Importance

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Abstract

The invention provides for a cryptographic method for digital signature.A set S1 of k polynomial functions P.sub.k(x.sub.1, . . . , x.sub.n+v, y.sub.1, . . . , y.sub.k) are supplied as a public key, where k, v, and n are integers, x.sub.1, . . . , x.sub.n+v are n+v variables of a first type, and y.sub.1, . . . , y.sub.k are k variables of a second type, the set S1 being obtained by applying a secret key operation on a given set S2 of k polynomial functions P'.sub.k(a.sub.1, . . . , a.sub.n+v, y.sub.1, . . . , y.sub.k), a.sub.1, . . . , a.sub.n+v designating n+v variables including a set of n 'oil' and v 'vinegar' variables.A message to be signed is provided and submitted to a hash function to produce a series of k values b.sub.1, . . . , b.sub.k. These k values are substituted for the k variables y.sub.1, . . . . , y.sub.k of the set S2 to produce a set S3 of k polynomial functions P''.sub.k(a.sub.1, . . . , a.sub.n+v), and v values a'.sub.n+1, . . . , a'.sub.n+1, are selected for the v 'vinegar' variables. A set of equations P''.sub.k(a.sub.1, . . . , a'.sub.n+v)=0 is solved to obtain a solution for a'.sub.1, . . . , a'.sub.n and the secret key operation is applied to transform the solution to the digital signature.

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First Claim