Category Archives: Uncategorized

GMNO and related hypergraph embeddings

In this post, we shall discuss the notion of the GMNO hypergraph embedding. This graph/hypergraph embedding is related to the -spectral radii and satisfies similar properties to the -spectral radii, MPO word embeddings, and also embeddings obtained from eigenvectors of the Laplacian matrix of a graph. Even though I have published this post, I willContinue reading “GMNO and related hypergraph embeddings”

Empirical observations of L_{2,d} spectral radii and other functions

In this post, we shall make a few experimental observations about the -spectral radius and dimensionality reduction that given evidence that the -spectral radius and dimensionality reduction will eventually have a deep mathematical theory behind it and also become more applicable to machine learning. I have not been able to prove these empirical observations, soContinue reading “Empirical observations of L_{2,d} spectral radii and other functions”

MPO optimized word embeddings: mapping tokens to matrices

In this post, we will not talk about cryptography, but we will talk about another application and generalization of the -spectral radius to producing word embeddings and graph embeddings for machine learning applications. We shall call these word embeddings matrix product optimized (MPO) word embeddings. These MPO word embeddings and graph embeddings do not requireContinue reading “MPO optimized word embeddings: mapping tokens to matrices”

Measuring block cipher round function security using spectral radii

In this post, we shall show how spectral radii and more specifically -spectral radii measure the security of block cipher round functions with small round key size and message size. This post will be mathematical, and it will incorporate subjects such as probability, linear algebra, and some quantum information theory. This post will be basedContinue reading “Measuring block cipher round function security using spectral radii”

Lower dimensional approximations to the L_2-spectral radius

In this post, we shall discuss various generalizations of the notion of the spectral radius to a sort of spectral radius for collections of multiple operators, and we shall develop the theory of the -spectral radius . This post consists of the new mathematical research on spectral radii which I will apply to measure theContinue reading “Lower dimensional approximations to the L_2-spectral radius”

Invariants of block cipher round functions and definability

In this post, we shall discuss a problem with measuring the cryptographic security of a block cipher round function along with a solution to this problem that works for block ciphers like the AES. For this post, the reader is supposed to understand the basics of model theory, some group theory, universal algebra, and cryptographyContinue reading “Invariants of block cipher round functions and definability”

Do the round maps of your block cipher generate the alternating or symmetric group?

This is the first post in a series of posts about block ciphers. From now on, I will try to produce more technical posts that involve more mathematics. This series of posts will be about symmetric encryption and related algorithms, but I do not have any plans in the immediate future of posting about publicContinue reading “Do the round maps of your block cipher generate the alternating or symmetric group?”