| 摘要 |
Method consisting in transforming a digital message M by an operation of exponentiation of M by a number e, modulo N, all these numbers being long integers, with n bits, which uses a suite of two successive operations, the first of the form:… Bi = ai.X + T.2<m>… where Bi and X are calculation variables, where ai is an m-bit extract of another calculation variable A whose value stems from a preceding operations step, which extract is taken in the decreasing order of significance of A at rank i, and T a totalisation variable serving in the calculation of A, and the second operation consisting in reducing the length of the variable Bi. …<??>The method according to the invention uses a quasi-reduction modulo N since it is an approximation (to within a small multiple of N), and can be applied systematically and without a sign test during a given number of successive operations which is chosen and fixed. After which, a supplementary and systematic reduction is performed according to the same method. A quotient q, approached by default, of Bi/N is used, for which a p-bits format is provided, greater than the m-bits format of ai. …<IMAGE>… |
