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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 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.
And no surprise, it’s a data leak in some implementations of the Extended Euclidean Algorithm (EEA), a component of an Elliptical Curve Digital Signature Algorithm (ECDSA). OK, time to step back.