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Bytecode Behavior Specification of Deposit Contract

Here we summarize all possible behaviors of the compiled bytecode of the deposit contract that we formally verified. We do not explicitly specify the out-of-gas exceptional behaviors.

Refer to deposit-spec.ini for the full formal specification.

Storage state variables

  • deposit_count (an unsigned 256-bit integer) keeps track of the number of deposits made.
  • branch and zero_hashes (arrays of 32-byte words of size 32) are internal data structures for the incremental Merkle tree algorithm.

Constructor __init__() (executed once at the deployment)

Behavior:

  • It reverts when the call value is non-zero.
  • Otherwise, it updates the storage state as follows:
    zero_hashes[i] <- ZERO_HASHES(i)  for 1 <= i < 32

Here ZERO_HASHES(i) is recursively defined as follows:

ZERO_HASHES(i+1) = #sha256(#buf(32, ZERO_HASHES(i)) ++ #buf(32, ZERO_HASHES(i)))  for 0 <= i < 31
ZERO_HASHES(0) = 0

where #sha256 denotes the SHA2-256 hash function, #buf(SIZE, DATA) denotes the byte representation of DATA in SIZE bytes, and ++ denotes the byte concatenation.

Common behavior at the entry of the deployed bytecode

  • It reverts when calldatasize < 4.
  • It reverts when msg.data[0..4] does not match the signature of any public functions get_deposit_root(), get_deposit_count(), or deposit(bytes,bytes,bytes,bytes32).

Here BUF [ START .. WIDTH ] denotes the segment of BUF beginning with START of width WIDTH.

Function get_deposit_count()

Behavior:

  • It reverts when the call value is non-zero.
  • It does not alter the storage state.
  • It silently ignores any extra contents in msg.data. (We have not yet found any attack that can exploit this behavior.)
  • It returns #encodeArgs(#bytes(#buf(32, LE(deposit_count))[24..8])).

Here:

#encodeArgs is defined in eDSL which formalizes the ABI encoding specification,

and:

LE(V) is essentially the return value of to_little_endian_64(V), i.e., the 64-bit little-endian representation of V, defined as follows. For 0 <= V < 2^64:

LE(V) = (Y7(V) * 256) + (X7(V) & 255)
Y7(V) = (Y6(V) * 256) + (X6(V) & 255)
Y6(V) = (Y5(V) * 256) + (X5(V) & 255)
Y5(V) = (Y4(V) * 256) + (X4(V) & 255)
Y4(V) = (Y3(V) * 256) + (X3(V) & 255)
Y3(V) = (Y2(V) * 256) + (X2(V) & 255)
Y2(V) = (Y1(V) * 256) + (X1(V) & 255)
Y1(V) =                 (X0(V) & 255)

where:

X7(V) = floor(X6(V) / 256)
X6(V) = floor(X5(V) / 256)
X5(V) = floor(X4(V) / 256)
X4(V) = floor(X3(V) / 256)
X3(V) = floor(X2(V) / 256)
X2(V) = floor(X1(V) / 256)
X1(V) = floor(X0(V) / 256)
X0(V) = V

Note that LE(deposit_count) is well defined because deposit_count < 2^32 < 2^64.

The byte sequence of the return value is as follows (in hexadecimal notation):

0x0000000000000000000000000000000000000000000000000000000000000020
  0000000000000000000000000000000000000000000000000000000000000008
  deadbeefdeadbeef000000000000000000000000000000000000000000000000

This byte sequence encodes the returned byte array of type bytes[8], where the first 32 bytes (in the first line) denote the offset (32 = 0x20) to the byte array, the second 32 bytes (in the second line) denote the size of the byte array (8 = 0x8), and the deadbeefdeadbeef (in the third line) denotes the content of the byte array, i.e., the sequence of 8 bytes that consists of X0 & 255, X1 & 255, ..., and X7 & 255 in that order. The remaining 24 zero-bytes denote zero-padding for the 32-byte alignment. This byte sequence conforms to the ABI encoding specification. Note that the original sequence of bytes (i.e., the big-endian representation) of deposit_count consists of X7 & 255, X6 & 255, ..., and X0 & 255 in that order.

