Analysis of the cryptographic strength of the partially homomorphic encryption algorithm based on elliptic curves

Abstract

The problem this article deals with is cryptographic analysis of partially homomorphic encryption scheme by addition based on elliptic curves. Complexity of solving elliptic curve discrete logarithm problem using Pollard’s ρ-method is represented. Shown model de-termines the cryptographic stability of the basic asymmetric encryption based on the elliptic curves. A mathematical model that demonstrates the simplification of the problem of discrete logarithm on an elliptic curve with an increase in the number of elements of homomorphic summation with respect to the basic algorithm of asymmetric encryption is shown. The cryptographic stability of the partially homomorphic encryption algorithm on elliptic curves is determined.