The invention concerns a method whereby the proof is established by: m(.gtoreq.1) pairs of private Q.sub.i and public G.sub.i=g.sub.i.sup.2 values; a public module n formed by the product of f(.gtoreq.2) prime factors; an exponent v=2.sup.k(k>1), linked by the relationships of the type: G.sub.i-Q.sub.i.sup.v.ident.1. mod n or G.sub.i.ident.Q.sub.i.sup.v mod n. Among the m numbers obtained by increasing Q.sub.i or its inverse modulo n to modulo n square, k-1 times rank, at least one of them is different from .+-.g.sub.i. Among the 2m equations: x.sup.2.ident.g.sub.i mod n, x.sup.2.ident.-g.sub.i mod n, at least one of them has solutions in x in the ring of modulo n integers.