to be precomputed in order to save per-message computation. AES-GCM-SIV varies the authenticator key based on the nonce and so does not permit this.</t>

      <t>The performance for AES-GCM vs. AES-GCM-SIV on small machines can be
      roughly characterized by the number of AES operations and the number of
      GF(2^128) multiplications needed to process a message.</t>
<figure><artwork>
   Let a = (bytelen(additional-data) + 15) / 16 and 
       p = (bytelen(plaintext) + 15) / 16. 
</artwork></figure>
<t>
   Then AES-GCM requires p + 1 AES operations and p + a + 1 field
   multiplications.
</t>

      <t>Defined similarly, AES-GCM-SIV with AES-128 requires p + 5 AES operations and p + a + 1 field multiplications. With AES-256, that becomes p + 7 AES operations.</t>

      <t>With large machines, the available parallelism becomes far more important, and such simple performance analysis is no longer representative. For such machines, we find that decryption of AES-GCM-SIV is only about 5% slower than AES-GCM, as long as the message is at least a couple of kilobytes. Encryption tends to run about two-thirds the speed because of the additional pass required.</t>
    </section>

    <section title="Test Vectors">
      <section title="AEAD_AES_128_GCM_SIV">
        <figure align="center">
          <artwork align="left"><![CDATA[
Plaintext (0 bytes) =
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             00000000000000000000000000000000
POLYVAL result =            00000000000000000000000000000000
POLYVAL result XOR nonce =  03000000000000000000000000000000
... and masked =            03000000000000000000000000000000
Tag =                       dc20e2d83f25705bb49e439eca56de25
Initial counter =           dc20e2d83f25705bb49e439eca56dea5
Result (16 bytes) =         dc20e2d83f25705bb49e439eca56de25


Plaintext (8 bytes) =       0100000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            00000000000000004000000000000000
POLYVAL result =            eb93b7740962c5e49d2a90a7dc5cec74
POLYVAL result XOR nonce =  e893b7740962c5e49d2a90a7dc5cec74
... and masked =            e893b7740962c5e49d2a90a7dc5cec74
Tag =                       578782fff6013b815b287c22493a364c
Initial counter =           578782fff6013b815b287c22493a36cc
Result (24 bytes) =         b5d839330ac7b786578782fff6013b81
                            5b287c22493a364c


Plaintext (12 bytes) =      010000000000000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            00000000000000006000000000000000
POLYVAL result =            48eb6c6c5a2dbe4a1dde508fee06361b
POLYVAL result XOR nonce =  4beb6c6c5a2dbe4a1dde508fee06361b
... and masked =            4beb6c6c5a2dbe4a1dde508fee06361b
Tag =                       a4978db357391a0bc4fdec8b0d106639
Initial counter =           a4978db357391a0bc4fdec8b0d1066b9
Result (28 bytes) =         7323ea61d05932260047d942a4978db3
                            57391a0bc4fdec8b0d106639


Plaintext (16 bytes) =      01000000000000000000000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            00000000000000008000000000000000
POLYVAL result =            20806c26e3c1de019e111255708031d6
POLYVAL result XOR nonce =  23806c26e3c1de019e111255708031d6
... and masked =            23806c26e3c1de019e11125570803156
Tag =                       303aaf90f6fe21199c6068577437a0c4
Initial counter =           303aaf90f6fe21199c6068577437a0c4
Result (32 bytes) =         743f7c8077ab25f8624e2e948579cf77
                            303aaf90f6fe21199c6068577437a0c4


Plaintext (32 bytes) =      01000000000000000000000000000000
                            02000000000000000000000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            00000000000000000001000000000000
POLYVAL result =            ce6edc9a50b36d9a98986bbf6a261c3b
POLYVAL result XOR nonce =  cd6edc9a50b36d9a98986bbf6a261c3b
... and masked =            cd6edc9a50b36d9a98986bbf6a261c3b
Tag =                       1a8e45dcd4578c667cd86847bf6155ff
Initial counter =           1a8e45dcd4578c667cd86847bf6155ff
Result (48 bytes) =         84e07e62ba83a6585417245d7ec413a9
                            fe427d6315c09b57ce45f2e3936a9445
                            1a8e45dcd4578c667cd86847bf6155ff


Plaintext (48 bytes) =      01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            00000000000000008001000000000000
POLYVAL result =            81388746bc22d26b2abc3dcb15754222
POLYVAL result XOR nonce =  82388746bc22d26b2abc3dcb15754222
... and masked =            82388746bc22d26b2abc3dcb15754222
Tag =                       5e6e311dbf395d35b0fe39c2714388f8
Initial counter =           5e6e311dbf395d35b0fe39c2714388f8
Result (64 bytes) =         3fd24ce1f5a67b75bf2351f181a475c7
                            b800a5b4d3dcf70106b1eea82fa1d64d
                            f42bf7226122fa92e17a40eeaac1201b
                            5e6e311dbf395d35b0fe39c2714388f8


Plaintext (64 bytes) =      01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            00000000000000000002000000000000
POLYVAL result =            1e39b6d3344d348f6044f89935d1cf78
POLYVAL result XOR nonce =  1d39b6d3344d348f6044f89935d1cf78
... and masked =            1d39b6d3344d348f6044f89935d1cf78
Tag =                       8a263dd317aa88d56bdf3936dba75bb8
Initial counter =           8a263dd317aa88d56bdf3936dba75bb8
Result (80 bytes) =         2433668f1058190f6d43e360f4f35cd8
                            e475127cfca7028ea8ab5c20f7ab2af0
                            2516a2bdcbc08d521be37ff28c152bba
                            36697f25b4cd169c6590d1dd39566d3f
                            8a263dd317aa88d56bdf3936dba75bb8


