Related papers: Homomorphic Encryption Based on Post-Quantum Crypt…
In this paper we discuss the Hidden Subgroup Problem (HSP) in relation to post-quantum group-based cryptography. We review the relationship between HSP and other computational problems discuss an optimal solution method, and review the…
These are pedagogical notes on Shor's factoring algorithm, which is a quantum algorithm for factoring very large numbers (of order of hundreds to thousands of bits) in polynomial time. In contrast, all known classical algorithms for the…
A scheme to encode arbitrarily long integer pairs on degenerate optical parametric oscillations multiplexed in time is proposed. The classical entanglement between the polarization directions and the phases of the oscillating pulses,…
In quantum information processing (QIP), the quantum Fourier transform (QFT) has a plethora of applications [1] [2] [3]: Shor's algorithm and phase estimation are just a few well-known examples. Shor's quantum factorization algorithm, one…
Inspired by the concept of fault tolerance quantum computation, this article proposes a framework dubbed Exact Homomorphic Encryption, EHE, enabling exact computations on encrypted data without the need for pre-decryption. The introduction…
Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research.…
As quantum computing hardware continues to advance, the integration of such technology with quantum algorithms is anticipated to enable the decryption of ciphertexts produced by RSA and Elliptic Curve Cryptography (ECC) within polynomial…
Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but these are only useful if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a…
The advent of quantum computing poses a critical threat to RSA cryptography, as Shor's algorithm can factor integers in polynomial time. While post-quantum cryptography standards offer long-term solutions, their deployment faces significant…
Quantum computing has the potential to revolutionize cryptography by breaking classical public-key cryptography schemes, such as RSA and Diffie-Hellman. However, breaking the widely used 2048-bit RSA using Shor's quantum factoring algorithm…
Shor algorithm led to the discovery of multiple vulnerabilities in a number of cryptosystems. As a result, post-quantum cryptography attempts to provide cryptographic solutions that can face these attacks, ensuring the security of sensitive…
In this paper, we evaluate the different fully homomorphic encryption schemes, propose an implementation, and numerically analyze the applicability of gradient descent algorithms to solve quadratic programming in a homomorphic encryption…
A characterization of predicate encryption (PE) with support for homomorphic operations is presented and we describe the homomorphic properties of some existing PE constructions. Even for the special case of IBE, there are few known…
In this survey we propose to cover the prose of post-quantum cryptography over classical cryptography. We talk about the various cryptographic methods that are being practiced to safeguard our information. The future of secure communication…
Homomorphic permutation is fundamental to privacy-preserving computations based on batch-encoding homomorphic encryption. It underpins nearly all homomorphic matrix operations and predominantly influences their complexity. Permutation…
As quantum computing technology matures, it poses a threat to the security of mainstream asymmetric cryptographic methods. In response, the National Institute of Standards and Technology released the final version of post-quantum…
Shor's algorithm is one of the most important quantum algorithm proposed by Peter Shor [Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994, pp. 124--134]. Shor's algorithm can factor a large integer with…
We propose a novel hybrid universal network-coding cryptosystem (HUNCC) to obtain secure post-quantum cryptography at high communication rates. The secure network-coding scheme we offer is hybrid in the sense that it combines…
We introduce for non-uniform messages a novel hybrid universal network coding cryptosystem (NU-HUNCC) in the finite blocklength regime that provides Post-Quantum (PQ) security at high communication rates. Recently, hybrid cryptosystems…
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…