METHOD OF ENCRYPTION BASED ON THE FUNCTIONAL FIELD OF THE HERMITIAN GROUP ENHANCED BY HOMOMORPHIC TRANSFORMATION
DOI:
https://doi.org/10.18372/2225-5036.29.18071Keywords:
MST3 cryptosystem, Hermitian group, logarithmic signatures, homomorphic transformationAbstract
The challenge of implementing a commercial model for a powerful quantum computer is poised to compromise existing cryptographic primitives within asymmetric cryptography. Shor's quantum algorithm, capable of solving integer factorization and discrete logarithms, threatens the security of cryptosystems like RSA and ECC. Globally, national and international competitions are underway to develop new post-quantum standards for asymmetric encryption systems, digital signature schemes, and key distribution methods. A promising direction in developing cryptosystems resistant to quantum attacks involves utilizing problems that are highly complex to solve in certain groups. This article explores the method of directional encryption, enhanced by homomorphic transformation, within a cryptographic system based on an unsolved word problem. This system employs a special type of factorization known as logarithmic signatures within the Hermitian group. We substantiate that this implementation offers enhanced secrecy and demonstrate the feasibility of creating a secure cryptosystem using group computations in a small finite field. Furthermore, the application of homomorphic encryption to random coverages in a logarithmic signature provides protection against known attacks targeting logarithmic signature implementations.
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