13 citations · 43 across the 21 of their papers we have counts for
27 papers
On the Etzion-Silberstein conjecture for block Ferrers diagrams
Marco Calderini, Marta Messia, Alessandro Neri
Ferrers diagram rank-metric codes are rank-metric codes with prescribed support, and their dimension is bounded from above by the Etzion--Silberstein bound. In this paper, we study…
Zeros of special polynomials and their impact on a class of APN functions
Daniele Bartoli, Marco Calderini, Giuseppe Marino +1
In 2021, Calderini et al. introduced a construction for APN functions on in bivariate form $$ f(x,y)=\big(xy,\, x^{2^r+1} + x^{2^{r+m/2}} y^{2^{m/2}} + bxy^{2…
A geometric invariant of linear rank-metric codes
Valentina Astore, Martino Borello, Marco Calderini +1
Rank-metric codes have been a central topic in coding theory due to their theoretical and practical significance, with applications in network coding, distributed storage, crisscro…
A new multivariate primitive from CCZ equivalence
Marco Calderini, Alessio Caminata, Irene Villa
Multivariate Cryptography is one of the candidates for Post-quantum Cryptography. Multivariate schemes are usually constructed by applying two secret affine invertible transformati…
Optimal s-boxes against alternative operations and linear propagation
Marco Calderini, Roberto Civino, Riccardo Invernizzi
Civino et al. (2019) have shown how some diffusion layers can expose a Substitution-Permutation Network to vulnerability from differential cryptanalysis when employing alternative…
Differential experiments using parallel alternative operations
Marco Calderini, Roberto Civino, Riccardo Invernizzi
The use of alternative operations in differential cryptanalysis, or alternative notions of differentials, are lately receiving increasing attention. Recently, Civino et al. managed…
On Dillon's property of -functions
Matteo Abbondati, Marco Calderini, Irene Villa
Dillon observed that an APN function over with greater than must satisfy the condition $\{F(x) + F(y) + F(z) + F(x + y + z) \,:\, x,y,z \in\mathbb{F}…
Two new families of bivariate APN functions
Marco Calderini, Kangquan Li, Irene Villa
In this work, we present two new families of quadratic APN functions. The first one (F1) is constructed via biprojective polynomials. This family includes one of the two APN famili…
Low c-differential uniformity for functions modified on subfields
Daniele Bartoli, Marco Calderini, Constanza Riera +1
In this paper, we construct some piecewise defined functions, and study their -differential uniformity. As a by-product, we improve upon several prior results. Further, we look…
Higher Order -Differentials
Aaron Geary, Marco Calderini, Constanza Riera +1
EFRST20, the notion of -differentials was introduced as a potential expansion of differential cryptanalysis against block ciphers utilizing substitution boxes. Drawing inspirati…
On the infiniteness of a family of APN functions
Daniele Bartoli, Marco Calderini, Olga Polverino +1
APN functions play a fundamental role in cryptography against attacks on block ciphers. Several families of quadratic APN functions have been proposed in the recent years, whose co…
On construction and (non)existence of -(almost) perfect nonlinear functions
Daniele Bartoli, Marco Calderini
Functions with low differential uniformity have relevant applications in cryptography. Recently, functions with low -differential uniformity attracted lots of attention. In part…
Some group-theoretical results on Feistel Networks in a long-key scenario
Riccardo Aragona, Marco Calderini, Roberto Civino
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-li…
Differentially low uniform permutations from known 4-uniform functions
Marco Calderini
Functions with low differential uniformity can be used in a block cipher as S-boxes since they have good resistance to differential attacks. In this paper we consider piecewise con…
Primitivity of the group of a cipher involving the action of the key-schedule
Marco Calderini
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 re…
Wave-Shaped Round Functions and Primitive Groups
Riccardo Aragona, Marco Calderini, Roberto Civino +2
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 compositio…
A note on some algebraic trapdoors for block ciphers
Marco Calderini
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, rec…
On Hidden Sums Compatible with A Given Block Cipher Diffusion Layer
Carlo Brunetta, Marco Calderini, Massimiliano Sala
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…
On properties of translation groups in the affine general linear group with applications to cryptography
Marco Calderini, Roberto Civino, Massimiliano Sala
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 a…
On the primitivity of PRESENT and other lightweight ciphers
Riccardo Aragona, Marco Calderini, Antonio Tortora +1
We provide two sufficient conditions to guarantee that the round functions of a translation based cipher generate a primitive group. Furthermore, under the same hypotheses, and ass…
Bounding the optimal rate of the ICSI and ICCSI problem
Eimear Byrne, Marco Calderini
In this work we study both the index coding with side information (ICSI) problem introduced by Birk and Kol in 1998 and the more general problem of index coding with coded side inf…
A note on APN permutations in even dimension
Marco Calderini, Massimilano Sala, Irene Villa
APN permutations in even dimension are vectorial Boolean functions that play a special role in the design of block ciphers. We study their properties, providing some general result…
Error Correction for Index Coding With Coded Side Information
Eimear Byrne, Marco Calderini
Index coding is a source coding problem in which a broadcaster seeks to meet the different demands of several users, each of whom is assumed to have some prior information on the d…
On differential uniformity of maps that may hide an algebraic trapdoor
Marco Calderini, Massimiliano Sala
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 , inducing…