scholarly journals Quantum-safe cryptography: crossroads of coding theory and cryptography

2021 ◽  
Vol 65 (1) ◽  
Author(s):  
Jiabo Wang ◽  
Ling Liu ◽  
Shanxiang Lyu ◽  
Zheng Wang ◽  
Mengfan Zheng ◽  
...  
Keyword(s):  
Coding Theory ◽  
Linear Codes ◽  
Point Of View ◽  
Future Research ◽  
Information Theoretic ◽  
Wiretap Channels ◽  
Information Theoretic Security ◽  
Theoretic Point ◽  
Standardization Process ◽  
Post Quantum Cryptography

AbstractWe present an overview of quantum-safe cryptography (QSC) with a focus on post-quantum cryptography (PQC) and information-theoretic security. From a cryptographic point of view, lattice and code-based schemes are among the most promising PQC solutions. Both approaches are based on the hardness of decoding problems of linear codes with different metrics. From an information-theoretic point of view, lattices and linear codes can be constructed to achieve certain secrecy quantities for wiretap channels as is intrinsically classical- and quantum-safe. Historically, coding theory and cryptography are intimately connected since Shannon’s pioneering studies but have somehow diverged later. QSC offers an opportunity to rebuild the synergy of the two areas, hopefully leading to further development beyond the NIST PQC standardization process. In this paper, we provide a survey of lattice and code designs that are believed to be quantum-safe in the area of cryptography or coding theory. The interplay and similarities between the two areas are discussed. We also conclude our understandings and prospects of future research after NIST PQC standardisation.

scholarly journals Designing Efficient Dyadic Operations for Cryptographic Applications

2020 ◽  
Vol 14 (1) ◽  
pp. 95-109
Author(s):  
Gustavo Banegas ◽  
Paulo S. L. M. Barreto ◽  
Edoardo Persichetti ◽  
Paolo Santini
Keyword(s):  
Automorphism Group ◽  
Quantum Cryptography ◽  
Coding Theory ◽  
Linear Codes ◽  
Key Exchange ◽  
Independent Interest ◽  
Symmetric Matrices ◽  
Cryptographic Primitives ◽  
Standardization Process ◽  
Post Quantum Cryptography

AbstractCryptographic primitives from coding theory are some of the most promising candidates for NIST’s Post-Quantum Cryptography Standardization process. In this paper, we introduce a variety of techniques to improve operations on dyadic matrices, a particular type of symmetric matrices that appear in the automorphism group of certain linear codes. Besides the independent interest, these techniques find an immediate application in practice. In fact, one of the candidates for the Key Exchange functionality, called DAGS, makes use of quasi-dyadic matrices to provide compact keys for the scheme.

scholarly journals Revisiting and Improving Algorithms for the 3XOR Problem

2018 ◽  
pp. 254-276
Author(s):  
Charles Bouillaguet ◽  
Claire Delaplace ◽  
Pierre-Alain Fouque
Keyword(s):  
Black Box ◽  
Specific Form ◽  
Point Of View ◽  
Difficult Case ◽  
Huge Amount ◽  
Information Theoretic ◽  
Random Functions ◽  
Geometric Problems ◽  
Birthday Problem ◽  
Theoretic Point

The 3SUM problem is a well-known problem in computer science and many geometric problems have been reduced to it. We study the 3XOR variant which is more cryptologically relevant. In this problem, the attacker is given black-box access to three random functions F,G and H and she has to find three inputs x, y and z such that F(x) ⊕ G(y) ⊕ H(z) = 0. The 3XOR problem is a difficult case of the more-general k-list birthday problem. Wagner’s celebrated k-list birthday algorithm, and the ones inspired by it, work by querying the functions more than strictly necessary from an information-theoretic point of view. This gives some leeway to target a solution of a specific form, at the expense of processing a huge amount of data. However, to handle such a huge amount of data can be very difficult in practice. This is why we first restricted our attention to solving the 3XOR problem for which the total number of queries to F, G and H is minimal. If they are n-bit random functions, it is possible to solve the problem with roughly

scholarly journals The Entropy of Words—Learnability and Expressivity across More Than 1000 Languages

