This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
Cryptographic Number Theory
Mathematica's extensive base of state-of-the-art algorithms, efficient handling of very long integers, and powerful built-in language 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
FactorInteger complete or incomplete integer factorization
MultiplicativeOrder compute the discrete logarithm
EulerPhi Euler totient function
Reduce solve multivariate quadratic polynomials
Tally find frequencies of elements in a list
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
Other Forms of Cryptography
CellularAutomaton efficiently compute general block maps