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Quantum Circuit Designs of Point Doubling for Binary Elliptic Curves. (arXiv:2306.07530v1 [quant-ph])
cs.CR updates on arXiv.org arxiv.org
In the past years, research on Shor's algorithm for solving elliptic curves
for discrete logarithm problems (Shor's ECDLP), the basis for cracking elliptic
curve-based cryptosystems (ECC), has started to garner more significant
interest. To achieve this, most works focus on quantum point addition
subroutines to realize the double scalar multiplication circuit, an essential
part of Shor's ECDLP, whereas the point doubling subroutines are often
overlooked. In this paper, we investigate the quantum point doubling circuit
for the stricter assumption of …
addition algorithm binary cracking ecc elliptic focus interest point problems quantum research shor