Related papers: Cryptanalysis of the CFVZ cryptosystem
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
Let f be an arbitrary positive integer valued function. The goal of this note is to show that one can construct a finitely generated group in which the discrete log problem is polynomially equivalent to computing the function f. In…
Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. Remaining instances are built over finite fields of large characteristic and…
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…
In this paper, we have proposed a public key cryptography using recursive block matrices involving generalized Fibonacci numbers over a finite field Fp. For this, we define multinacci block matrices, a type of upper triangular matrix…
We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear…
We propose a new cryptosystem based on polycyclic groups. The cryptosystem is based on the fact that the word problem can be solved effectively in polycyclic groups, while the known solutions to the conjugacy problem are far less efficient.
An algorithm is presented that in context of public key use of Elliptic Curve Cryptography allows discovery of the private key in worst case O(n).
Importance of Elliptic Curves in Cryptography was independently proposed by Neal Koblitz and Victor Miller in 1985.Since then, Elliptic curve cryptography or ECC has evolved as a vast field for public key cryptography (PKC) systems. In PKC…
In this paper, we first define the quantum discrete logarithm problem (QDLP)which is similar to classical discrete logarithm problem. But, this problem cannot be solved by Shor's quantum algorithm. Based on quantum discrete logarithm…
The discrete logarithm in a finite group of large order has been widely applied in public key cryptosystem. In this paper, we will present a probabilistic algorithm for discrete logarithm.
Transparency is one of the key benefits of public blockchains. However, the public visibility of transactions potentially compromises users' privacy. The fundamental challenge is to balance the intrinsic benefits of blockchain openness with…
We consider a key exchange procedure whose security is based on the difficulty of computing discrete logarithms in a group, and where exponentiation is hidden by a conjugation. We give a platform-dependent cryptanalysis of this protocol.…
Confidentiality and Integrity are two paramount objectives in the evaluation of information and communication technology. In this paper, we propose an arithmetic approach for designing asymmetric key cryptography. Our method is based on the…
We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly…
Most modern cryptographic systems, such as RSA and the Diffie-Hellman Key Exchange, rely on "trapdoor" mathematical functions that are presumed to be computationally difficult with existing tools. However, quantum computers will be able to…
Fully homomorphic encryption (FHE) allows an untrusted party to evaluate arithmetic cir- cuits, i.e., perform additions and multiplications on encrypted data, without having the decryp- tion key. One of the most efficient class of FHE…
Elliptic curves are planar curves which can be used to define an abelian group. The efficient computation of discrete logarithms over this group is a longstanding problem relevant to cryptography. It may be possible to efficiently compute…
The promise of quantum computation and its consequences for complexity-theoretic cryptography motivates an immediate search for cryptosystems which can be implemented with current technology, but which remain secure even in the presence of…
We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over $GF(2^m)$. We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of…