Related papers: ECCFROG522PP: An Enhanced 522 bit Weierstrass Elli…
Whilst many key exchange and digital signature systems still rely on NIST P-256 (secp256r1) and secp256k1, offering around 128-bit security, there is an increasing demand for transparent and reproducible curves at the 256-bit security…
Whilst many key exchange and digital signature methods use the NIST P256 (secp256r1) and secp256k1 curves, there is often a demand for increased security. With these curves, we have a 128-bit security. These security levels can be increased…
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…
Elliptic curve cryptography (ECC) is foundational to modern secure communication, yet existing standard curves have faced scrutiny for opaque parameter-generation practices. This work introduces a Selmer-inspired framework for constructing…
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…
Precise suites of benchmarks are required to assess the progress of early fault-tolerant quantum computers at economically impactful applications such as cryptanalysis. Appropriate challenges exist for factoring but those for elliptic curve…
Elliptic Curve Cryptography (ECC) is a fundamental component of modern public-key cryptosystems that enable efficient and secure digital signatures, key exchanges, and encryption. Its core operation, scalar multiplication, denoted as $k…
The SECP256K1 elliptic curve algorithm is fundamental in cryptocurrency wallets for generating secure public keys from private keys, thereby ensuring the protection and ownership of blockchain-based digital assets. However, the literature…
Cryptographic algorithms are computationally costly and the challenge is more if we need to execute them in resource constrained embedded systems. Field Programmable Gate Arrays (FPGAs) having programmable logic de- vices and processing…
The development of secure cryptographic protocols and the subsequent attack mechanisms have been placed in the literature with the utmost curiosity. While sophisticated quantum attacks bring a concern to the classical cryptographic…
Elliptic curve cryptography (ECC) has emerged as the dominant public-key protocol, with NIST standardizing parameters for binary field GF(2^m) ECC systems. This work presents a hardware implementation of a Hybrid Multiplication technique…
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…
This paper introduces Elliptic Curve Modulation (ECM), a novel modulation scheme that can be leveraged to effectively shuffle transmitted data while maintaining symbol error probability (SEP) performance equivalent to unencrypted systems.…
A directly public verifiable signcryption scheme is introduced in this paper that provides the security attributes of message confidentiality, authentication, integrity, non-repudiation, unforgeability, and forward secrecy of message…
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…
Cryptography is the study of techniques for ensuring the secrecy and authentication of the information. Public-key encryption schemes are secure only if the authenticity of the public-key is assured. Elliptic curve arithmetic can be used to…
We discuss the use of elliptic curves in cryptography on high-dimensional surfaces. In particular, instead of a Diffie-Hellman key exchange protocol written in the form of a bi-dimensional row, where the elements are made up with 256 bits,…
Efficient computation of all distinct solutions of nonlinear problems is essential in many scientific and engineering applications. Although high-order parallel iterative schemes offer fast convergence, their practical performance is often…
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…
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…