Structure of parallel multipliers for a class of fields GF(2m)
Information and Computation
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
A fast addition algorithm for elliptic curve arithmetic in GF(2n) using projective coordinataes
Information Processing Letters
A Fast Algorithm for Multiplicative Inversion in GF(2m) Using Normal Basis
IEEE Transactions on Computers
VLSI Designs for Multiplication over Finite Fields GF (2m)
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)
SAC '98 Proceedings of the Selected Areas in Cryptography
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
A Fast Implementation of Multiplicative Inversion Over GF(2^m )
ITCC '05 Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC'05) - Volume I - Volume 01
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
An O(m2)-depth quantum algorithm for the elliptic curve discrete logarithm problem over GF(2m)a
Quantum Information & Computation
Quantum universality by state distillation
Quantum Information & Computation
Low complexity bit parallel architectures for polynomial basis multiplication over GF(2m)
IEEE Transactions on Computers
Quantum binary field inversion: improved circuit depth via choice of basis representation
Quantum Information & Computation
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Elliptic curves over finite fields F2n play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with affine or projective coordinates. In this paper we show that changing the curve representation allows a substantial reduction in the number of T-gates needed to implement the curve arithmetic. As a tool, we present a quantum circuit for computing multiplicative inverses in F2n in depth O(n log2 n) using a polynomial basis representation, which may be of independent interest.