Plaintext (8 bytes) =       0200000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            08000000000000004000000000000000
POLYVAL result =            b26781e7e2c1376f96bec195f3709b2a
POLYVAL result XOR nonce =  b16781e7e2c1376f96bec195f3709b2a
... and masked =            b16781e7e2c1376f96bec195f3709b2a
Tag =                       3b0a1a2560969cdf790d99759abd1508
Initial counter =           3b0a1a2560969cdf790d99759abd1588
Result (24 bytes) =         1e6daba35669f4273b0a1a2560969cdf
                            790d99759abd1508


Plaintext (12 bytes) =      020000000000000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            08000000000000006000000000000000
POLYVAL result =            111f5affb18e4cc1164a01bdc12a4145
POLYVAL result XOR nonce =  121f5affb18e4cc1164a01bdc12a4145
... and masked =            121f5affb18e4cc1164a01bdc12a4145
Tag =                       08299c5102745aaa3a0c469fad9e075a
Initial counter =           08299c5102745aaa3a0c469fad9e07da
Result (28 bytes) =         296c7889fd99f41917f4462008299c51
                            02745aaa3a0c469fad9e075a


Plaintext (16 bytes) =      02000000000000000000000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            08000000000000008000000000000000
POLYVAL result =            79745ab508622c8a958543675fac4688
POLYVAL result XOR nonce =  7a745ab508622c8a958543675fac4688
... and masked =            7a745ab508622c8a958543675fac4608
Tag =                       8f8936ec039e4e4bb97ebd8c4457441f
Initial counter =           8f8936ec039e4e4bb97ebd8c4457449f
Result (32 bytes) =         e2b0c5da79a901c1745f700525cb335b
                            8f8936ec039e4e4bb97ebd8c4457441f


Plaintext (32 bytes) =      02000000000000000000000000000000
                            03000000000000000000000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            08000000000000000001000000000000
POLYVAL result =            2ce7daaf7c89490822051255b12eca6b
POLYVAL result XOR nonce =  2fe7daaf7c89490822051255b12eca6b
... and masked =            2fe7daaf7c89490822051255b12eca6b
Tag =                       e6af6a7f87287da059a71684ed3498e1
Initial counter =           e6af6a7f87287da059a71684ed3498e1
Result (48 bytes) =         620048ef3c1e73e57e02bb8562c416a3
                            19e73e4caac8e96a1ecb2933145a1d71
                            e6af6a7f87287da059a71684ed3498e1


Plaintext (48 bytes) =      02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            08000000000000008001000000000000
POLYVAL result =            9ca987715d69c1786711dfcd22f830fc
POLYVAL result XOR nonce =  9fa987715d69c1786711dfcd22f830fc
... and masked =            9fa987715d69c1786711dfcd22f8307c
Tag =                       6a8cc3865f76897c2e4b245cf31c51f2
Initial counter =           6a8cc3865f76897c2e4b245cf31c51f2
Result (64 bytes) =         50c8303ea93925d64090d07bd109dfd9
                            515a5a33431019c17d93465999a8b005
                            3201d723120a8562b838cdff25bf9d1e
                            6a8cc3865f76897c2e4b245cf31c51f2


Plaintext (64 bytes) =      02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            05000000000000000000000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            05000000000000000000000000000000
                            08000000000000000002000000000000
POLYVAL result =            ffcd05d5770f34ad9267f0a59994b15a
POLYVAL result XOR nonce =  fccd05d5770f34ad9267f0a59994b15a
... and masked =            fccd05d5770f34ad9267f0a59994b15a
Tag =                       cdc46ae475563de037001ef84ae21744
Initial counter =           cdc46ae475563de037001ef84ae217c4
Result (80 bytes) =         2f5c64059db55ee0fb847ed513003746
                            aca4e61c711b5de2e7a77ffd02da42fe
                            ec601910d3467bb8b36ebbaebce5fba3
                            0d36c95f48a3e7980f0e7ac299332a80
                            cdc46ae475563de037001ef84ae21744


Plaintext (4 bytes) =       02000000
AAD (12 bytes) =            010000000000000000000000
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            60000000000000002000000000000000
POLYVAL result =            f6ce9d3dcd68a2fd603c7ecc18fb9918
POLYVAL result XOR nonce =  f5ce9d3dcd68a2fd603c7ecc18fb9918
... and masked =            f5ce9d3dcd68a2fd603c7ecc18fb9918
Tag =                       07eb1f84fb28f8cb73de8e99e2f48a14
Initial counter =           07eb1f84fb28f8cb73de8e99e2f48a94
Result (20 bytes) =         a8fe3e8707eb1f84fb28f8cb73de8e99
                            e2f48a14


Plaintext (20 bytes) =      03000000000000000000000000000000
                            04000000
AAD (18 bytes) =            01000000000000000000000000000000
                            0200
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            9000000000000000a000000000000000
POLYVAL result =            4781d492cb8f926c504caa36f61008fe
POLYVAL result XOR nonce =  4481d492cb8f926c504caa36f61008fe
... and masked =            4481d492cb8f926c504caa36f610087e
Tag =                       24afc9805e976f451e6d87f6fe106514
Initial counter =           24afc9805e976f451e6d87f6fe106594
Result (36 bytes) =         6bb0fecf5ded9b77f902c7d5da236a43
                            91dd029724afc9805e976f451e6d87f6
                            fe106514


