arXiv subjects

Rodrigo Martín Sánchez-Ledesma

Publications and source records attributed to Rodrigo Martín Sánchez-Ledesma.

8 recordsLinked to original sources

arXiv2026

Extensions of root-based attacks against PLWE via isomorphisms of rings

In the present work we address some key questions regarding the generalization of root-based attacks presented in [2]. In particular, we analyze potential root-based attacks extensions via the construction of explicit isomorphisms from vulnerable instances, and provide a formal proof that this approach will not yield any new vulnerabilities. To do so, we first construct an explicit isomorphism between fully-split polynomial rings and polynomial rings where previous attacks apply and show that the application of such an isomorphism will always distort the samples in a way that the resulting samples cannot be used to distinguish. Then, we prove that any isomorphism between fully-split polynomial rings must be of the form of the constructed isomorphism. Lastly, we study the generalization beyond fully split settings and show that the same distortion happens, regardless of the degree of the field extension.

cs.CR↗

arXiv2026

A blueprint for constructing 3-pass AKE protocols under commitment-based models

The commitment-based AKE model provides a formal security framework for key exchange protocols that avoid long-term cryptographic material, achieving authentication through a final out-of-band verification of session-derived values. Within this model, secure KA-based and KEM-based protocols were previously constructed via a commitment-based MT compiler, yielding optimized 4-pass protocols. In this work, we show that 3-pass protocols secure under this model exist for both primitives. These protocols are constructed ad hoc, following the core ideas of the commitment-based MT authenticator, and their SK security in the unauthenticated model is proved using the same game-based techniques, achieving bounds of the same form as those previously achieved. The resulting protocols provide one-way authentication in three message exchanges.

cs.CR↗

arXiv2026

A Commitment-based Authentication model for Key Exchange protocols

In this work we construct an alternative model for Authenticated Key Exchange, intended to build a theoretic security framework for protocols whose characteristics may not always concur with the specifics of already existing models for authenticated exchanges. This model is constructed in a modular way, from the notion of commitment schemes and employing ephemeral information, therefore avoiding the exchange of long-term cryptographic material. From this model, we propose a number of Commitment-based protocols to establish a shared secret between two parties, and study their resistance over unauthenticated channels. This means analyzing the security of the protocol itself, and its robustness against Man-in-the-Middle attacks, by formalizing their security under this model. The protocols are constructed from Key Agreement (KA) and Key Encapsulation (KEM) primitives, to show that this model can be applied to both established and new paradigms. We highlight the differences that arise naturally, due to the nature of KEM constructions, in terms of the protocol itself and the types of attacks that they are subject to. We provide practical go-to protocols instances to migrate to, both for KEM-based and KA-based cryptographic primitives.

cs.CR↗

arXiv2025

Cryptanalysis of PLWE based on zero-trace quadratic roots

We extend two of the attacks on the PLWE problem presented in (Y. Elias, K. E. Lauter, E. Ozman, and K. E. Stange, Ring-LWE Cryptography for the Number Theorist, in Directions in Number Theory, E. E. Eischen, L. Long, R. Pries, and K. E. Stange, eds., vol. 3 of Association for Women in Mathematics Series, Cham, 2016, Springer International Publishing, pp. 271-290) to a ring $R_q=\mathbb{F}_q[x]/(f(x))$ where the irreducible monic polynomial $f(x)\in\mathbb{Z}[x]$ has an irreducible quadratic factor over $\mathbb{F}_q[x]$ of the form $x^2+ρ$ with $ρ$ of suitable multiplicative order in $\mathbb{F}_q$. Our attack exploits the fact that the trace of the root is zero, and has overwhelming success probability as a function of the number of samples taken as input. An implementation in Maple and some examples of our attack are also provided.

cs.CR↗

arXiv2025

A Generalized Approach to Root-based Attacks against PLWE

The Polynomial Learning With Errors problem (PLWE) serves as the background of two of the three cryptosystems standardized in August 2024 by the National Institute of Standards and Technology to replace non-quantum resistant current primitives like those based on RSA, Diffie-Hellman or its elliptic curve analogue. Although PLWE is highly believed to be quantum resistant, this fact has not yet been established, contrariwise to other post-quantum proposals like multivariate and some code based ones. Moreover, several vulnerabilities have been encountered for a number of specific instances. In a search for more flexibility, it becomes fully relevant to study the robustness of PLWE based on other polynomials, not necessarily cyclotomic. In 2015, Elias et al found a good number of attacks based on different features of the roots of the polynomial. In the present work we present an overview of the approximations made against PLWE derived from this and subsequent works, along with several new attacks which refine those by Elias et al. exploiting the order of the trace of roots over finite extensions of the finite field under the three scenarios laid out by Elias et al., allowing to generalize the setting in which the attacks can be carried out.

cs.CR↗

arXiv2025

A Fast Multiplication Algorithm and RLWE-PLWE Equivalence for the Maximal Real Subfield of the $2^r p^s$-th Cyclotomic Field

This paper proves the RLWE-PLWE equivalence for the maximal real subfields of the cyclotomic fields with conductor $n = 2^r p^s$, where $p$ is an odd prime, and $r \geq 0$ and $s \geq 1$ are integers. In particular, we show that the canonical embedding as a linear transform has a condition number bounded above by a polynomial in $n$. In addition, we describe a fast multiplication algorithm in the ring of integers of these real subfields. The multiplication algorithm uses the fast Discrete Cosine Transform (DCT) and has computational complexity $\mathcal{O}(n \log n)$. Both the proof of the RLWE-PLWE equivalence and the fast multiplication algorithm are generalizations of previous results by Ahola et al., where the same claims are proved for a single prime $p = 3$.

cs.CR↗

arXiv2025

Fast Multiplication and the PLWE-RLWE Equivalence for an Infinite Family of Maximal Real Subfields of Cyclotomic Fields

We prove the equivalence between the Ring Learning With Errors (RLWE) and the Polynomial Learning With Errors (PLWE) problems for the maximal totally real subfield of the $2^r 3^s$-th cyclotomic field for $r \geq 3$ and $s \geq 1$. Moreover, we describe a fast algorithm for computing the product of two elements in the ring of integers of these subfields. This multiplication algorithm has quasilinear complexity in the dimension of the field, as it makes use of the fast Discrete Cosine Transform (DCT). Our approach assumes that the two input polynomials are given in a basis of Chebyshev-like polynomials, in contrast to the customary power basis. To validate this assumption, we prove that the change of basis from the power basis to the Chebyshev-like basis can be computed with $\mathcal{O}(n \log n)$ arithmetic operations, where $n$ is the problem dimension. Finally, we provide a heuristic and theoretical comparison of the vulnerability to some attacks for the $p$-th cyclotomic field versus the maximal totally real subextension of the $4p$-th cyclotomic field for a reasonable set of parameters of cryptographic size.

cs.CR↗

arXiv2023

A Feasible Hybrid Quantum-Assisted Digital Signature for Arbitrary Message Length

Currently used digital signatures based on asymmetric cryptography will be vulnerable to quantum computers running Shor's algorithm. In this work, we propose a new quantum-assisted digital signature protocol based on symmetric keys generated by QKD, that allows signing and verifying messages in a simple way implementing an integration of currently available classical and quantum technologies. The protocol is described for a three-user scenario composed of one sender and two receivers. In contrast to previous schemes, it is independent of the message length. The security of the protocol has been analyzed, as well as its integrity, authenticity and non-repudiation properties.

quant-ph↗