Related papers: Secure Montgomery Multiplication and Repeated Squa…
In this paper, we give the mutually unbiased bases on the p^2 -dimensional quantum system where p is an odd prime number, and construct the corresponding unitary transformation based on the properties of these mutually unbiased bases. Then,…
We study the numerical stability of polynomial based encoding methods, which has emerged to be a powerful class of techniques for providing straggler and fault tolerance in the area of coded computing. Our contributions are as follows: 1)…
Although squaring integers is deterministic, squares modulo a prime, $p$, appear to be random. First, because they are all generated by the multiplicative linear congruential equation, $x_{i+1} = g^2 x_i \mod p$, where $x_0 = 1$ and $g$ is…
Randomized smoothing is a powerful tool for certifying robustness to adversarial perturbations, including poisoning attacks via randomized training and evasion attacks via randomized inference. Extending these guarantees to backdoor…
In this work, we consider the problem of secure multi-party computation (MPC), consisting of $\Gamma$ sources, each has access to a large private matrix, $N$ processing nodes or workers, and one data collector or master. The master is…
A simulation method based on the RG blocking is shown to yield statistical errors smaller than that of the crude MC using absolute values of the original measures. The new method is particularly suitable to apply to the sign problem of…
The cryptographic security provided by various techniques of random number generator (RNG) construction is one of the developing researches areas today. Among various types of RNG, the true random bit generator (TRBG) can be considered as…
A delegation scheme allows a computationally weak client to use a server's resources to help it evaluate a complex circuit without leaking any information about the input (other than its length) to the server. In this paper, we consider…
A major obstacle to implementing Shor's quantum number-factoring algorithm is the large size of modular-exponentiation circuits. We reduce this bottleneck by customizing reversible circuits for modular multiplication to individual runs of…
We generalize the spectral sum rule preserving density matrix numerical renormalization group (DM-NRG) method in such a way that it can make use of an arbitrary number of not necessarily Abelian, local symmetries present in the quantum…
Multigrid methods despite being known to be asymptotically optimal algorithms, depend on the careful selection of their individual components for efficiency. Also, they are mostly restricted to standard cycle types like V-, F-, and…
We consider the problem of designing secure and private codes for distributed matrix-matrix multiplication. A master server owns two private matrices and hires worker nodes to help compute their product. The matrices should remain…
In traditional runtime verification, a system is typically observed by a monolithic monitor. Enforcing privacy in such settings is computationally expensive, as it necessitates heavy cryptographic primitives. Therefore, privacy-preserving…
The Rabin public-key cryptosystem is revisited with a focus on the problem of identifying the encrypted message unambiguously for any pair of primes. In particular, a deterministic scheme using quartic reciprocity is described that works…
Numerical approaches are an important tool to study strongly correlated quantum systems. However, their fragility with respect to rounding errors is not well studied and numerically verified enclosures of the results are not available. In…
The Gram matrix of a matrix $A$ is defined as $AA^T$ (or $A^T\!A$). Computing the Gram matrix is an important operation in many applications, such as linear regression with the least squares method, where the explicit solution formula…
This paper introduces a new logic structure for reversible quantum circuit synthesis. Our synthesis method aims to minimize the quantum cost of reversible quantum circuits with decoders. In this method, multi-valued input, binary output…
Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…
Security concerns for large language models (LLMs) have recently escalated, focusing on thwarting jailbreaking attempts in discrete prompts. However, the exploration of jailbreak vulnerabilities arising from continuous embeddings has been…
The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…