Plaintext (18 bytes) =      03000000000000000000000000000000
                            0400
AAD (20 bytes) =            01000000000000000000000000000000
                            02000000
Key =                       01000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = d9b360279694941ac5dbc6987ada7377
Record encryption key =     4004a0dcd862f2a57360219d2d44ef6c
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            a0000000000000009000000000000000
POLYVAL result =            75cbc23a1a10e348aeb8e384b5cc79fd
POLYVAL result XOR nonce =  76cbc23a1a10e348aeb8e384b5cc79fd
... and masked =            76cbc23a1a10e348aeb8e384b5cc797d
Tag =                       bff9b2ef00fb47920cc72a0c0f13b9fd
Initial counter =           bff9b2ef00fb47920cc72a0c0f13b9fd
Result (34 bytes) =         44d0aaf6fb2f1f34add5e8064e83e12a
                            2adabff9b2ef00fb47920cc72a0c0f13
                            b9fd

Plaintext (0 bytes) =
AAD (0 bytes) =
Key =                       e66021d5eb8e4f4066d4adb9c33560e4
Nonce =                     f46e44bb3da0015c94f70887
Record authentication key = 036ee1fe2d7926af68898095e54e7b3c
Record encryption key =     5e46482396008223b5c1d25173d87539
POLYVAL input =             00000000000000000000000000000000
POLYVAL result =            00000000000000000000000000000000
POLYVAL result XOR nonce =  f46e44bb3da0015c94f7088700000000
... and masked =            f46e44bb3da0015c94f7088700000000
Tag =                       a4194b79071b01a87d65f706e3949578
Initial counter =           a4194b79071b01a87d65f706e39495f8
Result (16 bytes) =         a4194b79071b01a87d65f706e3949578


Plaintext (3 bytes) =       7a806c
AAD (5 bytes) =             46bb91c3c5
Key =                       36864200e0eaf5284d884a0e77d31646
Nonce =                     bae8e37fc83441b16034566b
Record authentication key = 3e28de1120b2981a0155795ca2812af6
Record encryption key =     6d4b78b31a4c9c03d8db0f42f7507fae
POLYVAL input =             46bb91c3c50000000000000000000000
                            7a806c00000000000000000000000000
                            28000000000000001800000000000000
POLYVAL result =            43d9a745511dcfa21b96dd606f1d5720
POLYVAL result XOR nonce =  f931443a99298e137ba28b0b6f1d5720
... and masked =            f931443a99298e137ba28b0b6f1d5720
Tag =                       711bd85bc1e4d3e0a462e074eea428a8
Initial counter =           711bd85bc1e4d3e0a462e074eea428a8
Result (19 bytes) =         af60eb711bd85bc1e4d3e0a462e074ee
                            a428a8


Plaintext (6 bytes) =       bdc66f146545
AAD (10 bytes) =            fc880c94a95198874296
Key =                       aedb64a6c590bc84d1a5e269e4b47801
Nonce =                     afc0577e34699b9e671fdd4f
Record authentication key = 43b8de9cea62330d15cccfc84a33e8c8
Record encryption key =     8e54631607e431e095b54852868e3a27
POLYVAL input =             fc880c94a95198874296000000000000
                            bdc66f14654500000000000000000000
                            50000000000000003000000000000000
POLYVAL result =            26498e0d2b1ef004e808c458e8f2f515
POLYVAL result XOR nonce =  8989d9731f776b9a8f171917e8f2f515
... and masked =            8989d9731f776b9a8f171917e8f2f515
Tag =                       d6a9c45545cfc11f03ad743dba20f966
Initial counter =           d6a9c45545cfc11f03ad743dba20f9e6
Result (22 bytes) =         bb93a3e34d3cd6a9c45545cfc11f03ad
                            743dba20f966


Plaintext (9 bytes) =       1177441f195495860f
AAD (15 bytes) =            046787f3ea22c127aaf195d1894728
Key =                       d5cc1fd161320b6920ce07787f86743b
Nonce =                     275d1ab32f6d1f0434d8848c
Record authentication key = 8a51df64d93eaf667c2c09bd454ce5c5
Record encryption key =     43ab276c2b4a473918ca73f2dd85109c
POLYVAL input =             046787f3ea22c127aaf195d189472800
                            1177441f195495860f00000000000000
                            78000000000000004800000000000000
POLYVAL result =            63a3451c0b23345ad02bba59956517cf
POLYVAL result XOR nonce =  44fe5faf244e2b5ee4f33ed5956517cf
... and masked =            44fe5faf244e2b5ee4f33ed59565174f
Tag =                       1d02fd0cd174c84fc5dae2f60f52fd2b
Initial counter =           1d02fd0cd174c84fc5dae2f60f52fdab
Result (25 bytes) =         4f37281f7ad12949d01d02fd0cd174c8
                            4fc5dae2f60f52fd2b


Plaintext (12 bytes) =      9f572c614b4745914474e7c7
AAD (20 bytes) =            c9882e5386fd9f92ec489c8fde2be2cf
                            97e74e93
Key =                       b3fed1473c528b8426a582995929a149
Nonce =                     9e9ad8780c8d63d0ab4149c0
Record authentication key = 22f50707a95dd416df069d670cb775e8
Record encryption key =     f674a5584ee21fe97b4cebc468ab61e4
POLYVAL input =             c9882e5386fd9f92ec489c8fde2be2cf
                            97e74e93000000000000000000000000
                            9f572c614b4745914474e7c700000000
                            a0000000000000006000000000000000
POLYVAL result =            0cca0423fba9d77fe7e2e6963b08cdd0
POLYVAL result XOR nonce =  9250dc5bf724b4af4ca3af563b08cdd0
... and masked =            9250dc5bf724b4af4ca3af563b08cd50
Tag =                       c1dc2f871fb7561da1286e655e24b7b0
Initial counter =           c1dc2f871fb7561da1286e655e24b7b0
Result (28 bytes) =         f54673c5ddf710c745641c8bc1dc2f87
                            1fb7561da1286e655e24b7b0


