On Fast Calculation of Addition Chains for Isogeny-Based Cryptography
addition chains, post-quantum cryptography, isogeny-based cryptosystems, finite field
Digital Object Identifier (DOI)
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.
Was this content written or created while at USF?
Citation / Publisher Attribution
Information Security and Cryptology. Inscrypt 2016, p. 323-342
Scholar Commons Citation
Koziel, Brian; Azarderakhsh, Reza; Jao, David; and Mozaffari Kermani, Mehran, "On Fast Calculation of Addition Chains for Isogeny-Based Cryptography" (2016). Computer Science and Engineering Faculty Publications. 42.