## Result of ECDLP by learning ρ method

2018/11/05 Yasunori Ushiro (Kanagawa University)

2018/12/03 Modify

The learning λ method is an improvement of the learning ρ method, which is suitable for parallel learning.

The learning λ method achieves about five times faster than the learning ρ method.

The learning λ method and the ρ method show the result of decrypting elliptic curve cryptography

The solution time by both algorithm for 44 pieces of 60-bits encryption (about 70 bits) are shown.

One core of Intel Core i7 6700k (4 Ghz) is used for calculation.

In multi-precision calculation, the learning λ method used self-made function and ρ method used gnu gmp.

Data is five sets of A, B, C, D and E. Since the ρ method takes long time, only A is measured.

The learning λ method is about 3.6 seconds, the ρ method is about 10 hours.

The learning λ method is about 10000 times faster than the ρ method.

### 1. Result of learning λ method

Average time is 3.6 seconds. The learning information is 2.0GB

Learning time of the this method is GPU (GTX 1080) using 1.5 day

(1) Data-A

(2) Data-B

(3) Data-C

(4) Data-D

(5) Data-E

### 2. Result of ρ method

Over 10 hours.

(1) Data-A