相关论文: Two Public-Key Cryptosystems Based on Expanded Gab…
There are several public key establishment protocols as well as complete public key cryptosystems based on allegedly hard problems from combinatorial (semi)group theory known by now. Most of these problems are search problems, i.e., they…
In AFRICACRYPT 2010, Abdalla et al. first proposed a slight modification to the computations steps of the BD protocol, called mBD+P. Then they extended mBD+P protocol into mBD+S protocol. In this paper, we show that both of mBD+P and mBD+S…
We discuss the decoding of Gabidulin and interleaved Gabidulin codes. We give the full presentation of a decoding algorithm for Gabidulin codes, which as Loidreau's seminal algorithm consists in localizing errors in the spirit of…
Surface codes have historically been the dominant choice for quantum error correction due to their superior error threshold performance. However, recently, a new class of Generalized Bicycle (GB) codes, constructed from binary circulant…
Let $f=(f_0,f_1,\dots, f_{\nu-1})$ be a collection of one-to-one functions from some space~$X$ into itself such that the sets $f_j(X)$ are disjoint. If $w=w_1w_2\cdots w_k$ is a word on the alphabet $\{0,1,\dots,\nu-1\}$, let $\Phi_{f,w} =…
In the last decade, a number of public key cryptosystems based on com- binatorial group theoretic problems in braid groups have been proposed. We survey these cryptosystems and some known attacks on them. This survey includes: Basic facts…
The braid group is an important non commutative group, at the same time, it is an important tool in quantum field theory with better topological structure, and often used as a research carrier for anti-quantum cryptographic algorithms. This…
We give a polynomial time attack on the McEliece public key cryptosystem based on subcodes of algebraic geometry (AG) codes. The proposed attack reposes on the distinguishability of such codes from random codes using the Schur product.…
The capacity of the quantum dense key distribution (QDKD) [Phys. Rev. A69, 032310 (2004)] is doubled by introducing the dense coding. The security of the improved QDKD against eavesdropping is pointed out to be easily proven. In both the…
This paper investigates a quantum version of McEliece public-key encryption (PKE) scheme, and analyzes its security. As is well known, the security of classical McEliece PKE is not stronger than the onewayness of related classical one-way…
This article defines multi-twisted Goppa (MTG) codes as subfield subcodes of duals of multi-twisted Reed-Solomon (MTRS) codes and examines their properties. We show that if $t$ is the degree of the MTG polynomial defining an MTG code, its…
Let $\mathcal{C}$ be a set of $m$ by $n$ matrices over $\mathbb{F}_q$ such that the rank of $A-B$ is at least $d$ for all distinct $A,B\in \mathcal{C}$. Suppose that $m\leqslant n$. If $\#\mathcal{C}= q^{n(m-d+1)}$, then $\mathcal{C}$ is a…
Motivated by applications in DNA-based data storage, constrained codes have attracted a considerable amount of attention from both academia and industry. We study the maximum cardinality of constrained codes for which the constraints can be…
We revisit the 3-pass code-based identification scheme proposed by Stern at Crypto'93, and give a new 5-pass protocol for which the probability of the cheater is 1/2 (instead of 2/3 in the original Stern's proposal). Furthermore, we propose…
The interesting properties of classical Goppa code and its effective decoding algorithm (algorithm of patterson) make the most appropriate candidate for use in the MC Eliece cryptosystem. Information leakage which results from the…
A class of linear codes that extends classic Goppa codes to a non-commutative context is defined. An efficient decoding algorithm, based on the solution of a non-commutative key equation, is designed. We show how the parameters of these…
We consider a modified version of the BB84 quantum key distribution protocol in which the angle between two different bases are less than $\pi/4$. We show that the channel parameter estimate becomes the same as the original protocol with…
Existing error correction mechanisms in lattice-based public key encryption (PKE) rely on either naive modulation or its concatenation with error correction codes (ECC). This paper shows that lattice coding, as a joint ECC and modulation…
We propose variations of the class of hidden monomial cryptosystems in order to make it resistant to all known attacks. We use identities built upon a single bivariate polynomial equation with coefficients in a finite field. Indeed, it can…
The Rank metric decoding problem is the main problem considered in cryptography based on codes in the rank metric. Very efficient schemes based on this problem or quasi-cyclic versions of it have been proposed recently, such as those in the…