US Patent 7913088 Digital signature and authentication method and apparatus

A signing technique of a disclosed identification/digital signature method hereof uses a mixing system based on multiplication in a ring and reduction modulo an ideal q in that ring, while a disclosed verification technique uses special properties of products of elements whose validity depends on elementary probability theory. The security of the identification/digital signature scheme comes from the interaction of reduction modulo q and the difficulty of forming products with special properties. In an embodiment of the identification/digital signature scheme hereof that employs a quotient ring of polynomials, the security also relies on the experimentally observed fact that for most lattices, it is very difficult to find a vector whose length is only a little bit longer than the shortest vector, and it is also difficult to find a lattice vector that is quite close to a randomly chosen nonlattice vector.