On Fast Calculation of Addition Chains for Isogeny-Based Cryptography

Brian Koziel; Reza Azarderakhsh; David Jao; Mehran Mozaffari-Kermani

Paper 2016/1045

On Fast Calculation of Addition Chains for Isogeny-Based Cryptography

Brian Koziel, Reza Azarderakhsh, David Jao, and Mehran Mozaffari-Kermani

Abstract

Addition chain calculations play a critical role in determining the efficiency of cryptosystems based on isogenies on elliptic curves. However, finding a minimal length addition chain is not easy; a generalized version of the problem, in which one must find a chain that simultaneously forms each of a sequence of values, is NP-complete. For the special primes used in such cryptosystems, finding fast addition chains for finite field arithmetic such as inversion and square root is also not easy. In this paper, we investigate the shape of smooth isogeny primes and propose new methods to calculate fast addition chains. Further, we also provide techniques to reduce the temporary register consumption of these large exponentials, applicable to both software and hardware implementations utilizing addition chains. Lastly, we utilize our procedures to compare multiple isogeny primes by the complexity of the addition chains.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. INSCRYPT2016
Keywords: Addition chains post-quantum cryptography isogeny-based cryptosystems finite field
Contact author(s): azarderakhsh @ gmail com
kozielbrian @ gmail com
djao @ math uwaterloo ca
History: 2016-11-07: received
Short URL: https://ia.cr/2016/1045
License: CC BY

BibTeX

@misc{cryptoeprint:2016/1045,
      author = {Brian Koziel and Reza Azarderakhsh and David Jao and Mehran Mozaffari-Kermani},
      title = {On Fast Calculation of Addition Chains for Isogeny-Based Cryptography},
      howpublished = {Cryptology {ePrint} Archive, Paper 2016/1045},
      year = {2016},
      url = {https://eprint.iacr.org/2016/1045}
}