Cryptographic system including a mixed radix number generator with chosen statistical artifacts
First Claim
1. 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 p1, p2, p3 . . . , pk,(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 p1, p2, p3, . . . , pk; 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.
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Accused Products
Abstract
A cryptographic system (1000) is provided. The cryptographic system includes a data stream receiving means (DSRM), a number generator (NG), a mixed radix accumulator (MRA) and an encryptor. The DSRM (1002) receives a data stream (DS). The NG (702) generates a first number sequence (FNS) contained within a Galois Field GF[M]. The MRA (750) is configured to perform a first modification to a first number (FN) in FNS. The first modification involves summing the FN with a result of a modulo P operation performed on a second number in FNS that proceeds FN. The MRA is also configured to perform a second modification to FN utilizing a modulo P operation. The MRA is further configured to repeat the first and second modification for numbers in FNS to generate a second number sequence (SNS). The encryptor (1004) is configured to generate a modified data stream by combining SNS and DS.
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Citations
22 Claims
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1. A cryptographic system, comprising:
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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 p1, p2, p3 . . . , pk, (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 p1, p2, p3, . . . , pk; 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. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
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14. A cryptographic system, comprising:
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a data stream generating circuit configured to generate an input data stream including a first sequence of numbers with a known non-uniform probability distribution and 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 data stream generating 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 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 p1, p2, p3, . . . , pk, (2) subsequent to said first modification, perform a second modification to said first number comprising a modulo P operation, and (3) repeating said first and second modifications 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 p1, p2, p3, . . . , pk; and a cryptographic circuit configured to combine at least one of said plurality of output number sequences with a data signal to encrypt or decrypt said data signal. - View Dependent Claims (15, 16, 17, 18)
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19. A method for encrypting and decrypting an input data stream, comprising the steps of:
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receiving, by at least one electronic circuit, an input data stream; generating, by said electronic circuit, 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;performing, by said electronic circuit, 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 relatively prime with respect to a value of P and all of a plurality of relatively prime factors of P including p1, p2, p3, . . . , pk; performing, by said electronic circuit, a second modification subsequent to said first modification to said first number comprising a second modulo P operation; repeating, by said electronic circuit, said first and second modifications for a plurality of numbers comprising said first sequence of numbers to generate a second sequence of numbers; performing, by said electronic circuit, a third modification on said second sequence of numbers for simultaneously generating a plurality of output number sequences from said second sequence of numbers; and generating, by said electronic circuit, a modified data stream by combining at least one of said plurality of output number sequences with said input data stream; wherein said third modification comprises 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 p1, p2, p3, . . . , pk. - View Dependent Claims (20, 21, 22)
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Specification