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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 ▪ ...

Related Tech Notes

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Integer and Number Theoretic Functions

Related Guides

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Number Theoretic Functions

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Algebraic Number Theory

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General Number Theory

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Integer Functions

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Prime Numbers

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Finite Fields