Related papers: On Hidden Sums Compatible with A Given Block Ciphe…
It has been suggested that the algebraic structure of AES (and other similar block ciphers) could lead to a weakness exploitable in new attacks. In this paper, we use the algebraic structure of AES-like ciphers to construct a cipher…
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…
The algebraic structure of the group generated by the encryption functions of a block cipher depends on the key schedule algorithm used for generating the round keys. For such a reason, in general, studying this group does not appear to be…
Every day, millions of credit cards are swiped and transactions are carried out across the world. Due to numerous forms of unethical digital activities, users are vulnerable to credit card fraud, phishing, identity theft, etc. This paper…
The affine general linear group acting on a vector space over a prime field is a well-understood mathematical object. Its elementary abelian regular subgroups have recently drawn attention in applied mathematics thanks to their use in…
We investigate some differential properties for permutations in the affine group, of a vector space V over the binary field, with respect to a new group operation $\circ$, inducing an alternative vector space structure on $V$ .
The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian…
We study affine semigroup rings as algebras over subsemigroup rings. From this relative viewpoint with respect to a given subsemigroup ring, the fibered sum of two affine semigroup algebras is constructed. Such a construction is compared to…
We conjecture that one of the main obstacles to creating new non-abelian quantum hidden subgroup algorithms is the correct choice of a transversal.
It has been shown recently that cryptographic trilinear maps are sufficient for achieving indistinguishability obfuscation. In this paper we develop algebraic blinding techniques for constructing such maps. An earlier approach involving…
A symmetric key encryption scheme is described for blocks of general size N that is a product of powers of many prime numbers. This is accomplished by realising each number (representing a message unit) as a point in a product of affine…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
Deep learning (DL) approaches are achieving extraordinary results in a wide range of domains, but often require a massive collection of private data. Hence, methods for training neural networks on the joint data of different data owners,…
The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…
In this paper we model a class of stream and block ciphers as systems of (ordinary) explicit difference equations over a finite field. We call this class "difference ciphers" and we show that ciphers of application interest, as for example…
Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…
We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…
We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.
This paper shows that structured transmission schemes are a good choice for secret communication over interference networks with an eavesdropper. Structured transmission is shown to exploit channel asymmetries and thus perform better than…
Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult.…