14 citations · 73 across the 25 of their papers we have counts for
15 papers · 1 filter
Failing to hash into supersingular isogeny graphs
Jeremy Booher, Ross Bowden, Javad Doliskani +12
An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of "hard supersingular curves" that is, equation…
An atlas of the Richelot isogeny graph
Enric Florit, Benjamin Smith
We describe and illustrate the local neighbourhoods of vertices and edges in the (2, 2)-isogeny graph of principally polarized abelian surfaces, considering the action of automorph…
Deterministic factoring with oracles
Fran{\c c}ois Morain, Gu{é}na{ë}l Renault, Benjamin Smith
We revisit the problem of integer factorization with number-theoretic oracles, including a well-known problem: can we factor an integer unconditionally, in deterministic polyno…
Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication
Sean Ballentine, Aurore Guillevic, Elisa Lorenzo García +4
Schoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations…
Computing cardinalities of Q-curve reductions over finite fields
François Morain, Charlotte Scribot, Benjamin Smith
We present a specialized point-counting algorithm for a class of elliptic curves over F\_{p^2} that includes reductions of quadratic Q-curves modulo inert primes and, more generall…
Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes
Ping Ngai Chung, Craig Costello, Benjamin Smith
We give a general framework for uniform, constant-time one-and two-dimensional scalar multiplication algorithms for elliptic curves and Jacobians of genus 2 curves that operate by…