The PSLQ procedure can be regarded as a jazzed-up version of an integer-relation algorithm dating back more than 2,000 years to the Greek geometer Euclid of Alexandria (365–300 B.C.). The Euclidean ...

The Extended Euclidean algorithm calculates an associated factor at each step. It is the final value of this factor, the modular multiplicative inverse, that is the private key—29 in this case.