The development of encryption, distributed database systems and information technologies generally led us to the emergence of blockchain technology, which has not only many potential, but also already implemented useful applications. Blockchain is essentially a type of distributed data storage. The information in it is divided into a sequence of blocks connected in a "chain" using "links" - cryptographic methods. The cryptographic techniques used in the blockchain include cryptographic hash functions and asymmetric encryption algorithms. There are several basic asymmetric encryption algorithms (RSA, DES, El Gamal, DSA, ECDSA, etc.), based on di erent mathematical algorithms, and therefore having di erent characteristics. In the Bitcoin blockchain, as in the vast majority of other blockchains, the most e ective for speci c blockchain tasks, is the ECDSA encryption algorithm (previously the RSA algorithm was used). This algorithm is newer than, for example, the widespread RSA (which is a very strong but slow encryption algorithm). For the same security levels, ECDSA is much more compact than RSA. Accordingly, it makes it possible to process transactions faster, which is very important for the operations of the blockchain. In the work of the authors, a fundamentally new (for blockchain systems), exotic (according to the using of non-associative algebraic systems), suciently strong and at the same time more compact asymmetric encryption algorithm is proposed. It is based on a modi cation of the Vigenere cipher using non-associative algebraic one-way functions. It allows, without losing the strength of the cipher, to reduce the length of the encryption key, as well as to reduce the time of encryptiondecryption processes, which also makes it possible to process transactions faster.