Encryption system based on crossed inverse quasigroups
First Claim
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1. A computer implemented cryptography method, comprising:
- determining information M to be encrypted; and
encrypting said information to form encrypted information using a non-trivial ci-quasigroup as a key K to create a cipher C indicative of the information M as C=M*K, where * denotes a mathematical operation, where the non-trivial ci-quasigroup has properties that for the operation *, between any two elements in the non-trivial ci-quasigroup, a result of the operation is also in the non-trivial ci-quasigroup and for every K, as M takes in a different value, resulting value of C are each distinct, for every M, as K takes on all key values, the resulting values of C, are all distinct; and
that each key K in a keyspace P has a permutation K−
1 that decodes the encrypting, such that K−
1*(M*a)=M.
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Abstract
Encryption is carried out based on a non field, non group algebraic structure. Preferably the algebraic structure is at least one of non-associative or non-commutative. An embodiment is described in which the algebraic structure is a crossed inverse quasigroup. A crossed inverse quasigroup can be a very large quasigroup e.g. of size 1010. Either the quasigroup itself, or rules for calculating the values in the quasigroup can be distributed.
20 Citations
28 Claims
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1. A computer implemented cryptography method, comprising:
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determining information M to be encrypted; and encrypting said information to form encrypted information using a non-trivial ci-quasigroup as a key K to create a cipher C indicative of the information M as C=M*K, where * denotes a mathematical operation, where the non-trivial ci-quasigroup has properties that for the operation *, between any two elements in the non-trivial ci-quasigroup, a result of the operation is also in the non-trivial ci-quasigroup and for every K, as M takes in a different value, resulting value of C are each distinct, for every M, as K takes on all key values, the resulting values of C, are all distinct; and
that each key K in a keyspace P has a permutation K−
1 that decodes the encrypting, such that K−
1*(M*a)=M. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 27)
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16. A computer implemented cryptography method, comprising:
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determining information to be encrpted; and encrypting said information M to form encrpyted information using a Key K which is a crossed-inverse quasigroup to create a cipher C as C=M*K, where * denotes a mathematical operation, where the quasigroup has properties that for the operation *, between any two elements in the quasigroup, a result of the operation is also in the quasigroup, and for every K, as M takes on different values, resulting values of the cipher C, are each distinct, for every M, as K takes on all key values, the resulting values of the cipher C, are all distinct; and
that each key K in a keyspace P has a permutation K−
1 that decodes the encrypting, such that K−
1*(M*a)=M. - View Dependent Claims (17, 28)
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- 19. A cryptography method comprising encrypting information using an airthmetic with an algebraic structure, said albegraic structure being a non-group, nonfield structure.
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23. An apparatus comprising a program stored on a computer readable media including instructions to:
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encrypt a message M into an encrypted message_using a key K indicative of a crossed-inverse quasigroup representation, where the quasi has properties that for a operation *, between any two elements in the quasigroup, a result of the operation is also in the quasigroup, and for every K, as M takes on message values, resulting values of a cipher C, where C=M*K are each distinct, for every M, as K takes on all key values, resulting values of the cipher C, are all distinct; and
each key K in a keyspace P has a permutation K−
1 that decodes the encrypting, such that K31 1*(M*a)=M;send the encrypted message C; and decrypt the encrypted_message using information indicative of the same crossed-inverse quasigroup representation. - View Dependent Claims (24, 25, 26)
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Specification