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Machine learning models have demonstrated remarkable success across diverse domains but remain vulnerable to adversarial attacks. Empirical defense mechanisms often fail, as new attacks constantly emerge, rendering existing defenses…
We formally study iterated block ciphers that alternate between two sequences of independent and identically distributed (i.i.d.) rounds. It is demonstrated that, in some cases the effect of alternating increases security, while in other…
We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential…
Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factorization algorithm. Since then, his curves and the algorithms associated with them have become foundational in the implementation of elliptic…
The problem of inferring an inductive invariant for verifying program safety can be formulated in terms of binary classification. This is a standard problem in machine learning: given a sample of good and bad points, one is asked to find a…
This article proposes a new method to inject backdoors in RSA and other cryptographic primitives based on the Integer Factorization problem for balanced semi-primes. The method relies on mathematical congruences among the factors of the…
We analyze stochastic conditional gradient methods for constrained optimization problems arising in over-parametrized machine learning. We show that one could leverage the interpolation-like conditions satisfied by such models to obtain…
A partial password is a mode of password-based authentication that is widely used, especially in the financial sector. It is based on a challenge-response protocol, where at each login attempt, a challenge requesting characters from…
Eavesdropping attacks in inference systems aim to learn not the raw data, but the system inferences to predict and manipulate system actions. We argue that conventional information security measures can be ambiguous on the adversary's…
Federated Learning (FL) is a distributed learning paradigm that enhances users privacy by eliminating the need for clients to share raw, private data with the server. Despite the success, recent studies expose the vulnerability of FL to…
This article describes a lightweight additive homomorphic algorithm with the same encryption and decryption keys. Compared to standard additive homomorphic algorithms like Paillier, this algorithm reduces the computational cost of…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
The increasing integration of Large Language Models (LLMs) into society necessitates robust defenses against vulnerabilities from jailbreaking and adversarial prompts. This project proposes a recursive framework for enhancing the resistance…
We propose an iterative algorithm for low-rank matrix completion that can be interpreted as both an iteratively reweighted least squares (IRLS) algorithm and a saddle-escaping smoothing Newton method applied to a non-convex rank surrogate…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
We present a novel machine learning architecture that uses the exponential of a single input-dependent matrix as its only nonlinearity. The mathematical simplicity of this architecture allows a detailed analysis of its behaviour, providing…