2017 ◽  
Author(s):  
Christian Bentz ◽  
Dimitrios Alikaniotis ◽  
Michael Cysouw ◽  
Ramon Ferrer-i-Cancho
Keyword(s):  
Computational Linguistics ◽  
Estimation Method ◽  
Fundamental Property ◽  
Point Of View ◽  
Natural Languages ◽  
Information Theoretic ◽  
Parallel Corpora ◽  
The World ◽  
Theoretic Point ◽  
The Right

The choice associated with words is a fundamental property of natural languages. It lies at the heart of quantitative linguistics, computational linguistics, and language sciences more generally. Information-theory gives us tools at hand to measure precisely the average amount of choice associated with words—the word entropy. Here we use three parallel corpora—encompassing ca. 450 million words in 1916 texts and 1259 languages—to tackle some of the major conceptual and practical problems of word entropy estimation: dependence on text size, register, style and estimation method, as well as non-independence of words in co-text. We present three main results: 1) a text size of 50K tokens is sufficient for word entropies to stabilize throughout the text, 2) across languages of the world, word entropies display a unimodal distribution that is skewed to the right. This suggests that there is a trade-off between the learnability and expressivity of words across languages of the world. 3) There is a strong linear relationship between unigram entropies and entropy rates, suggesting that they are inherently linked. We discuss the implications of these results for studying the diversity and evolution of languages from an information-theoretic point of view.

scholarly journals Logic Programming, Substitutions and Finite Computability

1985 ◽  
Vol 13 (186) ◽  
Author(s):  
Gudmund Skovbjerg Frandsen
Keyword(s):  
Fixed Point ◽  
Logic Programming ◽  
Point Of View ◽  
Intermediate Step ◽  
Information Theoretic ◽  
Theoretic Point ◽  
Fixed Point Semantics ◽  
Fixed Point Methods ◽  
Resolution Algorithm ◽  
Herbrand Models

<p>Apt and van Emden have studied the semantics of logic programming by means of fixed point methods. From a model theoretic point of view, their formalisation is very nice. Least and greatest fixed points correspond to least and greatest Herbrand-models respectively.</p><p>Viewed operationally, there is an ugly asymmetry. The least fixed point expresses finite computability, but the greatest fixed point denotes negation by <em>trans</em>-finite failure, i.e. the underlying operator is not omega-continuous for decreasing chains in general.</p><p>We use the notion of finite computability inherent in Scott domains to build a domainlike construction (the cd-domain) that offers omega-continuity for increasing and decreasing chains equally. On this basis negation by finite failure is expressed in terms of a fixed point.</p><p>The fixed point semantics of Apt and van Emden is very abstract concerning the concept of substitution, although it is fundamental for any implementation. Hence it becomes quite tedious to prove the correctness of a concrete resolution algorithm. The fixed point semantics of this paper offers an intermediate step in this respect. Any commitments to specific resolution strategies are avoided, and the semantics may be the basis of sequential and parallel implementations equally. Simultaneously the set of substitution dataobjects is structured by a Scott information theoretic partial order, namely the cd-domain.</p>

scholarly journals Path Hopping: An MTD Strategy for Long-Term Quantum-Safe Communication

2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Reihaneh Safavi-Naini ◽  
Alireza Poostindouz ◽  
Viliam Lisy
Keyword(s):  
Quantum Computer ◽  
Transition Probabilities ◽  
Future Research ◽  
Security Measures ◽  
Information Theoretic ◽  
Information Theoretic Security ◽  
Diffie Hellman ◽  
Physical Assumption ◽  
Cryptographic System

Moving target defense (MTD) strategies have been widely studied for securing computer systems. We consider using MTD strategies to provide long-term cryptographic security for message transmission against an eavesdropping adversary who has access to a quantum computer. In such a setting, today’s widely used cryptographic systems including Diffie-Hellman key agreement protocol and RSA cryptosystem will be insecure and alternative solutions are needed. We will use a physical assumption, existence of multiple communication paths between the sender and the receiver, as the basis of security, and propose a cryptographic system that uses this assumption and an MTD strategy to guarantee efficient long-term information theoretic security even when only a single path is not eavesdropped. Following the approach of Maleki et al., we model the system using a Markov chain, derive its transition probabilities, propose two security measures, and prove results that show how to calculate these measures using transition probabilities. We define two types of attackers that we call risk-taking and risk-averse and compute our proposed measures for the two types of adversaries for a concrete MTD strategy. We will use numerical analysis to study tradeoffs between system parameters, discuss our results, and propose directions for future research.

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