Related papers: A simplified and generalized treatment of DES rela…
We define a cipher that is an extension of GOST, and study the permutation group generated by its round functions. We show that, under minimal assumptions on the components of the cipher, this group is the alternating group on the plaintext…
We consider the cryptographic problem of constructing an invertible random permutation from a public random function (i.e., which can be accessed by the adversary). This goal is formalized by the notion of indifferentiability of Maurer et…
The Feistel construction is a fundamental technique for building pseudorandom permutations and block ciphers. This paper shows that a simple adaptation of the construction is resistant, even to algorithm substitution attacks -- that is,…
We provide conditions under which the set of Rijndael functions considered as permutations of the state space and based on operations of the finite field $\GF (p^k)$ ($p\geq 2$ a prime number) is not closed under functional composition.…
A block cipher is a bijective function that transforms a plaintext to a ciphertext. A block cipher is a principle component in a cryptosystem because the security of a cryptosystem depends on the security of a block cipher. A Feistel…
Data Encryption Standard (DES) is based on the Feistel block cipher, developed in 1971 by IBM cryptography researcher Horst Feistel. DES uses 16 rounds of the Feistel structure. But with the changes in recent years, the internet is starting…
In a previous paper, we had proved that the permutation group generated by the round functions of an AES-like cipher is primitive. Here we apply the O'Nan Scott classification of primitive groups to prove that this group is the alternating…
We initiate the provable related-key security treatment for models of practical Feistel ciphers. In detail, we consider Feistel networks with four whitening keys $w_i(k)$ ($i=0,1,2,3$) and round-functions of the form $f(\gamma_i(k)\oplus…
We define a translation based cipher over an arbitrary finite field, and study the permutation group generated by the round functions of such a cipher. We show that under certain cryptographic assumptions this group is primitive. Moreover,…
Recent results by Alagic and Russell have given some evidence that the Even-Mansour cipher may be secure against quantum adversaries with quantum queries, if considered over other groups than $(\mathbb{Z}/2)^n$. This prompts the question as…
Recent results by Alagic and Russell have given some evidence that the Even-Mansour cipher may be secure against quantum adversaries with quantum queries, if considered over other groups than $(\mathbb{Z}/2)^n$. This prompts the question as…
The Feistel scheme is an important structure in the block ciphers. The security of the Feistel scheme is related to distinguishability with a random permutation. In this paper, efficient quantum algorithms for distinguishing classical…
The process of replacing an arbitrary Boolean function by a bijective one, a fundamental tool in reversible computing and in cryptography, is interpreted algebraically as a particular instance of a certain group homomorphism from the X-fold…
In this paper, we propose a quasigroup based block cipher design. The round functions of the encryption and decryption algorithms use quasigroup based string transformations. We show the robustness of the design against the standard…
In a XOR-based alternating block cipher the plaintext is masked by a sequence of layers each performing distinct actions: a highly nonlinear permutation, a linear transformation, and the bitwise key addition. When assessing resistance…
We answer a question of Paterson, showing that all block systems for the group generated by the round functions of a key-alternating block cipher are the translates of a linear subspace. Following up remarks of Paterson and Shamir, we…
S. S. Magliveras et al. have described symmetric and public key cryptosystems based on logarithmic signatures (also known as group bases) for finite permutation groups. In this paper we show that if $G$ is a nontrivial finite group which is…
The analysis of quantum algorithms which query random, invertible permutations has been a long-standing challenge in cryptography. Many techniques which apply to random oracles fail, or are not known to generalize to this setting. As a…
Fully homomorphic encryption (FHE) enables an entity to perform arbitrary computation on encrypted data without decrypting the ciphertexts. An ongoing group-theoretical approach to construct an FHE scheme uses a certain "compression"…
A block cipher is intended to be computationally indistinguishable from a random permutation of appropriate domain and range. But what are the properties of a random permutation? By the aid of exponential and ordinary generating functions,…