Function get_deposit_root()

Behavior:

  • It reverts when the call value is non-zero.
  • It does not alter the storage state.
  • It silently ignores any extra contents in msg.data. (We have not yet found any attack that can exploit this behavior.)
  • It returns #sha256(#buf(32, NODE(32)) ++ #buf(32, LE(deposit_count))[24..8] ++ #buf(24, 0)).

Here NODE(32) is the Merklee tree root value, recursively defined as follows:

NODE(i+1) = if SIZE(i) & 1 == 1
            then #sha256(#buf(32, branch[i]) ++ #buf(32, NODE(i)))
            else #sha256(#buf(32, NODE(i)) ++ #buf(32, zero_hashes[i]))
            for 0 <= i < 32
NODE(0) = 0

where:

SIZE(i+1) = floor(SIZE(i) / 2)  for 0 <= i < 32
SIZE(0) = deposit_count

LE(deposit_count) is the same with the one defined in the specification of the get_deposit_count() function above.

Function deposit(pubkey, withdrawal_credentials, signature, deposit_data_root)

Behavior:

  • It reverts if either of the following is not met:

    • old(deposit_count) < 2^32 - 1
    • DEPOSIT_AMOUNT >= 10^9
    • PUBKEY_ARGUMENT_SIZE == PUBKEY_LENGTH
    • WITHDRAWAL_CREDENTIALS_ARGUMENT_SIZE == WITHDRAWAL_CREDENTIALS_LENGTH
    • SIGNATURE_ARGUMENT_SIZE == SIGNATURE_LENGTH
    • NODE == deposit_data_root

    where old(deposit_count) denotes the value of deposit_count at the beginning of the function, and DEPOSIT_AMOUNT is the amount of deposit (in gwei), that is, floor(msg.value / 10^9).

  • Otherwise, it emits a DepositEvent log:

    #abiEventLog(THIS, "DepositEvent",
                 #bytes(#buf(PUBKEY_LENGTH, PUBKEY)),
                 #bytes(#buf(WITHDRAWAL_CREDENTIALS_LENGTH, WITHDRAWAL_CREDENTIALS)),
                 #bytes(#buf(32, LE(DEPOSIT_AMOUNT))[24..8]),
                 #bytes(#buf(SIGNATURE_LENGTH, SIGNATURE)),
                 #bytes(#buf(32, LE(old(deposit_count)))[24..8])
                )

    where #abiEventLog is defined in eDSL which formalizes the ABI event encoding specification, and LE(V) is the 64-bit little-endian representation of V which is defined in the specification of the get_deposit_count() function above. See below for the definition of the other event log arguments.

    Note that LE(DEPOSIT_AMOUNT) is well defined only when DEPOSIT_AMOUNT is less than 2^64 gwei (~ 18 billion Ether), which is very likely the case especially considering the current total supply of Ether (~ 110 million) and the history of its growth rate.

  • Also, it updates the storage state as follows:

    deposit_count <- old(deposit_count) + 1
    branch[K] <- NODE(K)

    where NODE(i) is recursively defined as follows:

    NODE(i+1) = #sha256(#buf(32, branch[i]) ++ #buf(32, NODE(i)))  for 0 <= i < 32
    NODE(0) = NODE

    and K is the largest index less than 32 such that:

    SIZE(i) & 1 == 0  for 0 <= i < K
    SIZE(K) & 1 == 1

    where SIZE(i) is recursively defined as follows:

    SIZE(i+1) = floor(SIZE(i) / 2)  for 0 <= i < 32
    SIZE(0) = old(deposit_count) + 1

    Note that such K always exists, since old(deposit_count) < 2^32 - 1 (because of the assertion at the beginning of the function). In other words, the loop always terminates by reaching the break statement, because of the assertion old(deposit_count) < 2^32 - 1.

