Supersingular Isogeny Diffie-Hellman (SIDH) for Post Quantum Computer Key Generation

A simpler explanation of isogenies is here.

Introduction

Okay. Strap yourself in, and, it might take a while to fully understand the basic procedure here, but, if you’re interested in a future quantum robust world, it may be worth it. Before we start, you might want to read up on RSA methods here, elliptic curve methods here, and for Diffie-Hellman methods here.

Our public key methods are typically used to sign data/provide identity and for shared key generation. The methods include the Diffie-Hellman method (for key exchange), Elliptic Curve Diffie-Hellman (for key exchange), Elliptic Curve DSA (for signing), and RSA (for signing). The RSA method generates a value of N from the multiplication of two prime numbers (P and Q). Unfortunately quantum computers will be able to factorize N into P and Q, within a reasonable cost. Elliptic Curve methods use elliptic curves where we take a point on an elliptic curve (P) and then generate another point (Q) by using a gradient value (n), and where Q=nP. Again quantum computers will crack this method for a reasonable cost. For Diffie-Hellman, we use discrete logarithms, where we calculate a value of G^x mod p, and where G is a generator value and p is a prime number. Again quantum computers can crack this…