相关论文: Quantum secret key encryption algorithm based on q…
Solving the discrete logarithm problem (DLP) with quantum computers is a fundamental task with important implications. Beyond Shor's algorithm, many researchers have proposed alternative solutions in recent years. However, due to current…
The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product semigroup $G\rtimes \mathrm{End}(G)$ for a finite semigroup $G$. Given $g\in G, \sigma\in…
Nowadays, predominant asymmetric cryptographic schemes are considered to be secure because discrete logarithms are believed to be hard to be computed. The algorithm of Shor can effectively compute discrete logarithms, i.e. it can brake such…
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete…
The quantum algorithm with polynomial time for discrete logarithm problem proposed by Shor is one of the most significant quantum algorithms, but a large number of qubits may be required in the Noisy Intermediate-scale Quantum (NISQ) era.…
The discrete logarithm problem (DLP) is the basis for several cryptographic primitives. Since Shor's work, it has been known that the DLP can be solved by combining a polynomial-size quantum circuit and a polynomial-time classical…
Quantum secret-sharing and quantum error-correction schemes rely on multipartite decoding protocols, yet the non-local operations involved are challenging and sometimes infeasible. Here we construct a quantum secret-sharing protocol with a…
This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of generic algorithms -- that is, algorithms that do not exploit any properties of the group…
Quantum cryptography allows one to distribute a secret key between two remote parties using the fundamental principles of quantum mechanics. The well-known established paradigm for the quantum key distribution relies on the actual…
We give an example of a wide class of problems for which quantum information protocols based on multi-system entanglement can be mapped into much simpler ones involving one system. Secret sharing is a cryptographic primitive which plays a…
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…
Quantum communication is an important application that derives from the burgeoning field of quantum information and quantum computation. Focusing on secure communication, quantum cryptography has two major directions of development, namely…
Shor's algorithm efficiently solves factoring and discrete logarithm problems using quantum computers, compromising all public key schemes used today. These schemes rely on assumptions on their computational complexity, which quantum…
This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…
Quantum computing had a profound impact on cryptography. Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a…
An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…
In Private Broadcasting, a single plaintext is broadcast to multiple recipients in an encrypted form, such that each recipient can decrypt locally. When the message is classical, a straightforward solution is to encrypt the plaintext with a…
The discrete logarithm problem (DLP) over finite fields, commonly used in classical cryptography, has no known polynomial-time algorithm on classical computers. However, Shor has provided its polynomial-time algorithm on quantum computers.…
Group-based cryptography is a relatively unexplored family in post-quantum cryptography, and the so-called Semidirect Discrete Logarithm Problem (SDLP) is one of its most central problems. However, the complexity of SDLP and its…
We propose quantum protection circuit (quantum lock), based on dark states of ensembles of two-level atoms in optical cavity. The secret key is the splitting of atoms into pairs, and publicly accessible part of the lock is the tensor…