Abstract: According to the invention, the secret key of the claimant is constituted by k numbers s.sub.1, s.sub.2, . . . , s.sub.k with a low public exponent. The verifier draws k numbers a.sub.1, a.sub.2, . . . , a.sub.k in which the number of non-zero a.sub.i is below a given number p. The claimant or signatory calculates an answer involving an exponential product of form s.sub.i.sup.a.sbsp.1 with i between 1 and k. The verifier calculates another exponential product of form v.sub.i.sup.a.sbsp.1, where the v.sub.i are numbers corresponding to the public key of the claimant or signatory. The verifier then verifies that the result obtained is correct. The choice of the public exponent and the limitation on p make it possible to reduce the number of secrets for equal security and an approximately equal number of multiplications.