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Marco Pedicini

Publications and source records attributed to Marco Pedicini.

9 recordsLinked to original sources

Thresholding Post-Quantum Signatures

Threshold signature schemes distribute the signing process among $T$ parties out of $N$. They enable a variety of applications and their research is also motivated by a recent NIST call. However, applications are dominated by pre-quantum signatures, which are more efficient but not secure in the post-quantum setting. This paper investigates existing post-quantum signatures, based on a variety of paradigms: lattice problems, one-way (hash) functions, cryptographic group actions, isogenies and multivariate systems. We propose a classification (divided by paradigm) of existing tools that are used to build $T$-out-of-$N$ schemes from digital signatures. We also include general approaches based on FHE, MPC or ZKP.

cs.CR

Portable Acceleration of Learning With Errors KEMs for Post-Quantum Cryptography

The transition to post-quantum cryptography (PQC) is driving demand for implementations that can meet the computational requirements of real-world applications. Among the proposed PQC constructions, Learning With Errors (LWE) based key encapsulation mechanisms (KEMs) are particularly attractive due to their strong security foundations, but they incur substantial computational costs from matrix operations and large-scale cryptographically secure random number generation. These characteristics position GPU acceleration as an effective approach for lowering the computational overhead of lattice based cryptographic schemes. In this work, we present a portable GPU implementation of a plain LWE based KEM using OpenMP Target offloading. Unlike most existing GPU implementations, which rely on CUDA specific optimizations, our approach uses a single source code base that executes on both NVIDIA and AMD accelerators. We evaluate the proposed implementation on different accelerator architectures, analyzing performance benchmarking, runtime profiling, scalability analysis, and energy to solution measurements. Experimental results show that OpenMP Target offloading delivers substantial acceleration over a multicore CPU baseline while preserving source level portability across heterogeneous GPU ecosystems. Cross platform analysis identifies NVIDIA GH200 and AMD MI300X as the most effective platforms for this memory bound workload, while profiling indicates that memory system organization and CPU GPU interaction play a more critical role than peak compute capability alone. These findings demonstrate that portable GPU acceleration can significantly reduce the computational overhead of PQC while avoiding vendor lock in, thereby facilitating the deployment of quantum resistant cryptographic infrastructures.

cs.CR

GPU Acceleration of Learning With Errors KEMs Using OpenACC for Post-Quantum Cryptography

Shor's algorithm proved that asymmetric cryptographic protocols based on the integer factorization and discrete logarithm problems are no longer safe in a world with large-scale quantum computers. As a result, Post-Quantum Cryptography (PQC) has been developed over the last few years, seeking cryptographic primitives resistant to quantum attacks. One of the main hard problems underlying PQC schemes is the Learning with Errors (LWE) problem, which is significantly more computationally intensive than its classical predecessors. In this work, we present a Key Encapsulation Mechanism (KEM) based on plain LWE and develop a GPU-oriented implementation using OpenACC. We evaluate the performance of our accelerated application in terms of both time-to-solution and energy-to-solution, considering bare-metal and containerized executions across multiple NVIDIA GPU models and generations. Our implementation achieves significant acceleration across all tested GPU platforms. In particular, on the NVIDIA Grace Hopper Superchip, it attains up to a $208\times$ speedup over a multithreaded CPU baseline and enables the execution of problem sizes that are impractical on CPU architectures due to memory and synchronization constraints. Energy consumption analysis also shows $\approx 2\times$ better efficiency when using the Superchip compared to systems equipped with x86-based CPUs and NVIDIA H100 GPUs. These results highlight the effectiveness of GPU acceleration for computationally demanding LWE-based cryptographic workloads.

cs.CR

Critical bases for ternary alphabets

Glendinning and Sidorov discovered an important feature of the Komornik-Loreti constant $q'\approx1.78723$ in non-integer base expansions on two-letter alphabets: in bases $1<q<q'$ only countably numbers have unique expansions, while for $q\ge q'$ there is a continuum of such numbers. We investigate the analogous question for ternary alphabets.

math.NT

Quantum entanglement and the Bell Matrix

We present a class of maximally entangled states generated by a high-dimensional generalisation of the \textsc{cnot} gate. The advantage of our approach is the simple algebraic structure of both entangling operator and resulting entangled states. In order to show that the method can be applied to any dimension, we introduce new sufficient conditions for global and maximal entanglement with respect to Meyer and Wallach's measure.

quant-ph

Typing a Core Binary Field Arithmetic in a Light Logic

We design a library for binary field arithmetic and we supply a core API which is completely developed in DLAL, extended with a fix point formula. Since DLAL is a restriction of linear logic where only functional programs with polynomial evaluation cost can be typed, we obtain the core of a functional programming setting for binary field arithmetic with built-in polynomial complexity.

cs.LO

Elementary Complexity and von Neumann Algebras

In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the hyperfinite $\mathrm{II}_1$ factor, starting from the class of Kalmar recursive functions. More methodologically, we address the problem of finding the right perspective from which to view the new relation between computation and combinatorial aspects in operator algebras. The rich structure of discrete invariants may provide a mathematical setting able to shed light on some basic combinatorial phenomena that are at the basis of our understanding of complexity.

cs.CC

Generalized golden ratios of ternary alphabets

Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in function of the alphabets.

math.NT

An Embedding of the BSS Model of Computation in Light Affine Lambda-Calculus

This paper brings together two lines of research: implicit characterization of complexity classes by Linear Logic (LL) on the one hand, and computation over an arbitrary ring in the Blum-Shub-Smale (BSS) model on the other. Given a fixed ring structure K we define an extension of Terui's light affine lambda-calculus typed in LAL (Light Affine Logic) with a basic type for K. We show that this calculus captures the polynomial time function class FP(K): every typed term can be evaluated in polynomial time and conversely every polynomial time BSS machine over K can be simulated in this calculus.

cs.LO