Abstract: Proof is established by means of the following parameters: m pairs of private values Q1 and public values G1 m>1, a public module n made of the product of f first factors pj, f>2, a public exponent v, linked to each other by relations of the type: G1.Qiv=1 mod n or G1=Q1v mod n. Said exponent v is such that v=2k where k>1 is a security parameter. Public value G1 is the square g12 of a base number gi that is lower than f first factors pj, so that the two equations: x2=gi mod n and x2=?g1 mod n do not have a solution in x in the ring of the modulo n integers and such that the equation xv=g12 mod n has solutions in x in the ring of the modulus n integers.

Abstract: The proof is provided by means of the following parameters: a public module n formed by the product of f prime factors pi, f>2; a public superscript v; m base numbers gi, m>1. The base numbers gi are such that the two equations: x2?gi mod n and x2??gi mod n cannot de solved in x in the ring of integers modulo n, and such that the equation xv?gi2 mod n can be solved in x in the ring of integers modulo n in the case where the public superscript v is in the form v=2k, wherein k is a security parameter.