UA9607U - Method of cryptographic transformation of information by using reduced hoppy codes - Google Patents

Abstract

The proposed method of cryptographic transformation of information by using reduced Hoppy codes consists in transforming the information into a code word by using block linear Hoppy code (n, k, d) for polynomial GF(q). As the encryption key in transforming the information, m symbols of reduced polynomial GF(q) are used.

Description

Description of the invention

The proposed useful model refers to the field of cryptographic protection of information with the help of 2 codes and can be used in means of encryption and impersonation-resistant coding in information processing systems to expand their capabilities.

There is a known method of asymmetric cryptographic transformation using algebraic codes |1), which is based on the fact that a known linear block code is masked by a non-degenerate matrix X of size КЧК with elements from ОК(4), a diagonal matrix О with non-zero elements on the diagonal from CE(d) , a permuted 70 matrix P of size n x n with elements from (da) and the information data is transformed into a cryptogram (a code word disguised as a random sequence) using devices for encoding a masked code.

Matrices X, R and O are used as a secret key, and the matrix H.O.R.O is used as a public key.

The disadvantage of this method is that for the cryptographic transformation of information it is necessary to store a large amount of key data - to store the public key, in the general case, it is necessary to store K x 79 n elements from it).

The closest to the proposed technical solution, chosen as a prototype, is the method of symmetric cryptographic transformation using Goppa algebraic codes |), which consists in the fact that the linear block (n, K, 4) Goppa code over SK(d) is given by its generation general matrix c with elements from CE(d) which is masked by a non-degenerate matrix X of size K x K with elements from CE(a4): сХ-о.Х.

The information data is converted into a cryptogram (a code word disguised as a random sequence) using devices for encoding a masked code with the addition of a random vector e-(e4, e",..., ep) with elements from SC(4). Matrix X is used as a secret key.

The disadvantage of the prototype method is a large amount of key data - to store the secret key in the form of a masking matrix, you need to store K x K elements from CE(4). -

The basis of a useful model is the task of creating a method of cryptographic transformation of information using shortened Goppa codes, which, due to the use of abbreviation symbols as a secret key, will be able to reliably mask the code and significantly reduce the volume of key data.

The task is solved by masking the linear block (p, K, 4) code of Goppa over og(a) - symbols of reduction and transformation of information data into a code word that is masked as a random (av) sequence (cryptogram). Instead of the generating matrix C of the Goppa code and the masking matrix X as a private key for masking the code, t symbols of reduction from CE(d) are used, which is significantly smaller than the ones for storing the parameters of the matrix X. (о)

The technical result that can be obtained by the implementation of the invention consists in reliable masking of the code and significantly reduced volumes of key data, which requires the process of cryptographic transformation.

The essence of the proposed method of cryptographic transformation of information using abbreviated Goppa codes is that the generating matrix C of the abbreviated linear block (n, K, 4) Goppa code over SC(4) is uniquely specified by t reduction symbols, and the information data is converted into a cryptogram - ( a code word that is disguised as a random sequence) using Goppa masked 70 abbreviated code encoding devices. The information about exactly which symbols are shortened is kept secret, i.e. the symbols of the Goppa code abbreviation are used as a secret key. The number of options for shortening the linear block (n, K, a) code to t symbols is determined by the formula:

Mt, that is, it is determined by the binomial coefficient .3 p by t". Thus, with proper p and t, the use of abbreviation symbols as a secret key allows you to reliably mask the code. In addition, significantly fewer keys are needed to store t abbreviation symbols

Me, data than for storing the secret parameters of the matrix X. o Sources of information 1. K. U. MeBEiPese. A Rybiis-Keu Stgiriozuviet Vazei op AIdebgaiis Tpeogu. / SOM Rgodgez Kerogi 42-44, dei "M Rgortsiiv op I ar. Razadepa, SA. dapyagu - Rergoagu, 1978.-R. 114-116. 2. T.K.M. Kao apa K.N. Mat, " Rgimaie-Keu aIdebgais-sodei sguriozuviet", ip Admapsez ip Sturioisdu-SKURTO 86. Mem Hogk, MU: Zrhipdeg, 1986. - R. 35-48.

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Claims (1)

The formula of the invention The method of cryptographic transformation of information using abbreviated Goppa codes, which consists in the fact that the information data is converted into a code word, which is masked under a random sequence (cryptogram) using coding devices of a masked linear block (n, K, 4) Goppa code over og (4), which differs in that when transforming information data, t abbreviation symbols from SE(4) are used as a private key for masking. Official bulletin "Industrial Property". Book 1 "Inventions, useful models, topographies of integrals 65 microcircuits", 2005, M 10, 15.10.2005. State Department of Intellectual Property of the Ministry of Education and Science of Ukraine.