Related papers: Some Mathematical Problems Behind Lattice-Based Cr…

We explore the computational implications of a superposition of spacetimes, a phenomenon hypothesized in quantum gravity theories. This was initiated by Shmueli (2024) where the author introduced the complexity class $\mathbf{BQP^{OI}}$…

We consider coGapSVP_\sqrt{n}, a gap version of the shortest vector in a lattice problem. This problem is known to be in AM\cap coNP but is not known to be in NP or in MA. We prove that it lies inside QMA, the quantum analogue of NP. This…

Quantum computers can break the RSA and El Gamal public-key cryptosystems, since they can factor integers and extract discrete logarithms. If we believe that quantum computers will someday become a reality, we would like to have…

The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…

Recent oracle separations [Kretschmer, TQC'21, Kretschmer et. al., STOC'23] have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if the polynomial hierarchy collapses. We…

This paper describes the work carried out by the Inter-American Development Bank, the IDB Lab, LACChain, Cambridge Quantum Computing (CQC), and Tecnologico de Monterrey to identify and eliminate quantum threats in blockchain networks. The…

The steady advancement in quantum computer error correction technology has pushed the current record to 48 stable logical qubits, bringing us closer to machines capable of running Shor's algorithm at scales that threaten RSA and ECC…

We give a deterministic algorithm for solving the (1+eps)-approximate Closest Vector Problem (CVP) on any n dimensional lattice and any norm in 2^{O(n)}(1+1/eps)^n time and 2^n poly(n) space. Our algorithm builds on the lattice point…

The current blockchain system for cryptocurrency exchanges primarily employs elliptic curve cryptography (ECC) for generating key pairs in wallets, and elliptic curve digital signature algorithms (ECDSA) for generating signatures in…

In recent years, the elliptic curve Qu-Vanstone (ECQV) implicit certificate scheme has found application in security credential management systems (SCMS) and secure vehicle-to-everything (V2X) communication to issue pseudonymous…

Crypto-wallets or digital asset wallets are a crucial aspect of managing cryptocurrencies and other digital assets such as NFTs. However, these wallets are not immune to security threats, particularly from the growing risk of quantum…

Lattice-based cryptography is a foundation for post-quantum security, with the Learning with Errors (LWE) problem as a core component in key exchange, encryption, and homomorphic computation. Structured variants like Ring-LWE (RLWE) and…

In this paper, we propose new classes of trapdoor functions to solve the closest vector problem in lattices. Specifically, we construct lattices based on properties of polynomials for which the closest vector problem is hard to solve unless…

Quantum computing threatens the security foundations of consumer electronics (CE). Preparing the diverse CE ecosystem, particularly resource-constrained devices, for the post-quantum era requires quantitative understanding of…

The shortest vector problem (SVP) is one of the lattice problems and is mathematical basis for the lattice-based cryptography, which is expected to be post-quantum cryptography. The SVP can be mapped onto the Ising problem, which in…

The convergence of the Internet of Things (IoT) and quantum computing is redefining the security paradigm of interconnected digital systems. Classical cryptographic algorithms such as RSA, Elliptic Curve Cryptography (ECC), and Advanced…

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…

The rapid advancement of quantum computing poses a critical threat to classical cryptographic algorithms such as RSA and ECC, particularly in Internet of Things (IoT) devices, where secure communication is essential but often constrained by…

Recent advancements in post-quantum cryptographic algorithms have led to their standardization by the National Institute of Standards and Technology (NIST) to safeguard information security in the post-quantum era. These algorithms,…

Quantum computing is reshaping the security landscape of modern telecommunications. The cryptographic foundations that secure todays 5G systems, including RSA, Elliptic Curve Cryptography (ECC), and Diffie-Hellman (DH), are all susceptible…