Related papers: On the Discrete Logarithm Problem for elliptic cur…
This whitepaper seeks to elucidate implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and mitigation strategies. First, we provide new resource estimates for breaking the 256-bit…
Assuming GRH, we present an algorithm which inputs a prime $p$ and outputs the set of fundamental discriminants $D<0$ such that the reduction map modulo a prime above $p$ from elliptic curves with CM by $\order_{D}$ to supersingular…
In todays world, Cloud computing has attracted research communities as it provides services in reduced cost due to virtualizing all the necessary resources. Even modern business architecture depends upon Cloud computing .As it is a internet…
Solving the Elliptic Curve Discrete Logarithm Problem (ECDLP) is critical for evaluating the quantum security of widely deployed elliptic-curve cryptosystems. Consequently, minimizing the number of logical qubits required to execute this…
It has recently been shown that cryptographic trilinear maps are sufficient for achieving indistinguishability obfuscation. In this paper we develop a method for constructing such maps on the Weil descent (restriction) of abelian varieties…
In this paper, we evaluate the different fully homomorphic encryption schemes, propose an implementation, and numerically analyze the applicability of gradient descent algorithms to solve quadratic programming in a homomorphic encryption…
Confidentiality in our digital world is based on the security of cryptographic algorithms. These are usually executed transparently in the background, with people often relying on them without further knowledge. In the course of…
Shor's algorithm is well-known for its capability to address the elliptic curve discrete logarithm problem (ECDLP) in polynomial time. The enhancement of its quantum resources continues to be a crucial focus of research. Nevertheless, the…
The signcryption is a relatively new cryptographic technique that is supposed to fulfill the functionalities of encryption and digital signature in a single logical step. Several signcryption schemes are proposed throughout the years, each…
By analogy with the developed cryptographic theory of discrete logarithm problems, we define several hard problems in Entropoid based cryptography, such as Discrete Entropoid Logarithm Problem (DELP), Computational Entropoid Diffie-Hellman…
Elliptic curves with a known number of points over a given prime field with n elements are often needed for use in cryptography. In the context of primality proving, Atkin and Morain suggested the use of the theory of complex multiplication…
We lay the foundations for a blockchain scheme, whose consensus is reached via a proof of work algorithm based on the solution of consecutive discrete logarithm problems over the point group of elliptic curves. In the considered…
We present several new heuristic algorithms to compute class polynomials and modular polynomials modulo a prime $p$ by revisiting the idea of working with supersingular elliptic curves. The best known algorithms to this date are based on…
This paper introduces a new public key cryptosystem based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli) and the discrete logarithm problem. These two hard…
In this work, a new digital signature based on elliptic curves is presented. We established its efficiency and security. The method, derived from a variant of ElGamal signature scheme, can be seen as a secure alternative protocol if known…
In the past two decades, Elliptic Curve Cryptography (ECC) have become increasingly advanced. ECC, with much smaller key sizes, offers equivalent security when compared to other asymmetric cryptosystems. In this survey, an comprehensive…
The signcryption is a relatively new cryptographic technique that is supposed to fulfill the functionalities of encryption and digital signature in a single logical step. Although several signcryption schemes are proposed over the years,…
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…
A succinct histogram captures frequent items and their frequencies across clients and has become increasingly important for large-scale, privacy-sensitive machine learning applications. To develop a rigorous framework to guarantee privacy…
Shor's quantum algorithm for discrete logarithms applied to elliptic curve groups forms the basis of a "quantum attack" of elliptic curve cryptosystems. To implement this algorithm on a quantum computer requires the efficient implementation…