learning Rho Algorithm for ECDLP

 2018/10/01 Yasunori Ushiro (Kanagawa University)


 I discovered that the ρ algorithm can reduce the number of iterations by learning.
 This is the discovery of Columbus egg.


1. Concept of learning ρ algorithm

 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 ρ algorithm 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 ρ algorithm. Learning ρ algorithm shortened to 30 seconds.

2. Numerical experiment result

 Result

3. AI posibility for Learning Rho Method

 AI posibility

4. Learning ρ Details of algorithm

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