Related papers: An Efficient Elliptic Curve Cryptography Arithmeti…
We present a detailed analysis of how to implement the computation of modular symbols for a given elliptic curve by using numerical approximations. This method turns out to be more efficient than current implementation as the conductor of…
Despite the cloud enormous technical and financial advantages, security and privacy have always been the primary concern for adopting cloud computing facility, especially for government agencies and commercial sectors with high-security…
For avoiding the exposure of plaintexts in cloud environments, some homomorphic hashing algorithms have been proposed to generate the hash value of each plaintext, and cloud environments only store the hash values and calculate the hash…
When deploying wireless sensor networks (WSNs) in public environments it may become necessary to secure their data storage and transmission against possible attacks such as node-compromise and eavesdropping. The nodes feature only small…
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…
This paper describes several new improvements of modular arithmetic and how to exploit them in order to gain more efficient implementations of commonly used algorithms, especially in cryptographic applications. We further present a new…
Code that is highly optimized poses a problem for program-level verification: programmers can employ various clever tricks that are non-trivial to reason about. For cryptography on low-power devices, it is nonetheless crucial that…
Secret Sharing techniques are now the building blocks of several security protocols. A (t;n) threshold secret sharing scheme is one in which t or more participant can join together to retrieve the secret.Traditional single secret sharing…
The first step in elliptic curve scalar multiplication algorithms based on scalar decompositions using efficient endomorphisms-including Gallant-Lambert-Vanstone (GLV) and Galbraith-Lin-Scott (GLS) multiplication, as well as…
In this paper, we will present how to find keys elliptic curve cryptosystems (ECC) with simple tools of Delphi 7 console application, using the software problem solving of the scalar point multiplication in the field GF(p), where p is an…
Elliptic curve cryptography is better than traditional cryptography based on RSA and discrete logarithm of finite field in terms of efficiency and security. In this paper, we show how to exploit elliptic curve with high rank, which has not…
In modern critical infrastructure such as power grids, it is crucial to ensure security of data communications between network-connected devices while following strict latency criteria. This necessitates the use of cryptographic hardware…
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…
Elliptic curve cryptography (ECC) is a remarkable mathematical tool that offers the same level of security as traditional public-key cryptography (PKC) with a significantly smaller key size and lower computational requirements. The use of…
We give a deterministic algorithm that very quickly proves the primality or compositeness of the integers N in a certain sequence, using an elliptic curve E/Q with complex multiplication by the ring of integers of Q(sqrt(-7)). The algorithm…
For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…
This paper proposes the hardware implementation of RSA encryption/decryption algorithm using the algorithms of Ancient Indian Vedic Mathematics that have been modified to improve performance. The recently proposed hierarchical overlay…
Secret sharing in user hierarchy represents a challenging area for research. Although a lot of work has already been done in this direc- tion, this paper presents a novel approach to share a secret among a hierarchy of users while…
Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…
Specific quantum algorithms exist to-in theory-break elliptic curve cryptographic protocols. Implementing these algorithms requires designing quantum circuits that perform elliptic curve arithmetic. To accurately judge a cryptographic…