pyUmbral

pyUmbral is the reference implementation of the Umbral threshold proxy re-encryption scheme. It is open-source, built with Python, and uses OpenSSL and Cryptography.io.

Using Umbral, Alice (the data owner) can delegate decryption rights to Bob for any ciphertext intended to her, through a re-encryption process performed by a set of semi-trusted proxies or Ursulas. When a threshold of these proxies participate by performing re-encryption, Bob is able to combine these independent re-encryptions and decrypt the original message using his private key.

pyUmbral is the cryptographic engine behind nucypher, a proxy re-encryption network to empower privacy in decentralized systems.

Usage

Key Generation

As in any public-key cryptosystem, users need a pair of public and private keys. Additionally, users that delegate access to their data (like Alice, in this example) need a signing keypair.

from umbral import SecretKey, Signer

# Generate Umbral keys for Alice.
alices_secret_key = SecretKey.random()
alices_public_key = alices_secret_key.public_key()

alices_signing_key = SecretKey.random()
alices_signer = Signer(alices_signing_key)
alices_verifying_key = alices_signing_key.public_key()

# Generate Umbral keys for Bob.
bobs_secret_key = SecretKey.random()
bobs_public_key = bobs_secret_key.public_key()

Encryption

Now let's encrypt data with Alice's public key. Invocation of pre.encrypt returns both the ciphertext and a capsule. Note that anyone with Alice's public key can perform this operation.

Since data was encrypted with Alice's public key, Alice can open the capsule and decrypt the ciphertext with her private key.

from umbral import encrypt, decrypt_original

# Encrypt data with Alice's public key.
plaintext = b'Proxy Re-Encryption is cool!'
capsule, ciphertext = encrypt(alices_public_key, plaintext)

# Decrypt data with Alice's private key.
cleartext = decrypt_original(alices_secret_key, capsule, ciphertext)

Re-Encryption Key Fragments

When Alice wants to grant Bob access to open her encrypted messages, she creates re-encryption key fragments, or "kfrags", which are next sent to N proxies or Ursulas.

from umbral import generate_kfrags

# Alice generates "M of N" re-encryption key fragments (or "KFrags") for Bob.
# In this example, 10 out of 20.
kfrags = generate_kfrags(delegating_sk=alices_secret_key,
                         receiving_pk=bobs_public_key,
                         signer=alices_signer,
                         threshold=10,
                         shares=20)

Re-Encryption

Bob asks several Ursulas to re-encrypt the capsule so he can open it. Each Ursula performs re-encryption on the capsule using the kfrag provided by Alice, obtaining this way a "capsule fragment", or cfrag.

Bob collects the resulting cfrags from several Ursulas. Bob must gather at least threshold cfrags in order to activate the capsule.

from umbral import reencrypt

# Several Ursulas perform re-encryption, and Bob collects the resulting `cfrags`.
cfrags = list()           # Bob's cfrag collection
for kfrag in kfrags[:10]:
    cfrag = pre.reencrypt(capsule=capsule, kfrag=kfrag)
    cfrags.append(cfrag)    # Bob collects a cfrag

Decryption by Bob

Finally, Bob activates the capsule by attaching at least threshold cfrags, and then decrypts the re-encrypted ciphertext.

from umbral import decrypt_reencrypted

bob_cleartext = pre.decrypt_reencrypted(receiving_sk=bobs_secret_key,
                                        delegating_pk=alices_public_key,
                                        capsule=capsule,
                                        cfrags=cfrags,
                                        ciphertext=ciphertext)
assert bob_clea