# A note on some algebraic trapdoors for block ciphers

## TL;DR

This paper establishes conditions under which translation-based block ciphers are resistant to a specific algebraic trapdoor, highlighting limitations of group-based security assessments against such vulnerabilities.

## Contribution

It provides new sufficient conditions to prevent partition-based trapdoors in translation-based ciphers and discusses the limitations of group analysis for security guarantees.

## Key findings

- Identifies conditions ensuring resistance to partition-based trapdoors.
- Shows that group generated by round functions may not guarantee security.
- Extends understanding of algebraic vulnerabilities in block ciphers.

## Abstract

We provide sufficient conditions to guarantee that a translation based cipher is not vulnerable with respect to the partition-based trapdoor. This trapdoor has been introduced, recently, by Bannier et al. (2016) and it generalizes that introduced by Paterson in 1999. Moreover, we discuss the fact that studying the group generated by the round functions of a block cipher may not be sufficient to guarantee security against these trapdoors for the cipher.