Ро-метод Полларда для нахождения дискретного логарифма в случае его малого веса
To protect communication systems from unauthorized access, data theft and falsification of transmitted messages, cryptographic methods are used. In particular, they underlie the protocols for the exchange of interbank information, as well as interactions within law enforcement and government structures.
Cryptographic methods are based on mathematical transformations of digitized texts. In this case, the discrete logarithm function is of great importance for cryptography.
The article presents a modification of Pollard's ro- method for finding a discrete logarithm in the case when it is expressed by a binary vector of relatively small weight.
The proposed algorithm can be effectively applied to a fairly large number of computing nodes. The paper considers the case when some close approximation of the discrete logarithm is known. To form the algorithm, we used estimates for binomial coefficients and the Berry–Esseen theorem for the Bernoulli scheme.