Inferring Sequences Produced by a Linear Congruential Generator on Elliptic Curves Using Coppersmith's Methods

International audienceWe analyze the security of the Elliptic Curve Linear Con-gruential Generator (EC-LCG). We show that this generator is insecure if sufficiently many bits are output at each iteration. In 2007, Gutierrez and Ibeas showed that this generator is insecure given a certain amount of most significant bits of some consecutive values of the sequence. Using the Coppersmith's methods, we are able to improve their security bounds

Recovering zeros of polynomials modulo a prime

Let $p$ be a prime and $\mathbb{F}_p$ the finite field with $p$ elements. We show how, when given an irreducible bivariate polynomial $F \in \mathbb{F}_p[X,Y]$ and an approximation to a zero, one can recover the root efficiently, if the approximation is good enough. The strategy can be generalized to polynomials in the variables $X_1,\ldots ,X_m$ over the field $\mathbb{F}_p$. These results have been motivated by the predictability problem for nonlinear pseudorandom number generators and other potential applications to cryptography

On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators

In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degreegrowth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical systems and show that they admit much stronger estimates than in the general case and thus can be of use for pseudorandom number generation.Comment: Mathematics of Computation (to appear

Probabilistic Arguments in Mathematics

This thesis addresses a question that emerges naturally from some observations about contemporary mathematical practice. Firstly, mathematicians always demand proof for the acceptance of new results. Secondly, the ability of mathematicians to tell if a discourse gives expression to a proof is less than perfect, and the computers they use are subject to a variety of hardware and software failures. So false results are sometimes accepted, despite insistence on proof. Thirdly, over the past few decades, researchers have also developed a variety of methods that are probabilistic in nature. Even if carried out perfectly, these procedures only yield a conclusion that is very likely to be true. In some cases, these chances of error are precisely specifiable and can be made as small as desired. The likelihood of an error arising from the inherently uncertain nature of these probabilistic algorithms can therefore be made vanishingly small in comparison to the chances of an error arising when implementing an equivalent deductive algorithm. Moreover, the structure of probabilistic algorithms tends to minimise these Implementation Errors too. So overall, probabilistic methods are sometimes more reliable than deductive ones. This invites the question: ‘Are mathematicians rational in continuing to reject these probabilistic methods as a means of establishing mathematical claims?

Cache-based Side-Channel Attacks in Multi-Tenant Public Clouds and Their Countermeasures

Cloud computing is gaining traction due to the business agility, resource scalability and operational efficiency that it enables. However, the murkiness of the security assurances offered by public clouds to their tenants is one of the major impediments to enterprise and government adoption of cloud computing. This dissertation explores one of the major design flaws in modern public clouds, namely insufficient isolation among cloud tenants as evidenced by the cloud's inability to prevent side-channel attacks between co-located tenants, in both Infrastructure-as-a-Service (IaaS) clouds and Platform-as-a-Service (PaaS) clouds. Specifically, we demonstrate that one virtual machine (VM) can successfully exfiltrate cryptographic private keys from another VM co-located on the same physical machine using a cache-based side-channel attack, which calls into question the established belief that the security isolation provided by modern virtualization technologies remains adequate under the new threat model in multi-tenant public IaaS clouds. We have also demonstrated in commercial PaaS clouds that cache-based side channels can penetrate container-based isolation by extracting sensitive information from the execution paths of the victim applications, thereby subverting their security. Finally, we devise two defensive techniques for the IaaS setting, which can be adopted by cloud tenants immediately on modern cloud platforms without extra help from cloud providers, to address side-channel threats: (1) for tenants requiring a high degree of security and physical isolation, a tool to facilitate cloud auditing of such isolation; and (2) for tenants who use multi-tenant cloud services, an operating-system-level defense to defend against cache-based side-channel threats on their own.Doctor of Philosoph

Jornadas Nacionales de Investigación en Ciberseguridad: actas de las VIII Jornadas Nacionales de Investigación en ciberseguridad: Vigo, 21 a 23 de junio de 2023

Jornadas Nacionales de Investigación en Ciberseguridad (8ª. 2023. Vigo)atlanTTicAMTEGA: Axencia para a modernización tecnolóxica de GaliciaINCIBE: Instituto Nacional de Cibersegurida