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+…+K2ht2h+K2h+1t2h+I, where all coefficients K0,…, K2h+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
