Related papers: PQC: Extended Triple Decomposition Problem (XTDP) …
Let $\mathbf{f}=(f\_1,\ldots,f\_m)$ and $\mathbf{g}=(g\_1,\ldots,g\_m)$ be two sets of $m\geq 1$ nonlinear polynomials over $\mathbb{K}[x\_1,\ldots,x\_n]$ ($\mathbb{K}$ being a field). We consider the computational problem of finding -- if…
Quantum cryptanalysis is essential for evaluating the security of cryptographic systems against the threat of quantum computing. Recently, Shi {\it et al.} introduced a dedicated quantum attack on block cipher constructions based on…
Shor's and Grover's algorithms' efficiency and the advancement of quantum computers imply that the cryptography used until now to protect one's privacy is potentially vulnerable to retrospective decryption, also known as \emph{harvest now,…
We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent…
We study the potential of general quantum operations, Trace-Preserving Completely-Positive Maps (TPCPs), as encoding and decoding mechanisms in quantum authentication protocols. The study shows that these general operations do not offer…
Elliptic Curve Scalar Multiplication denoted as kP operation is the basic operation in all Elliptic Curve based cryptographic protocols. The atomicity principle and different atomic patterns for kP algorithms were proposed in the past as…
In the recently emerging field of nonabelian group-based cryptography, a prominently used one-way function is the Conjugacy Search Problem (CSP), and two important classes of platform groups are polycyclic and matrix groups. In this paper,…
The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time variant of the well-known Differential Dynamic Programming (DDP) technique with a Gauss-Newton Hessian approximation. This family of methods has gained popularity in the…
The National Institute of Standards and Technology (NIST) has finalized the selection of post-quantum cryptographic (PQC) algorithms for use in the era of quantum computing. Despite their integration into TLS protocol for key establishment…
In this paper, we present a novel method for solving a class of quadratically constrained quadratic optimization problems using only additions and multiplications. This approach enables solving constrained optimization problems on private…
We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is "secure" against any polynomial-time quantum adversary. Our problem,…
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…
We study the ternary quadratic problem (TQP), a quadratic optimization problem with linear constraints where the variables take values in $\{0, \pm 1\}$. While semidefinite programming (SDP) techniques are well established for $\{0,1\}$-…
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…
We study the Quadratic Cycle Cover Problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and…
Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…
As quantum computing advances, the cryptographic algorithms that underpin confidentiality, integrity, and authentication in Intelligent Transportation Systems (ITS) face increasing vulnerability to quantum-enabled attacks. To address these…
We introduce the \emph{linear centralizer method}, and use it to devise a provable polynomial time solution of the Commutator Key Exchange Problem, the computational problem on which, in the passive adversary model, the security of the…
A polynomial Turing compression (PTC) for a parameterized problem $L$ is a polynomial time Turing machine that has access to an oracle for a problem $L'$ such that a polynomial in the input parameter bounds each query. Meanwhile, a…
Blockchain is a Distributed Ledger Technology (DLT) that offers numerous benefits including decentralization, transparency, efficiency, and reduced costs. Hence, blockchain has been included in many fields. Blockchain relies on…