learning ρ and λ method for ECDLP
2018/10/01 Yasunori Ushiro (Kanagawa University)
2018/12/22 Addition for Learning λ method
Learning λ method is improved version of learning ρ method and parallel learning efficiency is good.
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 and λ 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 ρ algorithm. The learning ρ method shortened to about 30 seconds.
The learning λ method shortened to about 3.6 seconds. It is 10,000 times faster than the ρ method.
2. Numerical experiment result of ECDLP by learning λ method on SSD device
Learning ρ method Result on SSD
3. Numerical experiment result by learning λ method
Learning λ method Result
4. Numerical experiment result by learning ρ method
Learning ρ method Result
5. AI posibility for Learning λ Method
6. Details of algorithm for Learning ρ and λ method
It is scheduled to be released after publication in newspapers etc.