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Geometry-Based Symmetric Cryptosystem Method

  • US 20040105546A1
  • Filed: 11/06/2003
  • Published: 06/03/2004
  • Est. Priority Date: 11/19/2002
  • Status: Abandoned Application
First Claim
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1. A method of communicating information between users of a communication system includes the following steps of:

  • generating a module V over a ring R;

    generating an outer component P of encryption key that includes sequence (p1, p2, . . . , pk) where each member pj of the sequence belongs to the set {1, 2, . . . , m} (the length k of the sequence is arbitrary and thus repetitions are allowed in the sequence);

    generating an inner component Q of encryption key that includes elements v1, v2, . . . , vm of V and automorphisms g1, g2, . . . , gm of V;

    generating the encryption key K=(P;

    Q), where P is the outer component and Q is the inner component;

    generating an encryption automorphism Te of V based on the encryption key K, where Te includes a composition of certain automorphisms T1, T2, . . . , Tm of the module V, which composition is performed in the order prescribed by P;

    generating an encrypted message element E as a function of a message element M in V and of the encryption automorphism Te;

    transmitting the encrypted message element E along with the outer component P from one user to another;

    generating the outer component P′

    of decryption key that includes sequence (pk, pk−

    1
    , . . . , p1), i.e., the sequence that is reversed of that involved in producing the outer component P of the encryption key;

    generating the decryption key K′

    =(P′

    ;

    Q′

    ), where P′

    is the outer component of the decryption key and Q′

    is the inner component of the decryption key which is equal to the inner component Q of the encryption key;

    generating a decryption automorphism Td of V based on the decryption key K′

    , where Td includes a composition of the automorphisms T1, T2, . . . , Tm, which composition is performed in the order prescribed by P′

    , e.g., Td is the inverse automorphism of Te;

    determining the message element M as a function of the encrypted message element E and of the decryption automorphism Td, where the function is the same as that one used in generation of E (that is, the decryption method is symmetric to encryption;

    the decryption proceeds as the encryption, but with replacement of the outer component P with the outer component P′

    ).

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