| 摘要 |
A method for generating an electronic key from a prime number q contained in a specific interval of positive integers (wm, wM). The method includes the following operations: a) selecting a positive integer eta, where eta is the product of the first k prime numbers, with k as maximum so that there exist two positive integers epsilonm and epsilonM such that epsilonm is the higher round off of wm/eta, and epsilonM is the lower round off of (wM-wm)/eta, calculating II=epsilonm eta, generating two positive integers a and c belonging to the multiplicative group Z*II of integers modulo II, with c prime with II, calculating q=c+rho; b) testing the primality nature of q; c) if primality is verified, storing q; d) otherwise, updating c by calculating a.c mod II, and repeating the preceding operations from b) with the new value q=c+rho. The invention is applicable to cryptography.
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