Context-Aware Systems and Applications, and Nature of Computation and Communication. 7th EAI International Conference, ICCASA 2018, and 4th EAI International Conference, ICTCC 2018, Viet Tri City, Vietnam, November 22–23, 2018, Proceedings

Research Article

Post-quantum Cryptoschemes: New Finite Non-commutative Algebras for Defining Hidden Logarithm Problem

  • @INPROCEEDINGS{10.1007/978-3-030-06152-4_16,
        author={Hieu Nguyen and Nikolay Moldovyan and Alexandr Moldovyan and Nam Nguyen and Cong Tran and Ngoc Phieu},
        title={Post-quantum Cryptoschemes: New Finite Non-commutative Algebras for Defining Hidden Logarithm Problem},
        proceedings={Context-Aware Systems and Applications, and Nature of Computation and Communication. 7th EAI International Conference, ICCASA 2018, and 4th EAI International Conference, ICTCC 2018, Viet Tri City, Vietnam, November 22--23, 2018, Proceedings},
        proceedings_a={ICCASA \& ICTCC},
        year={2019},
        month={1},
        keywords={Finite algebra Ring Galois field Vector Local left unit element Bi-side unit element Associative multiplication Parameterized multiplication Cryptoscheme},
        doi={10.1007/978-3-030-06152-4_16}
    }
    
  • Hieu Nguyen
    Nikolay Moldovyan
    Alexandr Moldovyan
    Nam Nguyen
    Cong Tran
    Ngoc Phieu
    Year: 2019
    Post-quantum Cryptoschemes: New Finite Non-commutative Algebras for Defining Hidden Logarithm Problem
    ICCASA & ICTCC
    Springer
    DOI: 10.1007/978-3-030-06152-4_16
Hieu Nguyen1,*, Nikolay Moldovyan2,*, Alexandr Moldovyan2,*, Nam Nguyen1,*, Cong Tran3,*, Ngoc Phieu1,*
  • 1: Academy of Cryptography Techniques
  • 2: St. Petersburg Institute for Informatics and Automation of Russian Academy of Sciences
  • 3: Le Quy Don Technical University
*Contact email: hieuminhmta@gmail.com, nmold@mail.ru, maa1305@yandex.ru, nnhaivn61@gmail.com, manhtc@gmail.com, phieungochan@gmail.com

Abstract

In the article we present some properties of non-commutative finite algebras of four-dimension vectors with parameterized multiplication operation characterized in that different modifications of the multiplication operation are mutually associative. One of the introduced finite algebras represents ring. Other algebra contains no global unit element, its elements are invertible locally, and is characterized in that the multiplication operation possess compression property. Regarding the investigated ring, the detailed attention is paid to properties of the set of non-invertible elements of the ring. Formulas for zero-divisors and unit elements of different types are derived. The introduced finite algebras represent interest to define over them the hidden discrete logarithm problem that is a promising cryptographic primitive for post-quantum cryptography.