Abstract
The paper presents algorithms for generating a one-time two-factor authentication passwords where application of trigonometric functions have been considered. To protect the opening of a one-time password, a secret string is read that consists of a sequence of randomly generated characters. The second factor is due to the fact that that the code has a certain validity period. The presented password generators allow the formation of secret words and trigonometric functions that the proposed two-factor authentication method consists of. The algorithm presented was implemented in Java Script. The algorithm includes blocks for checking randomly generated words and functions.