i still don't get why people use elliptic curves instead of diffie-hellman since you can use it for public keys too. the index calculus cryptanalytic method appears to apply for the usage of F_q where q = pn for some prime p. it appears that if q is a large prime and q - 1 is divisible by a large prime, that covers the two biggest error cases
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https://cr.yp.to/papers/safecurves-20240809.pdf if you read section 10 and onwards there are just an incredible number of problems arising from elliptic curves not using integer bit strings as points where it becomes incredibly hard to tell whether anything is a legitimate point and that seems like a huge problem
and furthermore the index calculus method is not very well evaluated + it seems to apply to elliptic curves anyway
