1,219 research outputs found
Group theory in cryptography
This paper is a guide for the pure mathematician who would like to know more
about cryptography based on group theory. The paper gives a brief overview of
the subject, and provides pointers to good textbooks, key research papers and
recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor
typographical changes. To appear in Proceedings of Groups St Andrews 2009 in
Bath, U
Quantum Algorithms for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems
Decision of whether a Boolean equation system has a solution is an NPC
problem and finding a solution is NP hard. In this paper, we present a quantum
algorithm to decide whether a Boolean equation system FS has a solution and
compute one if FS does have solutions with any given success probability. The
runtime complexity of the algorithm is polynomial in the size of FS and the
condition number of FS. As a consequence, we give a polynomial-time quantum
algorithm for solving Boolean equation systems if their condition numbers are
small, say polynomial in the size of FS. We apply our quantum algorithm for
solving Boolean equations to the cryptanalysis of several important
cryptosystems: the stream cipher Trivum, the block cipher AES, the hash
function SHA-3/Keccak, and the multivariate public key cryptosystems, and show
that they are secure under quantum algebraic attack only if the condition
numbers of the corresponding equation systems are large. This leads to a new
criterion for designing cryptosystems that can against the attack of quantum
computers: their corresponding equation systems must have large condition
numbers
From Pre-Quantum to Post-Quantum IoT Security: A Survey on Quantum-Resistant Cryptosystems for the Internet of Things
© 2020 IEEE. This version of the article has been accepted for publication,
after peer review. Personal use of this material is permitted. Permission from
IEEE must be obtained for all other uses, in any current or future media,
including reprinting/republishing this material for advertising or promotional
purposes, creating new collective works, for resale or redistribution to servers
or lists, or reuse of any copyrighted component of this work in other works.[Absctract]: Although quantum computing is still in its nascent age, its evolution threatens the most popular public-key encryption systems. Such systems are essential for today's Internet security due to their ability for solving the key distribution problem and for providing high security in insecure communications channels that allow for accessing websites or for exchanging e-mails, financial transactions, digitally signed documents, military communications or medical data. Cryptosystems like Rivest-Shamir-Adleman (RSA), elliptic curve cryptography (ECC) or Diffie-Hellman have spread worldwide and are part of diverse key Internet standards like Transport Layer Security (TLS), which are used both by traditional computers and Internet of Things (IoT) devices. It is especially difficult to provide high security to IoT devices, mainly because many of them rely on batteries and are resource constrained in terms of computational power and memory, which implies that specific energy-efficient and lightweight algorithms need to be designed and implemented for them. These restrictions become relevant challenges when implementing cryptosystems that involve intensive mathematical operations and demand substantial computational resources, which are often required in applications where data privacy has to be preserved for the long term, like IoT applications for defense, mission-critical scenarios or smart healthcare. Quantum computing threatens such a long-term IoT device security and researchers are currently developing solutions to mitigate such a threat. This article provides a survey on what can be called post-quantum IoT systems (IoT systems protected from the currently known quantum computing attacks): the main post-quantum cryptosystems and initiatives are reviewed, the most relevant IoT architectures and challenges are analyzed, and the expected future trends are indicated. Thus, this article is aimed at providing a wide view of post-quantum IoT security and give useful guidelines...This work was supported in part
by the Xunta de Galicia under Grant ED431G2019/01, in part by the
Agencia Estatal de Investigación of Spain under Grant TEC2016-75067-C4-
1-R and Grant RED2018-102668-T, and in part by ERDF funds of the EU
(AEI/FEDER, UE).Xunta de Galicia; ED431G2019/0
Fast Quantum Algorithm for Solving Multivariate Quadratic Equations
In August 2015 the cryptographic world was shaken by a sudden and surprising
announcement by the US National Security Agency NSA concerning plans to
transition to post-quantum algorithms. Since this announcement post-quantum
cryptography has become a topic of primary interest for several standardization
bodies. The transition from the currently deployed public-key algorithms to
post-quantum algorithms has been found to be challenging in many aspects. In
particular the problem of evaluating the quantum-bit security of such
post-quantum cryptosystems remains vastly open. Of course this question is of
primarily concern in the process of standardizing the post-quantum
cryptosystems. In this paper we consider the quantum security of the problem of
solving a system of {\it Boolean multivariate quadratic equations in
variables} (\MQb); a central problem in post-quantum cryptography. When ,
under a natural algebraic assumption, we present a Las-Vegas quantum algorithm
solving \MQb{} that requires the evaluation of, on average,
quantum gates. To our knowledge this is the fastest algorithm for solving
\MQb{}
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