Related papers: Accelerating the Couveignes Rostovtsev Stolbunov k…
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…
We provide a security analysis for continuous variable quantum key distribution protocols based on the transmission of squeezed vacuum states measured via homodyne detection. We employ a version of the entropic uncertainty relation for…
We provide an explicit and algorithmic version of a theorem of Momose classifying isogenies of prime degree of elliptic curves over number fields, which we implement in Sage and PARI/GP. Combining this algorithm with recent work of…
Let p>3 be a prime and let E, E' be supersingular elliptic curves over F_p. We want to construct an isogeny phi: E --> E'. The currently fastest algorithm for finding isogenies between supersingular elliptic curves solves this problem by…
For $E$ an elliptic curve over a perfect field $K$, we present a proof of the existence of the dual isogeny $\hat{\phi}$ using computational methods linked to V\'elu's formulae instead of the standard Galois correspondence method.
This paper investigates a reconciliation method in order to establish an errorless secret key in a QKD protocol. Classical key distribution protocols are no longer unconditionally secure because computational complexity of mathematical…
The elliptic curve discrete logarithm problem is considered a secure cryptographic primitive. The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem. In this paper, we will argue…
Secure group communication in heterogeneous environment is gaining popularity due to the advent of wireless and ubiquitous computing. Although a number of protocols for group key agreement have been proposed, most of them are not applicable…
The paper reviews an implementation of an additional encrypted tunnel within TLS to further secure and authenticate the traffic of personal information between ProtonMail's frontends and the backend, implementing its key exchange, symmetric…
Recently, a new fast public key exchange protocol was presented by S. Bouftass. The protocol is based on the difficulty of inverting the function $F(x)=\lfloor (zx \mod 2^p)/ 2^q \rfloor$. In this paper, we describe a practical attack…
Here we concerned with quantum key distribution - a way to establish common cryptographic key between several parties. The work proposes a combination between quantum key distribution and systematic polar coding (an error correction…
We present a new approach to handling the case of Atkin primes in Schoof's algorithm for counting points on elliptic curves over finite fields. Our approach is based on the theory of polynomially cyclic algebras, which we recall as far as…
Castryck, Decru, and Smith used superspecial genus-2 curves and their Richelot isogeny graph for basing genus-2 isogeny cryptography, and recently, Costello and Smith devised an improved isogeny path-finding algorithm in the genus-2…
Post-Quantum Cryptography PQC attempts to find cryptographic protocols resistant to attacks using Shors polynomial time algorithm for numerical field problems or Grovers algorithm to find the unique input to a black-box function that…
Asymmetric password based key exchange is a key exchange protocol where a client and a server share a low entropic password while the server additionally owns a high entropic secret for a public key. There are simple solutions for this…
Recent study on certificateless authenticated key agreement focuses on bilinear pairing-free certificateless authenticated key agreement protocol. Yet it has got limitations in the aspect of computational amount. So it is important to…
The Deligne-Ogus-Shioda theorem guarantees the existence of isomorphisms between products of supersingular elliptic curves over finite fields. In this paper, we present methods for explicitly computing these isomorphisms in polynomial time,…
The continuous generalized exchange-driven growth model (CGEDG) is a system of integro-differential equations describing the evolution of cluster mass under mass exchange. The rate of exchange depends on the masses of the clusters involved…
Coupled elliptic quantum dots with different aspect ratios containing up to two electrons are studied using a model confinement potential in the presence of magnetic fields. Single and two particle Schroedinger equations are solved using…
Establishment of pairwise keys between sensor nodes in a sensor network is a difficult problem due to resource limitations of sensor nodes as well as vulnerability to physical captures of sensor nodes by the enemy. Public-key cryptosystems…