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Cryptographic authentication and/or establishment of shared cryptographic keys, including, but not limited to, password authenticated key exchange (PAKE)

  • US 20060291661A1
  • Filed: 05/01/2006
  • Published: 12/28/2006
  • Est. Priority Date: 05/03/2005
  • Status: Active Grant
First Claim
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1. A computer-implemented cryptographic authentication method for at least one of first and second computer systems to prove knowledge of a predefined value π

  • to the other one of the first and second computer systems, the method comprising the first computer system performing the following operations;

    (1) receiving data representing positive integer values N and x whose absolute values are greater than 1;

    (2) generating data representing an integer e and an integer b, where b is coprime to N;

    (3) generating data which define values y and z such that;

    y is congruent to xe mod N; and

    z is congruent to bP{overscore (π

    )}
    mod N;

    where;

    P{overscore (π

    )}=P/P
    π

    , Pπ

    is the product of one or more integers which form a proper subset θ



    ) of a set PP of non-zero integers, the subset θ



    ) being associated with the value π

    ; and

    P is the product of all the integers in the set PP;

    (4) sending the data which represent the values y and z to the second computer system without sending, to the second computer system, data which represent any one or more of the values e, b, Pπ

    , P{overscore (π

    )}
    .

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