Related papers: Criptografia com Curvas El\'ipticas
This paper contains a survey of supersingular isogeny graphs associated to supersingular elliptic curves and their various applications to cryptography. Within limitation of space, we attempt to address a broad audience and make this part…
Quantum computers have the potential to break classical cryptographic systems by efficiently solving problems such as the elliptic curve discrete logarithm problem using Shor's algorithm. While resource estimates for factoring-based…
The Diffie-Hellman key exchange plays a crucial role in conventional cryptography, as it allows two legitimate users to establish a common, usually ephemeral, secret key. Its security relies on the discrete-logarithm problem, which is…
With the development of Shor's algorithm, some nondeterministic polynomial (NP) time problems (e.g. prime factorization problems and discrete logarithm problems) may be solved in polynomial time. In recent years, although some homomorphic…
We investigate the isogeny graphs of supersingular elliptic curves over $\mathbb{F}_{p^2}$ equipped with a $d$-isogeny to their Galois conjugate. These curves are interesting because they are, in a sense, a generalization of curves defined…
The El-Gamal AA_{\beta} Public Key Cryptosystem is a new asymmetric cryptosystem based on the piecewise AA_{\beta}-function. The AA_{\beta}-function which is essentially a one way Boolean function was motivated by the squaring and…
This paper proposes a new signature scheme based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli, IFP) and the discrete logarithm problem(DLP). By combining…
In recent years, establishing secure visual communications has turned into one of the essential problems for security engineers and researchers. However, only limited novel solutions are provided for image encryption, and limiting the…
The emergence of small computing devices and the integration of processing units into everyday objects has made lightweight cryptography an essential part of the security landscape. Conventional cryptographic algorithms such as AES, RSA,…
Eker{\aa} and H{\aa}stad have introduced a variation of Shor's algorithm for the discrete logarithm problem (DLP). Unlike Shor's original algorithm, Eker{\aa}-H{\aa}stad's algorithm solves the short DLP in groups of unknown order. In this…
The advent of quantum computing poses a significant threat to the foundational cryptographic algorithms that secure modern digital communications. Protocols such as HTTPS, digital certificates, and public key infrastructures (PKIs) heavily…
Pairings have been widely used since their introduction to cryptography. They can be applied to identity-based encryption, tripartite Diffie-Hellman key agreement, blockchain and other cryptographic schemes. The Acceleration of pairing…
The session initiation protocol (SIP) is a powerful signaling protocol that controls communication on the Internet, establishing, maintaining, and terminating the sessions. The services that are enabled by SIP are equally applicable in the…
As society becomes more reliant on computers, cryptographic security becomes increasingly important. Current encryption schemes include the ElGamal signature scheme, which depends on the complexity of the discrete logarithm problem. It is…
We call a simple abelian variety over $\mathbb{F}_p$ super-isolated if its ($\mathbb{F}_p$-rational) isogeny class contains no other varieties. The motivation for considering these varieties comes from concerns about isogeny based attacks…
In this work, we investigate the security of Elliptic Curve Cryptosystem (ECC) implementations against Side-Channel Analysis (SCA). ECC is well known for its efficiency and strong security, yet vulnerable to SCA which exploits physical…
We describe implementations for solving the discrete logarithm problem in the class group of an imaginary quadratic field and in the infrastructure of a real quadratic field. The algorithms used incorporate improvements over previously-used…
Advances in quantum computing make Shor's algorithm for factorising numbers ever more tractable. This threatens the security of any cryptographic system which often relies on the difficulty of factorisation. It also threatens methods based…
A cryptographic protocol (CP) is a distributed algorithm designed to provide a secure communication in an insecure environment. CPs are used, for example, in electronic payments, electronic voting procedures, database access systems, etc.…
Most classical and post-quantum cryptographic assumptions, including integer factorization, discrete logarithms, and Learning with Errors (LWE), rely on algebraic structures such as rings or vector spaces. While mathematically powerful,…