Plaintext (15 bytes) =      0d8c8451178082355c9e940fea2f58
AAD (25 bytes) =            2950a70d5a1db2316fd568378da107b5
                            2b0da55210cc1c1b0a
Key =                       2d4ed87da44102952ef94b02b805249b
Nonce =                     ac80e6f61455bfac8308a2d4
Record authentication key = 0b00a29a83e7e95b92e3a0783b29f140
Record encryption key =     a430c27f285aed913005975c42eed5f3
POLYVAL input =             2950a70d5a1db2316fd568378da107b5
                            2b0da55210cc1c1b0a00000000000000
                            0d8c8451178082355c9e940fea2f5800
                            c8000000000000007800000000000000
POLYVAL result =            1086ef25247aa41009bbc40871d9b350
POLYVAL result XOR nonce =  bc0609d3302f1bbc8ab366dc71d9b350
... and masked =            bc0609d3302f1bbc8ab366dc71d9b350
Tag =                       83b3449b9f39552de99dc214a1190b0b
Initial counter =           83b3449b9f39552de99dc214a1190b8b
Result (31 bytes) =         c9ff545e07b88a015f05b274540aa183
                            b3449b9f39552de99dc214a1190b0b


Plaintext (18 bytes) =      6b3db4da3d57aa94842b9803a96e07fb
                            6de7
AAD (30 bytes) =            1860f762ebfbd08284e421702de0de18
                            baa9c9596291b08466f37de21c7f
Key =                       bde3b2f204d1e9f8b06bc47f9745b3d1
Nonce =                     ae06556fb6aa7890bebc18fe
Record authentication key = 21c874a8bad3603d1c3e8784df5b3f9f
Record encryption key =     d1c16d72651c3df504eae27129d818e8
POLYVAL input =             1860f762ebfbd08284e421702de0de18
                            baa9c9596291b08466f37de21c7f0000
                            6b3db4da3d57aa94842b9803a96e07fb
                            6de70000000000000000000000000000
                            f0000000000000009000000000000000
POLYVAL result =            55462a5afa0da8d646481e049ef9c764
POLYVAL result XOR nonce =  fb407f354ca7d046f8f406fa9ef9c764
... and masked =            fb407f354ca7d046f8f406fa9ef9c764
Tag =                       3e377094f04709f64d7b985310a4db84
Initial counter =           3e377094f04709f64d7b985310a4db84
Result (34 bytes) =         6298b296e24e8cc35dce0bed484b7f30
                            d5803e377094f04709f64d7b985310a4
                            db84


Plaintext (21 bytes) =      e42a3c02c25b64869e146d7b233987bd
                            dfc240871d
AAD (35 bytes) =            7576f7028ec6eb5ea7e298342a94d4b2
                            02b370ef9768ec6561c4fe6b7e7296fa
                            859c21
Key =                       f901cfe8a69615a93fdf7a98cad48179
Nonce =                     6245709fb18853f68d833640
Record authentication key = 3724f55f1d22ac0ab830da0b6a995d74
Record encryption key =     75ac87b70c05db287de779006105a344
POLYVAL input =             7576f7028ec6eb5ea7e298342a94d4b2
                            02b370ef9768ec6561c4fe6b7e7296fa
                            859c2100000000000000000000000000
                            e42a3c02c25b64869e146d7b233987bd
                            dfc240871d0000000000000000000000
                            1801000000000000a800000000000000
POLYVAL result =            4cbba090f03f7d1188ea55749fa6c7bd
POLYVAL result XOR nonce =  2efed00f41b72ee7056963349fa6c7bd
... and masked =            2efed00f41b72ee7056963349fa6c73d
Tag =                       2d15506c84a9edd65e13e9d24a2a6e70
Initial counter =           2d15506c84a9edd65e13e9d24a2a6ef0
Result (37 bytes) =         391cc328d484a4f46406181bcd62efd9
                            b3ee197d052d15506c84a9edd65e13e9
                            d24a2a6e70
]]></artwork>
        </figure>
      </section>
      <section title="AEAD_AES_256_GCM_SIV">
        <figure align="center">
          <artwork align="left"><![CDATA[
Plaintext (0 bytes) =
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             00000000000000000000000000000000
POLYVAL result =            00000000000000000000000000000000
POLYVAL result XOR nonce =  03000000000000000000000000000000
... and masked =            03000000000000000000000000000000
Tag =                       07f5f4169bbf55a8400cd47ea6fd400f
Initial counter =           07f5f4169bbf55a8400cd47ea6fd408f
Result (16 bytes) =         07f5f4169bbf55a8400cd47ea6fd400f


Plaintext (8 bytes) =       0100000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            00000000000000004000000000000000
POLYVAL result =            05230f62f0eac8aa14fe4d646b59cd41
POLYVAL result XOR nonce =  06230f62f0eac8aa14fe4d646b59cd41
... and masked =            06230f62f0eac8aa14fe4d646b59cd41
Tag =                       843122130f7364b761e0b97427e3df28
Initial counter =           843122130f7364b761e0b97427e3dfa8
Result (24 bytes) =         c2ef328e5c71c83b843122130f7364b7
                            61e0b97427e3df28


Plaintext (12 bytes) =      010000000000000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            00000000000000006000000000000000
POLYVAL result =            6d81a24732fd6d03ae5af544720a1c13
POLYVAL result XOR nonce =  6e81a24732fd6d03ae5af544720a1c13
... and masked =            6e81a24732fd6d03ae5af544720a1c13
Tag =                       8ca50da9ae6559e48fd10f6e5c9ca17e
Initial counter =           8ca50da9ae6559e48fd10f6e5c9ca1fe
Result (28 bytes) =         9aab2aeb3faa0a34aea8e2b18ca50da9
                            ae6559e48fd10f6e5c9ca17e


