Related papers: Formal Verification of the Safegcd Implementation
Elliptic curve cryptography (ECC) is a widely established cryptographic technique, recognized for its effectiveness and reliability across a broad range of applications such as securing telecommunications or safeguarding cryptocurrency…
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…
Most cryptocurrency systems or systems based on blockchain technology are currently using the elliptic curves digital signature algorithm (ECDSA) on the secp256k1 curve, which is susceptible to backdoors implemented by the curve creator…
With the advent of machine learning and quantum computing, the 21st century has gone from a place of relative algorithmic security, to one of speculative unease and possibly, cyber catastrophe. Modern algorithms like Elliptic Curve…
Advanced embedded algorithms are growing in complexity and they are an essential contributor to the growth of autonomy in many areas. However, the promise held by these algorithms cannot be kept without proper attention to the considerably…
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…
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…
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…
Shor's quantum algorithm for discrete logarithms applied to elliptic curve groups forms the basis of a "quantum attack" of elliptic curve cryptosystems. To implement this algorithm on a quantum computer requires the efficient implementation…
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…
Error Detection and Correction Codes (ECCs) are often used in digital designs to protect data integrity. Especially in safety-critical systems such as automotive electronics, ECCs are widely used and the verification of such complex logic…
We show in some detail how to implement Shor's efficient quantum algorithm for discrete logarithms for the particular case of elliptic curve groups. It turns out that for this problem a smaller quantum computer can solve problems further…
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…
We believe that there is no real data protection without our own tools. Therefore, our permanent aim is to have more of our own codes. In order to achieve that, it is necessary that a lot of young researchers become interested in…
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…
We describe a method for building composable and extensible verification procedures within the Coq proof assistant. Unlike traditional methods that rely on run-time generation and checking of proofs, we use verified-correct procedures with…
We propose an approach for modular verification of programs written in an object-oriented language where, like in C++, the same virtual method call is bound to different methods at different points during the construction or destruction of…
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…
We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a…
We lay the foundations for a blockchain scheme, whose consensus is reached via a proof of work algorithm based on the solution of consecutive discrete logarithm problems over the point group of elliptic curves. In the considered…