| 摘要 |
FIELD: radio engineering, communication.SUBSTANCE: Weber function-based quantum attack-secure encryption method employs Weber function cycles for elliptical curves on a number comparable with 1 modulo 8, and the cycles are determined by low-order Elkies isogenies. The next value of the Weber function is found as a root of an integer-valued symmetrical multinomial. The secret key is a list of integers (N, ?, N), where Nis the number of steps performed per cycle of Weber functions for an Elkies isogeny of the order l, and the public key is a value of the Weber function of the last isogeny. A positive direction on the cycle is given during the first calculation of the Weber function for the isogeny of the order l. To this end, the isogeny core is selected as divider of the power of the (l-1)/2 l-th division polynomial which determines the minimum expansion ratio in which points of the core lie, and the three most-significant coefficients of the polynomial, which defines the core, are used to calculate coefficients of the isogenic image of the elliptical curve. Steps on the cycle are performed according to the sign of the number N.EFFECT: protection from quantum attacks.3 cl, 2 dwg |