Plaintext (16 bytes) =      01000000000000000000000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            00000000000000008000000000000000
POLYVAL result =            74eee2bf7c9a165f8b25dea73db32a6d
POLYVAL result XOR nonce =  77eee2bf7c9a165f8b25dea73db32a6d
... and masked =            77eee2bf7c9a165f8b25dea73db32a6d
Tag =                       c9eac6fa700942702e90862383c6c366
Initial counter =           c9eac6fa700942702e90862383c6c3e6
Result (32 bytes) =         85a01b63025ba19b7fd3ddfc033b3e76
                            c9eac6fa700942702e90862383c6c366


Plaintext (32 bytes) =      01000000000000000000000000000000
                            02000000000000000000000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            00000000000000000001000000000000
POLYVAL result =            899b6381b3d46f0def7aa0517ba188f5
POLYVAL result XOR nonce =  8a9b6381b3d46f0def7aa0517ba188f5
... and masked =            8a9b6381b3d46f0def7aa0517ba18875
Tag =                       e819e63abcd020b006a976397632eb5d
Initial counter =           e819e63abcd020b006a976397632ebdd
Result (48 bytes) =         4a6a9db4c8c6549201b9edb53006cba8
                            21ec9cf850948a7c86c68ac7539d027f
                            e819e63abcd020b006a976397632eb5d


Plaintext (48 bytes) =      01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            00000000000000008001000000000000
POLYVAL result =            c1f8593d8fc29b0c290cae1992f71f51
POLYVAL result XOR nonce =  c2f8593d8fc29b0c290cae1992f71f51
... and masked =            c2f8593d8fc29b0c290cae1992f71f51
Tag =                       790bc96880a99ba804bd12c0e6a22cc4
Initial counter =           790bc96880a99ba804bd12c0e6a22cc4
Result (64 bytes) =         c00d121893a9fa603f48ccc1ca3c57ce
                            7499245ea0046db16c53c7c66fe717e3
                            9cf6c748837b61f6ee3adcee17534ed5
                            790bc96880a99ba804bd12c0e6a22cc4


Plaintext (64 bytes) =      01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
AAD (0 bytes) =
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            00000000000000000002000000000000
POLYVAL result =            6ef38b06046c7c0e225efaef8e2ec4c4
POLYVAL result XOR nonce =  6df38b06046c7c0e225efaef8e2ec4c4
... and masked =            6df38b06046c7c0e225efaef8e2ec444
Tag =                       112864c269fc0d9d88c61fa47e39aa08
Initial counter =           112864c269fc0d9d88c61fa47e39aa88
Result (80 bytes) =         c2d5160a1f8683834910acdafc41fbb1
                            632d4a353e8b905ec9a5499ac34f96c7
                            e1049eb080883891a4db8caaa1f99dd0
                            04d80487540735234e3744512c6f90ce
                            112864c269fc0d9d88c61fa47e39aa08


Plaintext (8 bytes) =       0200000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            08000000000000004000000000000000
POLYVAL result =            34e57bafe011b9b36fc6821b7ffb3354
POLYVAL result XOR nonce =  37e57bafe011b9b36fc6821b7ffb3354
... and masked =            37e57bafe011b9b36fc6821b7ffb3354
Tag =                       91213f267e3b452f02d01ae33e4ec854
Initial counter =           91213f267e3b452f02d01ae33e4ec8d4
Result (24 bytes) =         1de22967237a813291213f267e3b452f
                            02d01ae33e4ec854


Plaintext (12 bytes) =      020000000000000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            08000000000000006000000000000000
POLYVAL result =            5c47d68a22061c1ad5623a3b66a8e206
POLYVAL result XOR nonce =  5f47d68a22061c1ad5623a3b66a8e206
... and masked =            5f47d68a22061c1ad5623a3b66a8e206
Tag =                       c1a4a19ae800941ccdc57cc8413c277f
Initial counter =           c1a4a19ae800941ccdc57cc8413c27ff
Result (28 bytes) =         163d6f9cc1b346cd453a2e4cc1a4a19a
                            e800941ccdc57cc8413c277f


Plaintext (16 bytes) =      02000000000000000000000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            08000000000000008000000000000000
POLYVAL result =            452896726c616746f01d11d82911d478
POLYVAL result XOR nonce =  462896726c616746f01d11d82911d478
... and masked =            462896726c616746f01d11d82911d478
Tag =                       b292d28ff61189e8e49f3875ef91aff7
Initial counter =           b292d28ff61189e8e49f3875ef91aff7
Result (32 bytes) =         c91545823cc24f17dbb0e9e807d5ec17
                            b292d28ff61189e8e49f3875ef91aff7


Plaintext (32 bytes) =      02000000000000000000000000000000
                            03000000000000000000000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            08000000000000000001000000000000
POLYVAL result =            4e58c1e341c9bb0ae34eda9509dfc90c
POLYVAL result XOR nonce =  4d58c1e341c9bb0ae34eda9509dfc90c
... and masked =            4d58c1e341c9bb0ae34eda9509dfc90c
Tag =                       aea1bad12702e1965604374aab96dbbc
Initial counter =           aea1bad12702e1965604374aab96dbbc
Result (48 bytes) =         07dad364bfc2b9da89116d7bef6daaaf
                            6f255510aa654f920ac81b94e8bad365
                            aea1bad12702e1965604374aab96dbbc


