# Is matrix elliptic curve discrete logarithm problem quantum-safe?

I can't be the first one to think of this and there must be a reason nobody design cryptosystem off this problem.

Let's define MECC as matrix of elliptic curve points, and MI as matrix of non-negative integers.

Given a MECC $$G$$, MI $$v$$, and MECC $$P=v\cdot G$$. How would a quantum computer calculate $$v$$ from $$P$$ and $$G$$?

• How is $\cdot$ defined in the question? As element-wise multiplication or as a matrix-matrix product? – SEJPM Sep 28 '20 at 14:49
• matrix-matrix product obviously. – DannyNiu Sep 28 '20 at 14:50

Reasoned it through just now. Given the ultimate generator of the elliptic curve group $$G'$$
1. Shor $$G$$ element-wise to obtain an MI $$H$$ such that $$G=H * (G')$$, where $$*$$ is element-wise multiplication.
2. Shor $$P$$ element-wise against $$(G')$$ to obtain an MI $$J$$
3. Calculate $$J\over H$$ using Gaussian elimination to obtain $$v$$