HYBRID ENCRYPTION BASED ON SYMMETRIC AND HOMOMORPHIC CIPHERS
Abstract
The purpose of this work is to develop and research a hybrid encryption algorithm based on
the joint application of the symmetric encryption algorithm Kuznyechik and homomorphic encryption
(Gentry scheme or BGV scheme). Such an encryption algorithm can be useful in situations
with limited computing resources. The point is that with the correct expression of the basic operations
of the symmetric encryption algorithm through Boolean functions, it becomes possible on the
transmitting side to encrypt the data with a symmetric cipher, and the secret encryption key - with
a homomorphic one. In this case, manipulations can be carried out on the receiving side so that
the original encrypted message is also encrypted only with a homomorphic cipher. In this case,
symmetric encryption is removed, but the information remains inaccessible to the node that processes
it. This property of secrecy makes it possible to carry out resource-intensive operations on
a powerful computing node, providing homomorphically encrypted data for a low-resource nodefor the purpose of their subsequent processing in encrypted form. The article presents the developed
hybrid algorithm. As a symmetric encryption algorithm, Kuznyechik encryption algorithm is
used, which is part of the GOST R34.12 - 2015 standard. In order to be able to apply
homomorphic encryption to data encrypted with the Kuznyechik cipher, the Kuznyechik algorithm
S-boxes is presented in a boolean form using the Zhegalkin polynomial. Also, the linear transformation
L is presented in the sequence form of performing the simplest operations of addition and
multiplication on the transformeddata. The primary modeling of the developed algorithm was
carried out on a simplified version of the KuzchyechikS-KN1 algorithm.
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