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Pollard Rho cryptanalysis attack is considered as the most powerful attack against elliptic curve discrete logarithm problem. Requirement for running Pollard Rho attack is quiet easy to get. The public key only is sufficient. In ECC using El-Gamal scenario the public key consist of:

1. the curve equation including: the finite field Fp, curve coefficient: a and b
2. the point generator in the elliptic curve
3. the generated point in the elliptic curve

Pollard Rho run through three work phases which are:

1. obtain the public key
2. simulate a random walk inside the finite field Fp to find a cycle
3. calculate the private key

(not done yet will be continued later)

understanding pollard rho for elliptic curve discrete logarithm problem overnight, is it possible for crypto new comer?

well, i’ll let you know how much i understand tomorrow

err, today is yesterday’s tomorrow so the result of my overnight study is: none

The Problem:

1. No ECC cryptosystem included in Android SDK: they actually use the famous BouncyCastle security and cryptography library but they strip out el-gamal and ecc from it
2. Pollard rho is currently the fastest cryptanalysis attack for ECC (CMIIW), it can be parallelized, and some random walks can speed up the breaking process just like Teske did with adding and mixed walk

The Goal:

1. Improve ECC strength against Pollard Rho for ECDLP (Elliptic Curve Discrete Logarithm Problem) with adding or mixed walk (still in choosing process) by reducing their speed up up to 10%
2. Implement the improved ECC in android SDK

The Way:

1. Find out how Pollard Rho with adding or mixed walk works, what are their specialities, what are their special cases, and so on,
2. Modify the ECC (curve, base field, key length, etc.) to nullify the Pollard Rho specialities
3. Implement and test the curve
4. Re-modify the ECC if test result indicate failure

Currently:

1. Stuck in learning Pollard Rho for ECDLP
2. To much browsing about what android phone to buy
3. Can’t take the 37 hours a week work in classroom
4. Nervous about the wedding
5. Discomforted by the fact that my belly overlaps my career