# 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: y^{2}=x^{3}+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.