# On Hidden Sums Compatible with A Given Block Cipher Diffusion Layer

## TL;DR

This paper explores the concept of hidden sums in block ciphers, providing a theoretical framework and an algorithm to identify algebraic trapdoors related to the cipher's diffusion layer.

## Contribution

It introduces a novel approach combining group theory and cryptography to characterize and efficiently detect hidden sums that could serve as trapdoors in block ciphers.

## Key findings

- Characterization of hidden sums related to regular subgroups of the affine group
- Development of an efficient algorithm for trapdoor exploitation
- Insights into algebraic structures that threaten cipher security

## Abstract

Sometimes it is possible to embed an algebraic trapdoor into a block cipher. Building on previous research, in this paper we investigate an especially dangerous algebraic structure, which is called a hidden sum and which is related to some regular subgroups of the affine group. Mixing group theory arguments and cryptographic tools, we pass from characterizing our hidden sums to designing an efficient algorithm to perform the necessary preprocessing for the exploitation of the trapdoor.