Setting the default curve¶
The best way to start using pyUmbral is to decide on an elliptic curve to use and set it as your default.
>>> from umbral import config >>> from umbral.curve import SECP256K1 >>> config.set_default_curve(SECP256K1)
For more information on curves, see Choosing and Using Curves.
Generate an Umbral key pair¶
First, let’s generate two asymmetric key pairs for Alice: A delegating key pair and a signing key pair.
>>> from umbral import keys, signing >>> alices_private_key = keys.UmbralPrivateKey.gen_key() >>> alices_public_key = alices_private_key.get_pubkey() >>> alices_signing_key = keys.UmbralPrivateKey.gen_key() >>> alices_verifying_key = alices_signing_key.get_pubkey() >>> alices_signer = signing.Signer(private_key=alices_signing_key)
Encrypt with a public key¶
Now let’s encrypt data with Alice’s public key.
pre.encrypt returns both the
ciphertext and a
Note that anyone with Alice’s public key can perform this operation.
>>> from umbral import pre >>> plaintext = b'Proxy Re-encryption is cool!' >>> ciphertext, capsule = pre.encrypt(alices_public_key, plaintext)
Decrypt with a private key¶
Since data was encrypted with Alice’s public key, Alice can open the capsule and decrypt the ciphertext with her private key.
>>> cleartext = pre.decrypt(ciphertext=ciphertext, ... capsule=capsule, ... decrypting_key=alices_private_key)
>>> from umbral import keys >>> bobs_private_key = keys.UmbralPrivateKey.gen_key() >>> bobs_public_key = bobs_private_key.get_pubkey()
Alice grants access to Bob by generating kfrags¶
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.
Alice must specify
N (the total number of kfrags),
threshold (the minimum number of kfrags needed to activate a capsule).
In the following example, Alice creates 20 kfrags,
but Bob needs to get only 10 re-encryptions to activate the capsule.
>>> kfrags = pre.generate_kfrags(delegating_privkey=alices_private_key, ... signer=alices_signer, ... receiving_pubkey=bobs_public_key, ... threshold=10, ... N=20)
Bob receives a capsule¶
Next, let’s generate a key pair for Bob, and pretend to send him the capsule through a side channel like S3, IPFS, Google Cloud, Sneakernet, etc.
# Bob receives the capsule through a side-channel: IPFS, Sneakernet, etc. capsule = <fetch the capsule through a side-channel>
Bob fails to open the capsule¶
If Bob attempts to open a capsule that was not encrypted for his public key, or re-encrypted for him by Ursula, he will not be able to open it.
>>> fail = pre.decrypt(ciphertext=ciphertext, ... capsule=capsule, ... decrypting_key=bobs_private_key) Traceback (most recent call last): ... umbral.pre.UmbralDecryptionError
Ursulas perform 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
provided by Alice, obtaining this way a “capsule fragment”, or
Let’s mock a network or transport layer by sampling
threshold random kfrags,
one for each required Ursula. Note that each Ursula must prepare the received
capsule before re-encryption by setting the proper correctness keys.
Bob collects the resulting cfrags from several Ursulas.
Bob must gather at least
threshold cfrags in order to activate the capsule.
>>> import random >>> kfrags = random.sample(kfrags, # All kfrags from above ... 10) # M - Threshold >>> capsule.set_correctness_keys(delegating=alices_public_key, ... receiving=bobs_public_key, ... verifying=alices_verifying_key) (True, True, True) >>> cfrags = list() # Bob's cfrag collection >>> for kfrag in kfrags: ... cfrag = pre.reencrypt(kfrag=kfrag, capsule=capsule) ... cfrags.append(cfrag) # Bob collects a cfrag
Bob attaches cfrags to the capsule¶
Bob attaches at least
threshold cfrags to the capsule,
which has to be prepared in advance with the necessary correctness keys.
Only then it can become activated.
>>> capsule.set_correctness_keys(delegating=alices_public_key, ... receiving=bobs_public_key, ... verifying=alices_verifying_key) (False, False, False) >>> for cfrag in cfrags: ... capsule.attach_cfrag(cfrag)
Bob activates and opens the capsule¶
Finally, Bob decrypts the re-encrypted ciphertext using the activated capsule.
>>> cleartext = pre.decrypt(ciphertext=ciphertext, ... capsule=capsule, ... decrypting_key=bobs_private_key)