Patent ID: 7457408

Claim:
A calculation device comprising: a cryptographic apparatus configured to execute at least one part of a cryptographic protocol including determining the inverse of an integer modulo a large number N, which apparatus includes: a precalculation circuit comprising a generator for generating a series of binary numbers S l to S k that are prime with and less than said large number N, a number from said series being the inverse of the product of the others modulo said large number, and a circuit for precalculating a number S 0 defined as S 0 = ( ∏ I = 1 k ⁢ S I ) - 1 modulo N; and a calculation unit comprising: a memory for storing the number S 0 received from said circuit for precalculating, means for dividing all the numbers of said series S l to S k into two groups at random, and means for multiplying the numbers of each group, the results of such multiplying constituting two required numbers that are the inverse of each other modulo the large number N, said means for multiplying the numbers of each group are constructed so as to calculate the products of the numbers of each group from the at least one of the binary numbers stored, and means for outputting the results of the multiplying to be used in said cryptographic protocol; and said cryptographic device further comprising: means for the cryptographic protocol using the results output by the means for outputting.