Computation of a 30750-Bit Binary Field Discrete Logarithm • Hacker News Board

Re: Computation of a 30750-Bit Binary Field Discrete Logarithm

#21

Post by MrXOR » Wed, Oct 07, 2020, 8:26 AM UTC

BlackFingolfin wrote: post #17

MrXOR wrote: post #14

Earlier quoted context omitted.

The end of DLP (over any field) is the end of ECC.

Why? Is there a reduction from EC DLP to FF DLP?

There are some attacks like MOV attack [1] and Frey-Rück attack [2].

[1] http://www.dima.unige.it/~morafe/MaterialeCTC/p80-menezes.pd...

[2] https://pdfs.semanticscholar.org/8823/54510ddc955c8d7e13c529...

[3] https://eprint.iacr.org/2015/1022.pdf

PS. I am a beginner in cryptography.

Re: Computation of a 30750-Bit Binary Field Discrete Logarithm

#22

Post by MrXOR » Wed, Oct 07, 2020, 9:44 AM UTC

thu2111 wrote: post #19

MrXOR wrote: post #14

Earlier quoted context omitted.

The end of DLP (over any field) is the end of ECC.

No it isn't. The curves used in all real systems are based on prime fields. The results against binary fields don't seem to generalise to curves deployed in the wild.

Binary fields are weaker than prime fields, but "I think" there are always shortcuts. Finding these shortcuts are hard and some good topics for future research in cryptography.

Re: Computation of a 30750-Bit Binary Field Discrete Logarithm

#23

Post by MrXOR » Wed, Oct 07, 2020, 9:57 AM UTC

MrXOR wrote: post #22

thu2111 wrote: post #19

Earlier quoted context omitted.

No it isn't. The curves used in all real systems are based on prime fields. The results against binary fields don't seem to generalise to curves deployed in the wild.

Binary fields are weaker than prime fields, but "I think" there are always shortcuts. Finding these shortcuts are hard and some good topics for future research in cryptography.

Hypothetical roadmap for next 10 years: Binary FF DLP --> Prime FF DLP --> EC in prime FF --> RSA? --> ElGamal? --> ...