Section: New Results

New families of fast elliptic curves

Benjamin Smith has pioneered the use of mod-$p$ reductions of Q-curves to produce elliptic curves with efficient scalar multiplication algorithms—which translates into faster encryption, decryption, signing, and signature verification operations on these curves. A theoretical article was presented at ASIACRYPT 2013 [9] , and the Journal of Cryptology has invited the submission of a longer version. The theory was put into practice in collaboration with Craig Costello (Microsoft Research) and Huseyin Hisil (Yasar University). Their resulting publicly available implementation, which represents the state of the art in constant-time (side-channel conscious) elliptic curve scalar multiplication on 64-bit Intel platforms at the 128-bit security level, can carry out a constant-time scalar multiplication in 145k cycles on Ivy Bridge architectures. This work will appear in EUROCRYPT 2014 [17] .