Earticle

초록

영어

Since quantum computer attacks will be threats to the current public key cryptographic systems, there has been a growing interest in Multivariate Public Key Cryptography (MPKC), which has the potential to resist such attacks. Finite field multiplication is playing a crucial role in the implementations of multivariate cryptography and most of them use two-input multipliers. However, there exist multiple multiplications of three elements in multivariate cryptography. This motivates our work of designing three-input multipliers, which extend the improvements on multiplication of three elements in three directions. First, since multivariate cryptography can be implemented over small composite fields, our multipliers are designed over such fields. Second, since it requires multiplications of two and three elements, our multipliers can execute both of them. Third, our multipliers adapt table look-up and polynomial basis, since they are faster over specific fields, respectively. We demonstrate the improvement of our design mathematically. We implement our design on a Field-Programmable Gate Array (FPGA), which shows that our design is faster than other two-input multipliers when computing multiplication of three elements, e.g. multiplier with field size 256 is 28.4% faster. Our multipliers can accelerate multivariate cryptography and mathematical applications, e.g. TTS is 14% faster.

목차

Abstract
 1. Introduction
 2. Preliminaries
  2.1. Finite Field Multiplier
  2.2. Multivariate Public Key Cryptography
 3. Design of Three-input Multipliers
  3.1. Overview of our Multipliers
  3.2. Multiplier over (2n) GF on Polynomial Basis
  3.3. Multiplier over (2n) GF on Table Look-up
  3.4. Multiplier over GF ((2n)2)
 4. Theoretical Evaluation of Performance
 5. Implementation
  5.1. Overview of the Implementation
  5.2. Multiplication over GF (2n)
  5.3. Multiplication over GF ((2n)2)
  5.4. Comparison
  5.5. Example
 6. Comparison
 7. Applications
  7.1. Gaussian Elimination over Finite Fields
  7.2. Multivariate Signature Schemes
 8. Conclusions and Future Improvements
 Acknowledgements
 References

키워드

저자

• Haibo Yi [ School of Computer Engineering, Shenzhen Polytechnic 518055 Shenzhen, China ]
• Weijian Li [ School of Computer Science, Guangdong Polytechnic Normal University 510665 Guangzhou, China ] Corresponding Author

참고문헌

발행기관

간행물

표지보기 관심저널 등록

• 간행물명

  International Journal of Security and Its Applications

• 간기

  격월간

• pISSN

  1738-9976

• 수록기간

  2008~2016

• 등재여부

  SCOPUS

• 십진분류

  KDC 505 DDC 605