Here:

The non-static-type function arguments (PUBKEY, WITHDRAWAL_CREDENTIALS, and SIGNATURE) are decoded as follows:

PUBKEY_OFFSET                 = (4 + msg.data[ 4..32]) mod 2^256
WITHDRAWAL_CREDENTIALS_OFFSET = (4 + msg.data[36..32]) mod 2^256
SIGNATURE_OFFSET              = (4 + msg.data[68..32]) mod 2^256

PUBKEY_ARGUMENT_SIZE                 = msg.data [ PUBKEY_OFFSET                 .. 32 ]
WITHDRAWAL_CREDENTIALS_ARGUMENT_SIZE = msg.data [ WITHDRAWAL_CREDENTIALS_OFFSET .. 32 ]
SIGNATURE_ARGUMENT_SIZE              = msg.data [ SIGNATURE_OFFSET              .. 32 ]

PUBKEY                 = msg.data [ (PUBKEY_OFFSET                 + 32) .. PUBKEY_LENGTH                 ]
WITHDRAWAL_CREDENTIALS = msg.data [ (WITHDRAWAL_CREDENTIALS_OFFSET + 32) .. WITHDRAWAL_CREDENTIALS_LENGTH ]
SIGNATURE              = msg.data [ (SIGNATURE_OFFSET              + 32) .. SIGNATURE_LENGTH              ]

NOTE: The argument decoding process of the Vyper-compiled bytecode does not explicitly check the well-formedness of the calldata (msg.data). Specifically, the addition overflow may happen when decoding the offsets (*_OFFSET). Also, the decoded offsets may be larger than the size of calldata, leading to out-of-bounds access, although the out-of-bounds access to calldata simply returns zero bytes. We note that the Solidity-compiled bytecode contains more runtime checks to avoid aforementioned behaviors. Currently, the deposit contract relies on the checksum (the deposit_data_root argument) to finally reject such ill-formed calldata. We have not yet found any attack that can exploit this behavior especially in the presence of the checksum.

Remark: When decoding the actual contents of arguments (i.e., PUBKEY, WITHDRAWAL_CREDENTIALS, and SIGNATURE), it reads the calldata using the expected size (*_LENGTH) not the decoded size (*_SIZE). Thanks to this, the amount of gas consumed by the decoding process is constant, regardless of the well-formedness of calldata, which is desired. On the other hand, the length-checking assertions ensures that the decoded size (*_SIZE) of arguments is equal to the expected value (*_LENGTH), but they are performed only after decoding the actual contents of arguments (PUBKEY, WITHDRAWAL_CREDENTIALS, and SIGNATURE). However, the length-checking assertions are still needed to prevent wasting gas, because without them, the later uses of the decoded arguments involve memory copies of them, whose gas cost depends on the decoded size (*_SIZE) which could be very large in certain ill-formed calldata.

The deposit data root NODE is computed as follows:

PUBKEY_ROOT    = #sha256(#buf(48, PUBKEY) ++ #buf(16, 0))
TMP1           = #sha256(#buf(96, SIGNATURE)[0..64])
TMP2           = #sha256(#buf(96, SIGNATURE)[64..32] ++ #buf(32, 0))
SIGNATURE_ROOT = #sha256(#buf(32, TMP1) ++ #buf(32, TMP2))
TMP3           = #sha256(#buf(32, PUBKEY_ROOT) ++ #buf(32, WITHDRAWAL_CREDENTIALS))
TMP4           = #sha256(#buf(32, LE(DEPOSIT_AMOUNT))[24..8] ++ #buf(24, 0) ++ #buf(32, SIGNATURE_ROOT))
NODE           = #sha256(#buf(32, TMP3) ++ #buf(32, TMP4))
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