A note on some algebraic trapdoors for block ciphers

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.Comment: to be published on Advances in Mathematics of Communication

Wave-Shaped Round Functions and Primitive Groups

Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks and Feistel Networks, are often obtained as the composition of different layers which provide confusion and diffusion, and key additions. The bijectivity of any encryption function, crucial in order to make the decryption possible, is guaranteed by the use of invertible layers or by the Feistel structure. In this work a new family of ciphers, called wave ciphers, is introduced. In wave ciphers, round functions feature wave functions, which are vectorial Boolean functions obtained as the composition of non-invertible layers, where the confusion layer enlarges the message which returns to its original size after the diffusion layer is applied. This is motivated by the fact that relaxing the requirement that all the layers are invertible allows to consider more functions which are optimal with regard to non-linearity. In particular it allows to consider injective APN S-boxes. In order to guarantee efficient decryption we propose to use wave functions in Feistel Networks. With regard to security, the immunity from some group-theoretical attacks is investigated. In particular, it is shown how to avoid that the group generated by the round functions acts imprimitively, which represent a serious flaw for the cipher

A note on some algebraic trapdoors for block ciphers

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.acceptedVersio

Partition-Based Trapdoor Ciphers

Trapdoors are a two-face key concept in modern cryptography. They are primarily related to the concept of trapdoor function used in asymmetric cryptography. A trapdoor function is a one-to-one mapping that is easy to compute, but for which its inverse function is difficult to compute without special information, called the trapdoor. It is a necessary condition to get reversibility between the sender and the receiver for encryption or between the signer and the verifier for digital signature. The trapdoor mechanism is always fully public and detailed. The second concept of trapdoor relates to the more subtle and perverse concept of mathematical backdoor, which is a key issue in symmetric cryptography. In this case, the aim is to insert hidden mathematical weaknesses, which enable one who knows them to break the cipher. Therefore, the existence of a backdoor is a strongly undesirable property. This book deals with this second concept and is focused on block ciphers or, more specifically, on substitution-permutation networks (SPN). Inserting a backdoor in an encryption algorithm gives an effective cryptanalysis of the cipher to the designer

Some group-theoretical results on Feistel Networks in a long-key scenario

Under embargo until: 2021-07-01The study of the trapdoors that can be hidden in a block cipher is and has always been a high-interest topic in symmetric cryptography. In this paper we focus on Feistel-network-like ciphers in a classical long-key scenario and we investigate some conditions which make such a construction immune to the partition-based attack introduced recently by Bannier et al.acceptedVersio

Some group-theoretical results on Feistel Networks in a long-key scenario

The study of the trapdoors that can be hidden in a block cipher is and has always been a high-interest topic in symmetric cryptography. In this paper we focus on Feistel-network-like ciphers in a classical long-key scenario and we investigate some conditions which make such a construction immune to the partition-based attack introduced recently by Bannier et al.Comment: Accepted for publication in Advances in Mathematics of Communication