21 citations · 110 across the 29 of their papers we have counts for
30 papers
A Geometric Characterization of Maximal Unrefinable Partitions via the Keith-Nath Transformation and Young Diagrams
Riccardo Aragona, Roberto Civino, Lorenzo Campioni
We investigate the combinatorial structure of unrefinable partitions through their correspondence with numerical sets and Young diagrams. Building on the bijection introduced by Ke…
A definitely periodic chain in the integral Lie ring of partitions
Riccardo Aragona, Roberto Civino, Norberto Gavioli
Given an integer , we introduce the integral Lie ring of partitions with bounded maximal part, whose elements are in one-to-one correspondence to integer partitions with parts i…
A modular idealizer chain and unrefinability of partitions with repeated parts
Riccardo Aragona, Roberto Civino, Norberto Gavioli
Recently Aragona et al. have introduced a chain of normalizers in a Sylow 2-subgroup of Sym(2^n), starting from an elementary abelian regular subgroup. They have shown that the ind…
The number of maximal unrefinable partitions
Riccardo Aragona, Lorenzo Campioni, Roberto Civino
This paper completes the classification of maximal unrefinable partitions, extending a previous work of Aragona et al. devoted only to the case of triangular numbers. We show that…
Verification and generation of unrefinable partitions
Riccardo Aragona, Lorenzo Campioni, Roberto Civino +1
Unrefinable partitions are a subset of partitions into distinct parts which satisfy an additional unrefinability property. More precisely, being an unrefinable partition means that…
On the maximal part in unrefinable partitions of triangular numbers
Riccardo Aragona, Lorenzo Campioni, Roberto Civino +1
A partition into distinct parts is refinable if one of its parts can be replaced by two different integers which do not belong to the partition and whose sum is , and it is…
Unrefinable partitions into distinct parts in a normalizer chain
Riccardo Aragona, Roberto Civino, Norberto Gavioli +1
In a recent paper on a study of the Sylow 2-subgroups of the symmetric group with 2^n elements it has been show that the growth of the first (n-2) consecutive indices of a certain…
On the primitivity of the AES-128 key-schedule
Riccardo Aragona, Roberto Civino, Francesca Dalla Volta
The key-scheduling algorithm in the AES is the component responsible for selecting from the master key the sequence of round keys to be xor-ed to the partially encrypted state at e…
On the primitivity of Lai-Massey schemes
Riccardo Aragona, Roberto Civino
In symmetric cryptography, the round functions used as building blocks for iterated block ciphers are often obtained as the composition of different layers providing confusion and…
Rigid commutators and a normalizer chain
Riccardo Aragona, Roberto Civino, Norberto Gavioli +1
The novel notion of rigid commutators is introduced to determine the sequence of the logarithms of the indices of a certain normalizer chain in the Sylow 2-subgroup of the symmetri…
A Chain of Normalizers in the Sylow -subgroups of the symmetric group on letters
Riccardo Aragona, Roberto Civino, Norberto Gavioli +1
On the basis of an initial interest in symmetric cryptography, in the present work we study a chain of subgroups. Starting from a Sylow -subgroup of AGL(2,n), each term of the c…
An Authenticated Key Scheme over Elliptic Curves for Topological Networks
Riccardo Aragona, Roberto Civino, Norberto Gavioli +1
Nodes of sensor networks may be resource-constrained devices, often having a limited lifetime, making sensor networks remarkably dynamic environments. Managing a cryptographic prot…
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…
Entropy and Compression: A simple proof of an inequality of Khinchin-Ornstein-Shields
Riccardo Aragona, Francesca Marzi, Filippo Mignosi +1
This paper concerns the folklore statement that ``entropy is a lower bound for compression''. More precisely we derive from the entropy theorem a simple proof of a pointwise inequa…
Normal form in Hecke-Kiselman monoids associated with simple oriented graphs
Riccardo Aragona, Alessandro D'Andrea
We generalize Kudryavtseva and Mazorchuk's concept of canonical form of elements in Kiselman's semigroups to the setting of a Hecke-Kiselman monoid associated with…
Regular subgroups with large intersection
Riccardo Aragona, Roberto Civino, Norberto Gavioli +1
In this paper we study the relationships between the elementary abelian regular subgroups and the Sylow -subgroups of their normalisers in the symmetric group $\mathrm{Sym}(\mat…
Type-Preserving Matrices and Security of Block Ciphers
Riccardo Aragona, Alessio Meneghetti
We provide a new property, called Non-Type-Preserving, for a mixing layer which guarantees protection against algebraic attacks based on the imprimitivity of the group generated by…
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…
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…
Several Proofs of Security for a Tokenization Algorithm
Riccardo Longo, Massimiliano Sala, Riccardo Aragona
In this paper we propose a tokenization algorithm of Reversible Hybrid type, as defined in PCI DSS guidelines for designing a tokenization solution, based on a block cipher with a…
A proof of security for a key-policy RS-ABE scheme
Federico Giacon, Riccardo Aragona, Massimiliano Sala
A revocable-storage attribute-based encryption (RS-ABE) scheme is an encryption scheme which extends attribute-based encryption by intro- ducing user revocation. A key-policy RS-AB…
A note on an infeasible linearization of some block ciphers
Riccardo Aragona, Anna Rimoldi, Massimiliano Sala
A block cipher can be easily broken if its encryption functions can be seen as linear maps on a small vector space. Even more so, if its round functions can be seen as linear maps…
The group generated by the round functions of a GOST-like cipher
R. Aragona, A. Caranti, M. Sala
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…
The role of Boolean functions in hiding sums as trapdoors for some block ciphers
Riccardo Aragona, Marco Calderini, Massimiliano Sala
Most modern block ciphers are built using components whose cryptographic strength is evaluated in terms of their resistance to attacks on the whole cipher. In particular, different…