N. I. Chervaykov, M. G. Babenko

The algorithms coding alphabets by the points of an elliptic curve are analyzed in the article. There are two major drawbacks of probabilistic method of coding: 1. With high power of the alphabet, the probability of failure not encoding increases and becomes greater than the probability of its corred coding. 2. With it is possible to encode the alphabet in times less than the number of points on an elliptic curve. A deterministic method of encoding alphabet, which uses the dual elliptic curve is considered in article. It is shown that the transition from very strong elliptic curve to the dual curve can lead to not very strong elliptic curve. A discrete logarithm problem can be solved for 4 hours and 30 minutes if modern technology can perform per second operations. A new encryption algorithm, intended for elliptic curves defined over the ring is suggested. Using elliptic curve over the ring allows us to perform a system of residual classes of arithmetic operations in the ring , which significantly reduces the execution time of arithmetic operations with the points on an elliptic curve. The time of encoding and decoding of information requires less computational power.