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Advances in quantum computing make Shor's algorithm for factorising numbers ever more tractable. This threatens the security of any cryptographic system which often relies on the difficulty of factorisation. It also threatens methods based…
Assuming the Generalized Riemann Hypothesis, we design a deterministic algorithm that, given a prime p and positive integer m=o(sqrt(p)/(log p)^4), outputs an elliptic curve E over the finite field F_p for which the cardinality of E(F_p) is…
Key-value data is a naturally occurring data type that has not been thoroughly investigated in the local trust model. Existing local differentially private (LDP) solutions for computing statistics over key-value data suffer from the…
Differentially private empirical risk minimization (DP-ERM) is a fundamental problem in private optimization. While the theory of DP-ERM is well-studied, as large-scale models become prevalent, traditional DP-ERM methods face new…
Security concerns in large-scale networked environments are becoming increasingly critical. To further improve the algorithm security from the design perspective of decentralized optimization algorithms, we introduce a new measure: Privacy…
Finding low-weight multiples of a binary polynomial is a difficult problem arising in the context of stream ciphers cryptanalysis. The classical algorithm to solve this problem is based on a time memory trade-off. We will present an…
The technique of hiding secret messages within seemingly harmless covertext to evade examination by censors with rigorous security proofs is known as provably secure steganography (PSS). PSS evolves from symmetric key steganography to…
Let $E$ be an elliptic curve over $\F_p$ without complex multiplication, and for each prime $p$ of good reduction, let $n_E(p) = | E(\F_p) |$. Let $Q_{E,b}(x)$ be the number of primes $p \leq x$ such that $b^{n_E(p)} \equiv b\,({\rm…
The discrete logarithm problem in Jacobians of curves of high genus $g$ over finite fields $\FF_q$ is known to be computable with subexponential complexity $L_{q^g}(1/2, O(1))$. We present an algorithm for a family of plane curves whose…
Polar codes are a new class of error correcting linear block codes, whose generator matrix is specified by the knowledge of transmission channel parameters, code length and code dimension. Moreover, regarding computational security, it is…
It is an important question to find constructions of quantum cryptographic protocols which rely on weaker computational assumptions than classical protocols. Recently, it has been shown that oblivious transfer and multi-party computation…
In the past decade analysis of big data has proven to be extremely valuable in many contexts. Local Differential Privacy (LDP) is a state-of-the-art approach which allows statistical computations while protecting each individual user's…
In this paper, a new algorithm to solve the discrete logarithm problem is presented which is similar to the usual baby-step giant-step algorithm. Our algorithm exploits the order of the discrete logarithm in the multiplicative group of a…
In this paper we study extensively the discrete logarithm problem in the group of non-singular circulant matrices. The emphasis of this study was to find the exact parameters for the group of circulant matrices for a secure implementation.…
We study $\left(\epsilon,\delta\right)$-differentially private algorithms for the problem of approximately computing the top singular vector of a matrix $A\in\mathbb{R}^{n\times d}$ where each row of $A$ is a data point in $\mathbb{R}^{d}$.…
With the advent of machine learning and quantum computing, the 21st century has gone from a place of relative algorithmic security, to one of speculative unease and possibly, cyber catastrophe. Modern algorithms like Elliptic Curve…
We study the computational cost of differential privacy in terms of memory efficiency. While the trade-off between accuracy and differential privacy is well-understood, the inherent cost of privacy regarding memory use remains largely…
The LPN (Learning Parity with Noise) problem has recently proved to be of great importance in cryptology. A special and very useful case is the RING-LPN problem, which typically provides improved efficiency in the constructed cryptographic…
The survey presents the evolution of Short Weierstrass elliptic curves after their introduction in cryptography. Subsequently, this evolution resulted in the establishment of present elliptic curve computational standards. We discuss the…
We describe a provably quasi-polynomial algorithm to compute discrete logarithms in the multiplicative groups of finite fields of small characteristic, that is finite fields whose characteristic is logarithmic in the order. We partially…