Related papers: Security Estimates for Quadratic Field Based Crypt…

The elliptic curve discrete logarithm problem is of fundamental importance in public-key cryptography. It is in use for a long time. Moreover, it is an interesting challenge in computational mathematics. Its solution is supposed to provide…

In this brief note we connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.

Block ciphers are versatile cryptographic ingredients that are used in a wide range of applications ranging from secure Internet communications to disk encryption. While post-quantum security of public-key cryptography has received…

Short Weierstrass's elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problems was widely used in Cryptographic applications. This paper introduces a new security notation 'trusted security' for computation methods of…

We discuss a new attack, termed a dimension or linear decomposition attack, on several known group-based cryptosystems. This attack gives a polynomial time deterministic algorithm that recovers the secret shared key from the public data in…

Methods of quantum mechanics promise information-theoretic security for various protocols in cryptography. However, impossibility of some cryptographic applications such as standard bit commitment, oblivious transfer, multiparty secure…

In symmetric key cryptography the sender as well as the receiver possess a common key. Asymmetric key cryptography involves generation of two distinct keys which are used for encryption and decryption correspondingly. The sender converts…

An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…

Many papers proved the security of quantum key distribution (QKD) system, in the asymptotic framework. The degree of the security has not been discussed in the finite coding-length framework, sufficiently. However, to guarantee any…

While the topic of mean-field games (MFGs) has a relatively long history, heretofore there has been limited work concerning algorithms for the computation of equilibrium control policies. In this paper, we develop a computable policy…

The ability to hide information from unauthorized individuals has been a prevalent issue over the years. Countless algorithms such as DES, AES and SHA have been developed. These algorithms depend on varying key length and key management…

In the recent years, pixel-based perceptual algorithms have been successfully applied for privacy-preserving deep learning (DL) based applications. However, their security has been broken in subsequent works by demonstrating a…

We report on two new records: the factorization of RSA-240, a 795-bit number, and a discrete logarithm computation over a 795-bit prime field. Previous records were the factorization of RSA-768 in 2009 and a 768-bit discrete logarithm…

We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can be solved in the field of cardinality…

The problem of implementation security in quantum key distribution (QKD) refers to the difficulty of meeting the requirements of mathematical security proofs in real-life QKD systems. Here, we provide a succint review on this topic,…

Computational grids are believed to be the ultimate framework to meet the growing computational needs of the scientific community. Here, the processing power of geographically distributed resources working under different ownerships, having…

The list of norm-Euclidean imaginary quadratic fields is known and finite. For each known case, we give a division algorithm that finds a remainder at distance less than the Euclidean minimum of the field.

Group-based cryptography is a relatively unexplored family in post-quantum cryptography, and the so-called Semidirect Discrete Logarithm Problem (SDLP) is one of its most central problems. However, the complexity of SDLP and its…

We consider a version of the nearest-codeword problem on finite fields $\mathbb{F}_q$ using the Manhattan distance, an analog of the Hamming metric for non-binary alphabets. Similarly to other lattice related problems, this problem is…

We study the private $k$-median and $k$-means clustering problem in $d$ dimensional Euclidean space. By leveraging tree embeddings, we give an efficient and easy to implement algorithm, that is empirically competitive with state of the art…