The Wolfram Language's extensive base of state-of-the-art algorithms and efficient handling of very long integers make it uniquely suited to both research and implementation of cryptographic number theory.

Encryption and Decryption

PowerMod — compute modular powers of integers

PowerModList — compute modular inverses, with negative and fractional powers

PolynomialMod  ▪  BitXor  ▪  BitAnd  ▪  BitOr  ▪  BitSet  ▪  BitGet

Key Generation

RandomPrime — pseudorandom prime

Prime — the n ^th prime

PrimeQ — test for primality

Mod  ▪  JacobiSymbol  ▪  PrimitiveRoot  ▪  PrimitiveRootList  ▪  CarmichaelLambda  ▪  MoebiusMu

$CryptographicEllipticCurveNames — supported standard elliptic curves

Cryptanalysis

FactorInteger — complete or incomplete integer factorization

MultiplicativeOrder — compute the discrete logarithm

EulerPhi — Euler totient function

Reduce — solve multivariate quadratic polynomials

CharacterCounts — compute -gram frequencies

Lattice-Oriented Problems

LatticeReduce — find short basis vectors in an integer lattice

LatticeData — properties of named lattices

Textual Data

Hash, FileHash — compute MD5 and other hash codes

ToCharacterCode, FromCharacterCode — convert between strings and character codes

ByteArray — raw array of arbitrary bytes

BaseDecode, BaseEncode — convert between a byte array and its Base64 representation

Other Forms of Cryptography

CellularAutomaton — efficiently compute general block maps

Practical Cryptography »

GenerateAsymmetricKeyPair — generate RSA, elliptic curve and other keys

Encrypt  ▪  Decrypt  ▪  PrivateKey  ▪  PublicKey  ▪  DigitalSignature  ▪  ...