Patent ID: 8320557

Claim:
A cryptographic system, comprising: a data stream receiving circuit configured to receive an input data stream; a number generator circuit configured to generate a first sequence of numbers contained within a punctured Galois field GF′[M] in which at least one element of a plurality of elements comprising a Galois field GF[M], has been removed; a mixed radix accumulator circuit electronically connected to said number generator circuit and configured to (1) perform a first modification to a first number in said first sequence of numbers comprising summing said first number with a result of a first modulo P operation plus a fixed offset performed on a second number of said first sequence that proceeds said first number, where a value of M is mutually prime with respect to a value of P and all of a plurality of relatively prime factors of P including p 1 , p 2 , p 3 . . . , p k , (2) subsequent to said first modification, perform a second modification to said first number comprising a second modulo P operation, and (3) repeating said first and second modification for a plurality of numbers comprising said first sequence of numbers to generate a second sequence of numbers; a plurality of arithmetic operator circuits each configured to perform a third modification on said second sequence of numbers for simultaneously generating a plurality of output number sequences from said second sequence of numbers, said third modification comprising a plurality of modulo p operations simultaneously performed upon each number in said second sequence of numbers to generate said plurality of output number sequences, where p includes a plurality of values selected from a group comprising p 1 , p 2 , p 3 , . . . , p k ; and an encryptor circuit electronically connected to said data stream receiving circuit and said plurality of arithmetic operator circuits, said encryptor circuit configured to generate a modified data stream by incorporating or combining at least one of said plurality of output number sequences with said input data stream.