Plaintext (48 bytes) =      02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            08000000000000008001000000000000
POLYVAL result =            2566a4aff9a525df9772c16d4eaf8d2a
POLYVAL result XOR nonce =  2666a4aff9a525df9772c16d4eaf8d2a
... and masked =            2666a4aff9a525df9772c16d4eaf8d2a
Tag =                       03332742b228c647173616cfd44c54eb
Initial counter =           03332742b228c647173616cfd44c54eb
Result (64 bytes) =         c67a1f0f567a5198aa1fcc8e3f213143
                            36f7f51ca8b1af61feac35a86416fa47
                            fbca3b5f749cdf564527f2314f42fe25
                            03332742b228c647173616cfd44c54eb


Plaintext (64 bytes) =      02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            05000000000000000000000000000000
AAD (1 bytes) =             01
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            05000000000000000000000000000000
                            08000000000000000002000000000000
POLYVAL result =            da58d2f61b0a9d343b2f37fb0c519733
POLYVAL result XOR nonce =  d958d2f61b0a9d343b2f37fb0c519733
... and masked =            d958d2f61b0a9d343b2f37fb0c519733
Tag =                       5bde0285037c5de81e5b570a049b62a0
Initial counter =           5bde0285037c5de81e5b570a049b62a0
Result (80 bytes) =         67fd45e126bfb9a79930c43aad2d3696
                            7d3f0e4d217c1e551f59727870beefc9
                            8cb933a8fce9de887b1e40799988db1f
                            c3f91880ed405b2dd298318858467c89
                            5bde0285037c5de81e5b570a049b62a0


Plaintext (4 bytes) =       02000000
AAD (12 bytes) =            010000000000000000000000
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            60000000000000002000000000000000
POLYVAL result =            6dc76ae84b88916e073a303aafde05cf
POLYVAL result XOR nonce =  6ec76ae84b88916e073a303aafde05cf
... and masked =            6ec76ae84b88916e073a303aafde054f
Tag =                       1835e517741dfddccfa07fa4661b74cf
Initial counter =           1835e517741dfddccfa07fa4661b74cf
Result (20 bytes) =         22b3f4cd1835e517741dfddccfa07fa4
                            661b74cf


Plaintext (20 bytes) =      03000000000000000000000000000000
                            04000000
AAD (18 bytes) =            01000000000000000000000000000000
                            0200
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            9000000000000000a000000000000000
POLYVAL result =            973ef4fd04bd31d193816ab26f8655ca
POLYVAL result XOR nonce =  943ef4fd04bd31d193816ab26f8655ca
... and masked =            943ef4fd04bd31d193816ab26f86554a
Tag =                       b879ad976d8242acc188ab59cabfe307
Initial counter =           b879ad976d8242acc188ab59cabfe387
Result (36 bytes) =         43dd0163cdb48f9fe3212bf61b201976
                            067f342bb879ad976d8242acc188ab59
                            cabfe307


Plaintext (18 bytes) =      03000000000000000000000000000000
                            0400
AAD (20 bytes) =            01000000000000000000000000000000
                            02000000
Key =                       01000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     030000000000000000000000
Record authentication key = b5d3c529dfafac43136d2d11be284d7f
Record encryption key =     b914f4742be9e1d7a2f84addbf96dec3
                            456e3c6c05ecc157cdbf0700fedad222
POLYVAL input =             01000000000000000000000000000000
                            02000000000000000000000000000000
                            03000000000000000000000000000000
                            04000000000000000000000000000000
                            a0000000000000009000000000000000
POLYVAL result =            2cbb6b7ab2dbffefb797f825f826870c
POLYVAL result XOR nonce =  2fbb6b7ab2dbffefb797f825f826870c
... and masked =            2fbb6b7ab2dbffefb797f825f826870c
Tag =                       cfcdf5042112aa29685c912fc2056543
Initial counter =           cfcdf5042112aa29685c912fc20565c3
Result (34 bytes) =         462401724b5ce6588d5a54aae5375513
                            a075cfcdf5042112aa29685c912fc205
                            6543

Plaintext (0 bytes) =
AAD (0 bytes) =
Key =                       e66021d5eb8e4f4066d4adb9c33560e4
                            f46e44bb3da0015c94f7088736864200
Nonce =                     e0eaf5284d884a0e77d31646
Record authentication key = e40d26f82774aa27f47b047b608b9585
Record encryption key =     7c7c3d9a542cef53dde0e6de9b580040
                            0f82e73ec5f7ee41b7ba8dcb9ba078c3
POLYVAL input =             00000000000000000000000000000000
POLYVAL result =            00000000000000000000000000000000
POLYVAL result XOR nonce =  e0eaf5284d884a0e77d3164600000000
... and masked =            e0eaf5284d884a0e77d3164600000000
Tag =                       169fbb2fbf389a995f6390af22228a62
Initial counter =           169fbb2fbf389a995f6390af22228ae2
Result (16 bytes) =         169fbb2fbf389a995f6390af22228a62


Plaintext (3 bytes) =       671fdd
AAD (5 bytes) =             4fbdc66f14
Key =                       bae8e37fc83441b16034566b7a806c46
                            bb91c3c5aedb64a6c590bc84d1a5e269
Nonce =                     e4b47801afc0577e34699b9e
Record authentication key = b546f5a850d0a90adfe39e95c2510fc6
Record encryption key =     b9d1e239d62cbb5c49273ddac8838bdc
                            c53bca478a770f07087caa4e0a924a55
POLYVAL input =             4fbdc66f140000000000000000000000
                            671fdd00000000000000000000000000
                            28000000000000001800000000000000
POLYVAL result =            b91f91f96b159a7c611c05035b839e92
POLYVAL result XOR nonce =  5dabe9f8c4d5cd0255759e9d5b839e92
... and masked =            5dabe9f8c4d5cd0255759e9d5b839e12
Tag =                       93da9bb81333aee0c785b240d319719d
Initial counter =           93da9bb81333aee0c785b240d319719d
Result (19 bytes) =         0eaccb93da9bb81333aee0c785b240d3
                            19719d


