When both of them are lattice-based methods and Dilithium is so much faster — And, so, NIST selected Dilithium for quantum robust digital signatures. But, they are also taking forward FALCON and SPHINCS+. While SPHINCS+ is a hash-based signature method, FALCON is a lattice method such as Dilithium. Why did NIST pick two lattice methods? Well, first we will analyse why Dilithium was selected…

Towards partial homomorphic encryption with elliptic curves — I think if John Napier were alive today he would wonder at how discrete logarithms have been used to secure our world. And, I am also sure he would strike up an immediate bond with Taher Elgamal and who, in 1985, published this classic paper [here]:

Few things protect your online environment like elliptic curves — One of the most beautiful things in our online world is humble elliptic curve. It is there whenever you connect to a Web site with the ECDH (Elliptic Curve Diffie Hellman) key exchange method, and in proving the identity of a Web site with ECDSA (Elliptic Curve Digital Signature Algorithm)…

We hardly ever use discrete logs these days, as Elliptic Curve Cryptography is just so much more efficient and faster. And, so I love converting discrete log proofs with Elliptic Curve methods. Basically, we convert a power into a multiplicative operation for the base point:

We all know how to shuffle (or mix) cards. But, a skilled dealer can trick us into thinking that cards have been shuffled, but where they manage to put certain cards in the right place. If done for gain, it is cheating, and if done for fun, it is probably…

Meet Microsoft Entra — Which area of cybersecurity is often not talked about, but it is actually one of the largest areas of development, and is at the core of the security for users and organisations? It’s identity and access management. Overall, it is the basic process of proving our identity and then mapping…

Since 2016, NIST has been assessing light-weight encryption methods, and, in 2022, NIST published the final 10: ASCON, Elephant, GIFT-COFB, Grain128-AEAD, ISAP, Photon-Beetle, Romulus, Sparkle, TinyJambu, and Xoodyak (Table 1). A particular focus is on the security of the methods, along with their performance on low-cost FPGAs/embedded processes and their…

What is the 7th root of 2 (mod 13)? Well, the answer is 11, and I will show you how we get this. In this article we will solve the kth root of n (modulo p) and find the result:

Sophie Germain (born 1776 in Paris) was a French mathematician and who used safe primes to investigate Fermat’s Last Theorem. She gained her knowledge of mathematics by studying the works of Euler and communicated her ideas with other famous mathematics scholars including Legendre, Fourier and Gauss. In fact, at the…