Related papers: Study of Zero-Knowledge protocols and Elliptic Cur…
This paper explores how zero-knowledge proofs can enhance Bitcoin's functionality and privacy. First, we consider Proof-of-Reserve schemes: by using zk-STARKs, a custodian can prove its Bitcoin holdings are more than a predefined threshold…
Zero-knowledge proofs (zk-Proofs) are communication protocols by which a prover can demonstrate to a verifier that it possesses a solution to a given public problem without revealing the content of the solution. Arbitrary computations can…
RSA(Rivest, Shamir and Adleman)is being used as a public key exchange and key agreement tool for many years. Due to large numbers involved in RSA, there is need for more efficient methods in implementation for public key cryptosystems.…
Passwords are ubiquitous and most commonly used to authenticate users when logging into online services. Using high entropy passwords is critical to prevent unauthorized access and password policies emerged to enforce this requirement on…
Zero-Knowledge Proofs (ZKPs) have emerged as a powerful tool for secure and privacy-preserving computation. ZKPs enable one party to convince another of a statement's validity without revealing anything else. This capability has profound…
Today, digital identity management for individuals is either inconvenient and error-prone or creates undesirable lock-in effects and violates privacy and security expectations. These shortcomings inhibit the digital transformation in…
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,…
The modern integrated circuit ecosystem is increasingly reliant on third-party intellectual property integration, which introduces security risks, including hardware Trojans and security vulnerabilities. Addressing the resulting trust…
The elliptic curve discrete logarithm problem is of fundamental importance in public-key cryptography. It is in use for a long time. Moreover, it is an interesting challenge in computational mathematics. Its solution is supposed to provide…
Zero-knowledge (ZK) protocols enable software developers to provide proofs of their programs' correctness to other parties without revealing the programs themselves. Regular expressions are pervasive in real-world software, and…
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…
The research described in this abstract was initiated by discussions between the author and Giovanni Di Crescenzo in Barcelona in early 2004. It was during Advanced Course on Contemporary Cryptology that Di Crescenzo gave a course on zero…
Blockchain technology is rapidly evolving, with scalability remaining one of its most significant challenges. While various solutions have been proposed and continue to be developed, it is essential to consider the blockchain trilemma --…
Zero-knowledge proofs allow verification of computations without revealing private information. However, existing systems require memory proportional to the computation size, which has historically limited use in large-scale applications…
Makaro is a logic puzzle with an objective to fill numbers into a rectangular grid to satisfy certain conditions. In 2018, Bultel et al. developed a physical zero-knowledge proof (ZKP) protocol for Makaro using a deck of cards, which allows…
This paper introduces quantum analogues of non-interactive perfect and statistical zero-knowledge proof systems. Similar to the classical cases, it is shown that sharing randomness or entanglement is necessary for non-trivial protocols of…
Card-based cryptography is a research area that realizes cryptographic protocols such as secure computation by applying shuffles to sequences of cards that encode input values. A single-cut full-open protocol is one that obtains an output…
Zero-knowledge proofs (ZKPs) are the cornerstone of programmable cryptography. They enable (1) privacy-preserving and verifiable computation across blockchains, and (2) an expanding range of off-chain applications such as credential…
Zero-Knowledge Proofs (ZKPs) are critical for privacy-preserving techniques and verifiable computation. Many ZKP protocols rely on key kernels such as the SumCheck protocol and Merkle Tree commitments to enable their key security…
Zero-knowledge proofs (ZKPs) are an emerging technology that has become the solution to efficiently provide security and privacy along with the transparency requirement of blockchains. ZKPs are usually expressed by means of arithmetic…