Plaintext (6 bytes) =       195495860f04
AAD (10 bytes) =            6787f3ea22c127aaf195
Key =                       6545fc880c94a95198874296d5cc1fd1
                            61320b6920ce07787f86743b275d1ab3
Nonce =                     2f6d1f0434d8848c1177441f
Record authentication key = e156e1f9b0b07b780cbe30f259e3c8da
Record encryption key =     6fc1c494519f944aae52fcd8b14e5b17
                            1b5a9429d3b76e430d49940c0021d612
POLYVAL input =             6787f3ea22c127aaf195000000000000
                            195495860f0400000000000000000000
                            50000000000000003000000000000000
POLYVAL result =            2c480ed9d236b1df24c6eec109bd40c1
POLYVAL result XOR nonce =  032511dde6ee355335b1aade09bd40c1
... and masked =            032511dde6ee355335b1aade09bd4041
Tag =                       6b62b84dc40c84636a5ec12020ec8c2c
Initial counter =           6b62b84dc40c84636a5ec12020ec8cac
Result (22 bytes) =         a254dad4f3f96b62b84dc40c84636a5e
                            c12020ec8c2c


Plaintext (9 bytes) =       c9882e5386fd9f92ec
AAD (15 bytes) =            489c8fde2be2cf97e74e932d4ed87d
Key =                       d1894728b3fed1473c528b8426a58299
                            5929a1499e9ad8780c8d63d0ab4149c0
Nonce =                     9f572c614b4745914474e7c7
Record authentication key = 0533fd71f4119257361a3ff1469dd4e5
Record encryption key =     4feba89799be8ac3684fa2bb30ade0ea
                            51390e6d87dcf3627d2ee44493853abe
POLYVAL input =             489c8fde2be2cf97e74e932d4ed87d00
                            c9882e5386fd9f92ec00000000000000
                            78000000000000004800000000000000
POLYVAL result =            bf160bc9ded8c63057d2c38aae552fb4
POLYVAL result XOR nonce =  204127a8959f83a113a6244dae552fb4
... and masked =            204127a8959f83a113a6244dae552f34
Tag =                       c0fd3dc6628dfe55ebb0b9fb2295c8c2
Initial counter =           c0fd3dc6628dfe55ebb0b9fb2295c8c2
Result (25 bytes) =         0df9e308678244c44bc0fd3dc6628dfe
                            55ebb0b9fb2295c8c2


Plaintext (12 bytes) =      1db2316fd568378da107b52b
AAD (20 bytes) =            0da55210cc1c1b0abde3b2f204d1e9f8
                            b06bc47f
Key =                       a44102952ef94b02b805249bac80e6f6
                            1455bfac8308a2d40d8c845117808235
Nonce =                     5c9e940fea2f582950a70d5a
Record authentication key = 64779ab10ee8a280272f14cc8851b727
Record encryption key =     25f40fc63f49d3b9016a8eeeb75846e0
                            d72ca36ddbd312b6f5ef38ad14bd2651
POLYVAL input =             0da55210cc1c1b0abde3b2f204d1e9f8
                            b06bc47f000000000000000000000000
                            1db2316fd568378da107b52b00000000
                            a0000000000000006000000000000000
POLYVAL result =            cc86ee22c861e1fd474c84676b42739c
POLYVAL result XOR nonce =  90187a2d224eb9d417eb893d6b42739c
... and masked =            90187a2d224eb9d417eb893d6b42731c
Tag =                       404099c2587f64979f21826706d497d5
Initial counter =           404099c2587f64979f21826706d497d5
Result (28 bytes) =         8dbeb9f7255bf5769dd56692404099c2
                            587f64979f21826706d497d5


Plaintext (15 bytes) =      21702de0de18baa9c9596291b08466
AAD (25 bytes) =            f37de21c7ff901cfe8a69615a93fdf7a
                            98cad481796245709f
Key =                       9745b3d1ae06556fb6aa7890bebc18fe
                            6b3db4da3d57aa94842b9803a96e07fb
Nonce =                     6de71860f762ebfbd08284e4
Record authentication key = 27c2959ed4daea3b1f52e849478de376
Record encryption key =     307a38a5a6cf231c0a9af3b527f23a62
                            e9a6ff09aff8ae669f760153e864fc93
POLYVAL input =             f37de21c7ff901cfe8a69615a93fdf7a
                            98cad481796245709f00000000000000
                            21702de0de18baa9c9596291b0846600
                            c8000000000000007800000000000000
POLYVAL result =            c4fa5e5b713853703bcf8e6424505fa5
POLYVAL result XOR nonce =  a91d463b865ab88beb4d0a8024505fa5
... and masked =            a91d463b865ab88beb4d0a8024505f25
Tag =                       b3080d28f6ebb5d3648ce97bd5ba67fd
Initial counter =           b3080d28f6ebb5d3648ce97bd5ba67fd
Result (31 bytes) =         793576dfa5c0f88729a7ed3c2f1bffb3
                            080d28f6ebb5d3648ce97bd5ba67fd


