TMVP-Friendly Primes for Efficient Elliptic Curve Cryptography


Taskin H. K. , CENK M.

13th International Conference on Information Security and Cryptology, ISCTURKEY 2020, Virtual, Ankara, Turkey, 3 - 04 December 2020, pp.80-87 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume:
  • Doi Number: 10.1109/iscturkey51113.2020.9307999
  • City: Virtual, Ankara
  • Country: Turkey
  • Page Numbers: pp.80-87
  • Keywords: Elliptic curve cryptography, Montgomery curves, Toeplitz-matrix vector product, Finite field multiplication

Abstract

© 2020 IEEE.The need for faster and practical cryptography is a research topic for decades. In case of elliptic curve cryptography, which was proposed by Koblitz and Miller in 1985 as a more efficient alternative to RSA, the applications in real life started after 2000s. Today, most of the popular applications and protocols like Whatsapp, Signal, iOS, Android, TLS, SSH, Bitcoin etc. make use of Elliptic curve cryptography. One of the important factor for high performance elliptic curve cryptography is the finite field multiplication. In this paper, we first describe how to choose proper prime fields that makes use of Topelitz-matrices to get faster field multiplication, then we give parameter choice details to select prime fields that supports Toeplitz-matrix vector product operations. Then, we introduce the safe curve selection rationale and discuss about security. We propose new curves, discuss implementation and benchmark results and conclude our work.