learning and method for ECDLP

@2018/10/01@Yasunori Ushiro (Kanagawa University)
@2018/12/03@Addition for Learning method

@Learning method is improved version of learning method and parallel learning efficiency is good.
@I discovered that the algorithm can reduce the number of iterations by learning.
@This is the discovery of Columbus egg.


1. Concept of learning and method

@Elliptic curve cryptography (ECC) consists of two different points P and Q on the same elliptic curve.
@ECC: y2=x3+ax+b (mod p). a,b,x,y are integers. r is a order. p and r are primes.
@I discovered the learning methods where the trajectory groups do not depend on P, Q in ECC points
@Decipherment of the 60-bit encryption 44 cases (equivalent to 70 bits).
@It takes 10 hours by algorithm. The learning method shortened to about 30 seconds.
@The learning method shortened to about 3.6 seconds. It is 10,000 times faster than the method.

2. Numerical experiment result by learning method

@Learning method Result

3. Numerical experiment result by learning method

@Learning method Result

4. AI posibility for Learning Method

@AI posibility

5. Details of algorithm for Learning and method

@It is scheduled to be released after publication in newspapers etc.