Entropically secure cipher for messages generated by Markov chains with unknown statistics

Abstract: In 2002, Russell and Wang proposed a definition of entropically security that was developed within the framework of secret key cryptography. An entropically-secure system is unconditionally secure, that is, unbreakable, regardless of the enemy's computing power. In 2004, Dodis and Smith developed the results of Russell and Wang and, in particular, stated that the concept of an entropy-protected symmetric encryption scheme is extremely important for cryptography, since it is possible to construct entropy-protected symmetric encryption schemes with keys much shorter than the keys. the length of the input data, which allows you to bypass the famous lower bound on the length of the Shannon key. In this report, we propose an entropy-protected scheme for the case where the encrypted message is generated by a Markov chain with unknown statistics. The length of the required secret key is proportional to the logarithm of the length of the message (as opposed to the length of the message itself for the one-time pad).