New Space-Efficient Quantum Algorithm for Binary Elliptic Curves using the Optimized Division Algorithm

Understand

In previous research, quantum resources were concretely estimated for solving Elliptic Curve Discrete Logarithm Problem(ECDLP).

• In [1], the quantum algorithm was optimized for the binary elliptic curves and the main optimization target was the number of the logical qubits.
• The division algorithm was mainly optimized in [1] since every ancillary qubit is used in the division algorithm.
• In this paper, we suggest a new quantum division algorithm on the binary field which uses a smaller number of qubits.