Concrete Quantum Cryptanalysis of Binary Elliptic Curves
Published in In *IACR Transactions on Cryptographic Hardware and Embedded Systems* (TCHES), 2020
This paper analyzes and optimizes quantum circuits for computing discrete logarithms on binary elliptic curves, including reversible circuits for fixed-base-point scalar multiplication and the full stack of relevant subroutines.
The main optimization target is the number of logical qubits, as this is currently the main obstacle to implementing Shor’s algorithm for elliptic curves. The paper achieves: