Collaborative Calculation and Data Science

Schoof's algorithm for counting points on elliptic curves, as presented in Lecture 8 of 18.783

Example showing two interpretations of Mx = b.

Code to compute and verify division polynomials of elliptic curves, as presented in Lecture 5 of 18.783

Demonstration of Rabin's root-finding algorithm and the Cantor-Zassenhaus algorithm for factoring polynomials in finite fields, as presented in Lecture 3 of 18.783

Implementation of the Elliptic curve factorization method (ECM) using the Montgomery ladder for scalar multiplication.

Simple implementation of Pollard p-1 algorithm for factoring integers, as presented in Lecture 10 of 18.783

Simple index calculus algorithm for computing discrete logarithms, as presented in Lecture 10 of 18.783

Simple algorithm to enumerate neighbors in the ell-isogeny graph of an elliptic curve over a finite field, used in Problem Set 11 of 18.783

Algorithm to compute solutions (t,v) to the norm equation 4p = t^2-v^D, where D is the discriminant of an order in an imaginary quadratic field, used in Problem Set 11 of 18.783

Algorithm to compute binary quadratic form corresponding to a prime ideal in an imaginary quadratic field.

Helper functions for Problem Set 12 of 18.783

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