https://waamm.github.io/Notes on the mathematics of cryptography. 2026-05-11T11:04:57+02:00 Wicher Malten https://waamm.github.io/ Jekyll © 2026 Wicher Malten /assets/img/favicons/favicon.ico /assets/img/favicons/favicon-96x96.png 2026-05-07T00:00:00+02:00 2026-05-11T11:04:21+02:00 https://waamm.github.io/posts/chacha/ waamm

“If you were plowing a field, which would you rather use: two strong oxen or 1024 chickens?” — Seymour Cray A stream cipher generates a long stream of random-looking numbers (called a keystream) and XORs them with data to encrypt or decrypt. ChaCha is a widely used stream cipher that appears in many modern cryptographic systems, including TLS, WireGuard and secure messaging protocols. One...

2026-03-04T00:00:00+01:00 2026-04-15T17:38:29+02:00 https://waamm.github.io/posts/dekart/ waamm

A zero-knowledge range proof allows one party to convince another party that a secret value (or a batch of vaues) lies within a given range — such as being non-negative or below a certain bound — without revealing anything else about the value itself. These proofs are used directly in various applications, including (sometimes auditable) confidential transactions (to verify non-negative transac...

2026-02-16T00:00:00+01:00 2026-05-07T14:53:16+02:00 https://waamm.github.io/posts/shplonked/ waamm

“The raison d’être of KZG commitments is the remarkable efficiency of evaluation-proof verification.” — Justin Thaler [Tha22, p. 233] The KZG1 protocol was the first construction of a polynomial commitment scheme and remains one of the most widely deployed today [KZG10]. Definition (informal). A polynomial commitment scheme (PCS) allows a prover to commit to a polynomial $f$ and later ...

2026-01-15T00:00:00+01:00 2026-04-15T17:38:29+02:00 https://waamm.github.io/posts/weil-pairing-part-ii/ waamm

“My mathematics work is proceeding beyond my wildest hopes, and I am even a bit worried — if it’s only in prison that I work so well, will I have to arrange to spend two or three months locked up every year?” — André Weil, letter to his wife Eveline from the Rouen prison, 7 April 1940 (around the time he discovered the Weil pairing and proved the Riemann hypothesis for curves over finite fie...

2025-12-18T00:00:00+01:00 2026-04-15T17:38:29+02:00 https://waamm.github.io/posts/weil-pairing-part-i/ waamm

“The Weil pairing, first introduced by André Weil in 1940, plays an important role in the theoretical study of the arithmetic of elliptic curves and Abelian varieties. It has also recently become extremely useful in cryptologic constructions related to those objects.” — Victor S. Miller in his seminal 2004 paper1 [Mil04] This quote foreshadowed the emergence of what is today a fully fledge...