DOI 10.17586/0021-3454-2019-62-4-320-330

DOI 10.17586/0021-3454-2019-62-4-320-330

**UDC 003.26**

## SYMMETRICAL CRYPTOGRAPHIC SYSTEM WITH A SHARED MEMORY BASED ON RECURRENT BASES IN THE TASK OF KNAPSACK PACKING

Vladimir State University, Department of Informatics and Information Security;

I. I. Sorokin

Vladimir State University, Department of Informatics and Information Security;

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**Abstract.**In terms of the bases of return sequences and their corresponding signatures for the backpacking problem, a class of binary return bases characterized by a slower growth compared to the binary ones is distinguished. The inclusion of bases in this class provides a departure from attack of reduction of the basis of Koester—Lagarias—Odlyzko and gives a packing density outside the interval (0,1). The constructions of such bases are employed to develope a symmetric block encryption algorithm that uses shared memory of sender and recipient in Shannon model of secret communication. The algorithm also uses the chaining mode of the ciphertext blocks and generates the corresponding hash function. An additive protocol for creating a symmetric key is given.

**Keywords:**shared memory, knapsack packing problem, sparse knapsacks, Koester—Lagarias—Odlyzko packing density, block cipher with block engagement mode, hash function, cryptographic protocol

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