Plaintext (18 bytes) =      b202b370ef9768ec6561c4fe6b7e7296
                            fa85
AAD (30 bytes) =            9c2159058b1f0fe91433a5bdc20e214e
                            ab7fecef4454a10ef0657df21ac7
Key =                       b18853f68d833640e42a3c02c25b6486
                            9e146d7b233987bddfc240871d7576f7
Nonce =                     028ec6eb5ea7e298342a94d4
Record authentication key = 670b98154076ddb59b7a9137d0dcc0f0
Record encryption key =     78116d78507fbe69d4a820c350f55c7c
                            b36c3c9287df0e9614b142b76a587c3f
POLYVAL input =             9c2159058b1f0fe91433a5bdc20e214e
                            ab7fecef4454a10ef0657df21ac70000
                            b202b370ef9768ec6561c4fe6b7e7296
                            fa850000000000000000000000000000
                            f0000000000000009000000000000000
POLYVAL result =            4e4108f09f41d797dc9256f8da8d58c7
POLYVAL result XOR nonce =  4ccfce1bc1e6350fe8b8c22cda8d58c7
... and masked =            4ccfce1bc1e6350fe8b8c22cda8d5847
Tag =                       454fc2a154fea91f8363a39fec7d0a49
Initial counter =           454fc2a154fea91f8363a39fec7d0ac9
Result (34 bytes) =         857e16a64915a787637687db4a951963
                            5cdd454fc2a154fea91f8363a39fec7d
                            0a49


Plaintext (21 bytes) =      ced532ce4159b035277d4dfbb7db6296
                            8b13cd4eec
AAD (35 bytes) =            734320ccc9d9bbbb19cb81b2af4ecbc3
                            e72834321f7aa0f70b7282b4f33df23f
                            167541
Key =                       3c535de192eaed3822a2fbbe2ca9dfc8
                            8255e14a661b8aa82cc54236093bbc23
Nonce =                     688089e55540db1872504e1c
Record authentication key = cb8c3aa3f8dbaeb4b28a3e86ff6625f8
Record encryption key =     02426ce1aa3ab31313b0848469a1b5fc
                            6c9af9602600b195b04ad407026bc06d
POLYVAL input =             734320ccc9d9bbbb19cb81b2af4ecbc3
                            e72834321f7aa0f70b7282b4f33df23f
                            16754100000000000000000000000000
                            ced532ce4159b035277d4dfbb7db6296
                            8b13cd4eec0000000000000000000000
                            1801000000000000a800000000000000
POLYVAL result =            ffd503c7dd712eb3791b7114b17bb0cf
POLYVAL result XOR nonce =  97558a228831f5ab0b4b3f08b17bb0cf
... and masked =            97558a228831f5ab0b4b3f08b17bb04f
Tag =                       9d6c7029675b89eaf4ba1ded1a286594
Initial counter =           9d6c7029675b89eaf4ba1ded1a286594
Result (37 bytes) =         626660c26ea6612fb17ad91e8e767639
                            edd6c9faee9d6c7029675b89eaf4ba1d
                            ed1a286594
]]></artwork>
        </figure>
      </section>
      <section title="Counter Wrap Tests">
        <t>The tests in this section use AEAD_AES_256_GCM_SIV and are crafted to test correct wrapping of the block counter.</t>
        <figure align="center">
          <artwork align="left"><![CDATA[
Plaintext (32 bytes) =      00000000000000000000000000000000
                            4db923dc793ee6497c76dcc03a98e108
AAD (0 bytes) =
Key =                       00000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     000000000000000000000000
Record authentication key = dc95c078a24089895275f3d86b4fb868
Record encryption key =     779b38d15bffb63d39d6e9ae76a9b2f3
                            75d11b0e3a68c422845c7d4690fa594f
POLYVAL input =             00000000000000000000000000000000
                            4db923dc793ee6497c76dcc03a98e108
                            00000000000000000001000000000000
POLYVAL result =            7367cdb411b730128dd56e8edc0eff56
POLYVAL result XOR nonce =  7367cdb411b730128dd56e8edc0eff56
... and masked =            7367cdb411b730128dd56e8edc0eff56
Tag =                       ffffffff000000000000000000000000
Initial counter =           ffffffff000000000000000000000080
Result (48 bytes) =         f3f80f2cf0cb2dd9c5984fcda908456c
                            c537703b5ba70324a6793a7bf218d3ea
                            ffffffff000000000000000000000000


Plaintext (24 bytes) =      eb3640277c7ffd1303c7a542d02d3e4c
                            0000000000000000
AAD (0 bytes) =
Key =                       00000000000000000000000000000000
                            00000000000000000000000000000000
Nonce =                     000000000000000000000000
Record authentication key = dc95c078a24089895275f3d86b4fb868
Record encryption key =     779b38d15bffb63d39d6e9ae76a9b2f3
                            75d11b0e3a68c422845c7d4690fa594f
POLYVAL input =             eb3640277c7ffd1303c7a542d02d3e4c
                            00000000000000000000000000000000
                            0000000000000000c000000000000000
POLYVAL result =            7367cdb411b730128dd56e8edc0eff56
POLYVAL result XOR nonce =  7367cdb411b730128dd56e8edc0eff56
... and masked =            7367cdb411b730128dd56e8edc0eff56
Tag =                       ffffffff000000000000000000000000
Initial counter =           ffffffff000000000000000000000080
Result (40 bytes) =         18ce4f0b8cb4d0cac65fea8f79257b20
                            888e53e72299e56dffffffff00000000
                            0000000000000000
]]></artwork>
        </figure>
      </section>
    </section>

    <section title="Acknowledgements" numbered="no">
      <t>The authors would like to thank Daniel Bleichenbacher, Uri Blumenthal, Deb Cooley's team at NSA Information Assurance, Scott Fluhrer, Tetsu Iwata, Tibor Jager, John Mattsson, Ondrej Mosnacek, Kenny Paterson, Bart Preneel, Yannick Seurin, and Bjoern Tackmann for their helpful suggestions and review.</t>
    </section>

  </back>
</rfc>