Danger

Nothing here should be used for any security purposes.

  • If you need cryptographic tools in a Python environment use pyca or PyNaCl.

  • If you need efficient and reliable abstract math utilities in a Python-like environment consider using SageMath.

Primitive RSA#

This page describes some of things that are part of the toy_crypto.rsa module. They are imported with:

from toy_crypto import rsa

Primitive RSA, as illustrated here, operates on integers and is deterministic. The former makes it impractical for direct use and the latter means that it immediately fails to meet IND-CPA security. See OAEP for discussion of and illustration of how those are properly addressed.

The original example#

Let’s see a simple example, from the original publication describing the RSA algorithm [Gardner, 1977]. This will require the text decoding scheme used then which is in toy_crypto.utils.Rsa129.decode().

import toy_crypto.rsa as rsa
from toy_crypto.utils import Rsa129

# From the challenge itself
modulus=114381625757888867669235779976146612010218296721242362562561842935706935245733897830597123563958705058989075147599290026879543541
pub_exponent=9007
ctext=96869613754622061477140922254355882905759991124574319874695120930816298225145708356931476622883989628013391990551829945157815154

# We have since learned p and q
p=3490529510847650949147849619903898133417764638493387843990820577
q=32769132993266709549961988190834461413177642967992942539798288533

priv_key = rsa.PrivateKey(p, q, pub_exponent = pub_exponent)

pub_key = priv_key.pub_key
assert pub_key.N == modulus

decrypted = priv_key.decrypt(ctext)  # This is a large int

# Now the Rsa129 text decoder
ptext = Rsa129.decode(decrypted)
print(ptext)

THE MAGIC WORDS ARE SQUEAMISH OSSIFRAGE

Primitive API#

class toy_crypto.rsa.PublicKey(modulus: int, public_exponent: int) → None[source]#

Public key from public values.

Parameters:

  • modulus (int)

  • public_exponent (int)

property N: int#

Public modulus N.

property e: int#

Public exponent e

encrypt(message: int) → int[source]#

Primitive encryption with neither padding nor nonce.

Raises:
Parameters:

message (int)

Return type:

int

oaep_encrypt(message: bytes, label: bytes = b'', hash_id: str = 'sha256', mgf_id: str = 'mgf1SHA256', _seed: bytes | None = None) → bytes[source]#

RSA OAEP encryption.

Parameters:

  • message (bytes) – The message to encrypt.

  • label (bytes, default: b'') – Rarely used. Just leave as default.

  • hash_id (str, default: 'sha256') – Name of the hash function.

  • mgf_id (str, default: 'mgf1SHA256') – Name of the MGF function (with hash).

  • _seed (bytes | None, default: None) – Used for testing only. OAEP is not supposed to be deterministic.

Raises:

  • ValueError – if hash or MGF is not recognized.

  • ValueError – if lengths of inputs exceed what modulus and hash sizes can accommodate.

Return type:

bytes

RFC 8017 Section 7.1.1

class toy_crypto.rsa.PrivateKey(p: int, q: int, pub_exponent: int = 65537) → None[source]#

RSA private key from primes p and q.

This does not perform any sanity checks on p and q. It is your responsibility to ensure that they are suitable primes. Consider using fips186_prime_gen() to generate primes.

Raises:

ValueError – if \(\gcd(e, \mathop{\mathrm{lcm}}(p - 1, q - 1)) \neq 1\).

Parameters:

  • p (int)

  • q (int)

  • pub_exponent (int, default: 65537)

decrypt(ciphertext: int) → int[source]#

Primitive decryption.

Parameters:

ciphertext (int) – Ciphertext as int

Raises:

ValueError – if ciphertext is out of range for this key.

Return type:

int

property e: int#

Public exponent.

oaep_decrypt(ciphertext: bytes, label: bytes = b'', hash_id: str = 'sha256', mgf_id: str = 'mgf1SHA256') → bytes[source]#

RSA OAEP decryption.

Parameters:

  • ciphertext (bytes) – The message to encrypt.

  • label (bytes, default: b'') – Rarely used.

  • hash_id (str, default: 'sha256') – Name of the hash function.

  • mgf_id (str, default: 'mgf1SHA256') – Name of the MGF function (with hash).

Raises:

  • ValueError – if hash or MGF is not recognized.

  • DecryptionError – on various decryption errors. If unsafe error reporting is enabled, details of decryption errors will be provided.

Return type:

bytes

property pub_key: PublicKey#

The public key corresponding to self.

The public key does not contain any secrets.