Cryptographic system configured for extending a repetition period of a random sequence
First Claim
1. A cryptographic system, comprising:
- a data stream receiving circuit configured to receive a data stream;
a ring generator circuit including(a) a computing module configured toperform a plurality of RNS arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values, said plurality of RNS residue values computed during said plurality of RNS arithmetic operations using a plurality of different modulus raised to different powers, andconvert each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit, and(b) a permutation module coupled to said computing module and configured to generate an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values, wherein said arbitrary permutation ordering is determined using a cyclic structure having n elements each having assigned thereto an output sequence number of said plurality of output sequence numbers and using a value of said select combination of digits to select an available unselected element in said cyclic structure, and wherein said arbitrary permutation ordering of said plurality of output sequence numbers is defined by an order of a selection of said n elements of said cyclic structure; and
an encryptor circuit coupled to said data stream receiving circuit and said ring generator circuit, said encryptor circuit configured to generate a modified data stream by incorporating or combining said plurality of output sequence numbers with said data stream.
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Abstract
A cryptographic system (CS) is provided. The CS (500) is comprised of a data stream receiving means (DSRM), a ring generator (RG) and an encryptor. The DSRM (602) provides a data stream (DS). The RG (400) includes a computing (404-408), converting (404-408) and permutation (410) means. The computing means is configured to perform RNS arithmetic operations to express a random number in a random number sequence as RNS residue values (RNSRV). The converting means is configured to convert each RNSRV to a relatively prime number system so that each RNSRV includes at least one digit. The permutation means is configured to generate an arbitrary permutation ordering of output sequence numbers (OSNs) using a select combination of digits associated with each RNSRV. The arbitrary permutation ordering is determined using a cyclic structure. The encryptor is configured to generate a modified data stream by combining the OSNs and DS.
112 Citations
23 Claims
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1. A cryptographic system, comprising:
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a data stream receiving circuit configured to receive a data stream; a ring generator circuit including (a) a computing module configured to perform a plurality of RNS arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values, said plurality of RNS residue values computed during said plurality of RNS arithmetic operations using a plurality of different modulus raised to different powers, and convert each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit, and (b) a permutation module coupled to said computing module and configured to generate an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values, wherein said arbitrary permutation ordering is determined using a cyclic structure having n elements each having assigned thereto an output sequence number of said plurality of output sequence numbers and using a value of said select combination of digits to select an available unselected element in said cyclic structure, and wherein said arbitrary permutation ordering of said plurality of output sequence numbers is defined by an order of a selection of said n elements of said cyclic structure; and an encryptor circuit coupled to said data stream receiving circuit and said ring generator circuit, said encryptor circuit configured to generate a modified data stream by incorporating or combining said plurality of output sequence numbers with said data stream. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
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13. A cryptographic system, comprising:
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a data stream receiving circuit configured to receive a data stream; a first ring generator circuit including (a) a computing module configured to perform a plurality of RNS arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values, said plurality of RNS residue values computed during said plurality of RNS arithmetic operations using a plurality of different modulus raised to different powers, and convert each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit, and (b)a permutation module configured to generate an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values, wherein said arbitrary permutation ordering is determined using a cyclic structure having n elements each having assigned thereto an output sequence number of said plurality of output sequence numbers and using a value of said select combination of digits to select an available unselected element in said cyclic structure, and wherein said arbitrary permutation ordering of said plurality of output sequence numbers is defined by an order of a selection of said n elements of said cyclic structure; and a diffusion operator circuit coupled to said data stream receiving circuit and said first ring generator circuit, said diffusion operator circuit configured to generate a diffused data stream by permuting said data stream using said arbitrary permutation ordering of a plurality of output sequence numbers. - View Dependent Claims (14, 15, 16, 17, 18, 19, 20, 21)
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22. A method for generating a modified data stream, comprising:
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receiving a data stream by an electronic circuit; performing, by said electronic circuit, a plurality of RNS arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values, said plurality of RNS residue values computed during said plurality of RNS arithmetic operations using a plurality of different modulus raised to different powers; converting, by said electronic circuit, each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit; generating, by said electronic circuit, an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values; and generating, by said electronic circuit, said modified data stream by incorporating or combining said plurality of output sequence numbers with said data stream; wherein said arbitrary permutation ordering is determined using a cyclic structure having n elements each having assigned thereto an output sequence number of said plurality of output sequence numbers and using a value of said select combination of digits to select an available unselected element in said cyclic structure; and wherein said arbitrary permutation ordering of said plurality of output sequence numbers is defined by an order of a selection of said n elements of said cyclic structure.
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23. A method for generating a diffused data stream, comprising:
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receiving, by an electronic circuit, a data stream; performing, by said electronic circuit, a plurality of RNS arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values, said plurality of RNS residue values computed during said plurality of RNS arithmetic operations using a plurality of different modulus raised to different powers; converting, by said electronic circuit, each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit; generating, by said electronic circuit, an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values; and generating, by said electronic circuit, said diffused data stream by permuting said data stream using said arbitrary permutation ordering of a plurality of output sequence numbers; wherein said arbitrary permutation ordering is determined using a cyclic structure having n elements each having assigned thereto an output sequence number of said plurality of output sequence numbers and using a value of said select combination of digits to select an available unselected element in said cyclic structure; and wherein said arbitrary permutation ordering of said plurality of output sequence numbers is defined by an order of a selection of said n elements of said cyclic structure.
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Specification