This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.
 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      Key Generation RandomPrime — pseudorandom prime Prime — the nth prime PrimeQ — test for primality      Cryptanalysis 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 TUTORIALS Integer and Number Theoretic Functions MORE ABOUT Number Theoretic Functions Algebraic Number Theory General Number Theory Integer Functions Prime Numbers Finite Fields Package RELATED LINKS Demonstrations related to Cryptographic Number Theory (The Wolfram Demonstrations Project)