What Makes Elliptic Curve Cryptography So Good? … Montgomery’s Ladder
Imagine you had to find a book on shelves that spanned up to the top of a building, but you don’t want to give away the shelf that you take the book from. Just imagine you could create a ladder which you could use no matter the shelve it is on, but where the ladder will always be the same length. Then the length of the ladder will not give away the shelf. This is like the way that the Montgomery Ladder works, and where we can create a fixed time method to multiply a point in an elliptic curve, with a scalar value.
Peter, RIP
Much of the core security of our current world is built on the amazing work done by individuals in the 1980s. It is to Ron Rivest (including RSA, digital signatures, and MD5), Adi Shamir (including RSA, Shamir Sharing, Cryptoanalysis, and Zero-Knowledge Proofs), Whitfield Diffie (the Diffie-Hellman method), Ralph Merkle (Merkle Trees) and many others, that we turn to for our core security. At the forefront of this was Peter Montgomery and who died on 18 Feb 2020. Peter was previously a researcher in Microsoft Research, and in his amazing career, he created Montgomery multiplication, Montgomery elliptic curves, and the Montgomery ladder. Here is one of his classic papers [here]:
