METHOD OF GENERATING AND VERIFYING ELECTRONIC DIGITAL SIGNATURE BASED ON ELLIPTIC OR HYPERELLIPTIC CURVE

摘要

FIELD: information technology.;SUBSTANCE: method involves transformation of bit strings and performing operations with bit stings, in which during generation or verification of a signature, at least one predetermined point (corresponding reduced divisor) P of the simple order q on the elliptic (corresponding hyperelliptic) curve is multiplied by an integer k via summation and doubling; when generating the signature, random selection of the number k is allowed, wherein the first step involves selecting a number w=-2 for q=1, 3 (mod 8) or w=2 for q=1, 7 (mod 8), the value t=√w (mod q) is calculated; and at the second step, the number k is transformed to a number system with base t: k=K₀+K₁t+…+K_2ht^2h+K_2h+1t^2h+I, where all coefficients K₀,…, K^2h+1 assume values 0, 1 or -1, and a number 2h close to log₂q, and during recursive transition to the previous chain of coefficients, n/2 doublings of the point (reduced divisor) R are carried out.;EFFECT: high speed of generating and verifying an electronic digital signature using elliptic or hyperelliptic curves.;4 cl, 1 app