NuCypher's Proxy Re-Encryption and Umbral

Link to their work (Proxy Re-Encryption): Proxy Re-Encryption

Link to their work (Umbral): Umbral

USE CASE

Proxy Re-Encryption is an algorithm that allows a message encrypted for User A to be re-encrypted by a proxy so that User B can decrypt it. The fantastic thing about this algorithm is that the act of re-encrypting the message (with a reencryption key generated by User A) never allows the proxy to see the underlying message, just converts the ciphertextA to ciphertextB directly. This allows messages that are meant for User A, to be transferred and re-encrypted semi-automatically (through a Proxy - which does not see the underlying message) for User B without User A having to be online.

The usual procedure is that User A would have to manually decrypt the ciphertextA with its secret key and encrypt again with User B's public key.

The following image explains the mechanism that Proxy Re-Encryption uses:

Umbral works in basically the same way that Proxy Re-Encryption does, with the important difference that it splits the re-encryption key - generated by User A into N fragments, and to correctly decrypt the message, you have to recover at least M fragments (M <= N) - M is chosen at the moment you split the re-encryption key. Doing this, you don't have to trust one single proxy, but instead, you split the responsibility between N proxys and only need M of them to respond with their corresponding fragment for User B to be able to correctly decrypt the message.

To show the capabilities of NuCypher's Re-Encryption and Umbral, 2 Proofs of Concepts (PoC) have been developed.

1. Proxy Re-Encryption
2. Umbral

Proxy Re-Encryption

The PoC for this concept is a web application:

Which has the following buttons:

Alice's Side

1. Generate
2. Encrypt
3. Decrypt
4. Reencrypt

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1. Generate: consumes the API "/genKeys" - generates keys for several users.

• Input: None
• Output (encoded to base 64):
  • sk_A = Secret Key of User A
  • pk_A = Public Key of User A
  • sk_B = Secret Key of User B
  • pk_B = Public Key of User B
  • sk_Eph = Secret Ephimeral Key
  • reeK = Reencryption Key - made with sk_A and sk_Eph

2. Encrypt: consumes the API "/encryptA" - encrypts a message with a public key of your choosing (in base 64)

• Input:
  • pk_A (encoded to base 64): Public key of User A
  • msg: Message that wants to be encrypted.
• Output (encoded to base 64):
  • emsg = Encrypted message

3. Decrypt: consumes the API "/decrypt" - decrypts an encrypted message with the secret key of the public key used to encrypt the original message.

• Input (encoded to base 64):
  • key = Key with which you wish to decrypt
  • emsg = Encrypted message
• Output:
  • msg = Decrypted message

4. Reencrypt: consumes the API "/reencrypt" - reencrypts an already encrypted message with a reencryption key previously generated, so that another user can decypher the message aftewards. Also encrypts the ephimeral key previously generated with the recipients public key (pk_B) so that they can decypher the message at the receiving end.

• Input (encoded to base 64):
  • emsg = Encrypted message
  • reeK = Reencryption key
  • pk_B = Public key of User B
  • EphSK = Secret Ephimeral key
• Output (encoded to base 64):
  • BEphPK = Secret Ephimeral key encrypted with Public key of User B - to be later sent to User B
  • remsg = Reencrypted message with reeK

---

Bob's side

5. DecryptEphKey
6. Decrypt message

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5. DecryptEphKey: consumes the API "/decryptEphKey" - decrypts the Secret Ephimeral Key with User B's Secret Key - this key is used to finally be able to decrypt the reencrypted message.

• Input (encoded to base 64):
  • sk_B: Secret Key of User B
  • BEphPK: Secret Ephimeral Key encrypted with User B's Public key
• Output (encoded to base 64):
  • EphPKDec: Secret Ephimeral key decrypted (should coincide with the Secret Ephimeral Key generated by Alice previously)

6. Decrypt message: consumes the same API as the decrypt button.

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Umbral

The PoC for this concept is also a web application:

It has the following buttons:

Alice's Side

1. Generate
2. Encrypt
3. Umbralize

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1. Generate: consumes the API "/genKeys" - generates keys for several users.

• Input: None
• Output (encoded to base 64):
  • sk_A = Secret Key of User A
  • pk_A = Public Key of User A
  • sk_B = Secret Key of User B
  • pk_B = Public Key of User B

2. Encrypt: consumes the API "/encrypt" - encrypts message with a public key.

• Input:
  • pk_A (encoded to base 64) = User A's Public Key
  • msg (byte string: ex. b'hola') = message that you wish to encrypt
• Output (encoded to base 64):
  • emsg = Encrypted message
  • capsule = Object that contains the information necessary to decrypt emsg

3. Umbralize: consumes the API "/umbralize" - creates and splits the reencryption key into N fragments, and to able to reencrypt the message correctly, you need to recover M (M <= N) fragments of the key.

• Input:
  • sk_A (encoded to base 64) = User A's Secret Key, it will be used to create the re-encryption key
  • pk_B (encoded to base 64) = User B's Public key of the person who you wish to re-encrypt the message to.
  • M (integer) = Number that represents how many pieces need to be assembled of the re-encryption key to be able to decypher correctly.
  • N (integer) = Number that represents in how many pieces the re-encryption key will be split into.
• Output (encoded to base 64):
  • bytekfrags = A list of the fragments generated by splitting the re-encryption key.

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Bob's Side

4. Decrypt

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4. Decrypt: consumes the API "/decrypt" - uses the capsule (previously mentioned) and the re-encryption key fragments recovered to decypher the re-encrypted message - if the amount of fragments recovered is less than the number M established earlier, the message returned will be: b'No se pudo descifrar el mensaje, se debe elegir mas fragmentos'. Other wise, it will return the decyphered message.

• Input (encoded to base 64):
  • kfragsSel = A list of the re-encryption fragments recovered
  • capsule = Object that contains the information necessary to decrypt emsg
  • sk_B = User B's Secret Key
  • pk_A = User A's Public Key
  • emsg = Encrypted message
• Output:
  • omsg = Decyphered message