The invention features a public key cryptography method based on the discrete logarithm which computes a value Gkmodp. Two solutions are proposed to reduce the number of multiplications, one consisting in generating "hollow" k exponents with few bits of value 1, but of sufficient length to maintain the total security of the system, and the other consisting in parallel g power computations in while combining the exponents with each other so as not to repeat the same power computations twice for a given exponent. The invention is useful for generating digital signatures, for authentication, forencryption.