Quote from: ranochigo on February 07, 2021, 09:34:24 AM

Shor's algorithm works on ECDSA, way easier than breaking RSA in fact[1] (I think 2x easier?). You can modify the algorithm slightly to defeat ECDSA which shouldn't be a problem.

Now that I think about it, it's basically trying to find a number that when multiplied by itself module N =equals 1. ie. b^2 mod N = 1 and b^2 - 1 mod N = mN (source). That last part kind of makes it clear that for ECDSA N doesn't have to be the curve order but could be the private key, and m could be the curve point.

I don't follow how this becomes easier to crack than RSA though. Now we have to find m=some encrypted data^(an encryption key + a decryption key) and N is actually the modulus. Multiplication alone should be slower for ECDSA than RSA because it's group items are points and not plain integers.