Towards Post-Quantum Blockchain: A Review on Blockchain Cryptography Resistant to Quantum Computing Attacks

[Abstract] Blockchain and other Distributed Ledger Technologies (DLTs) have evolved significantly in the last years and their use has been suggested for numerous applications due to their ability to provide transparency, redundancy and accountability. In the case of blockchain, such characteristics are provided through public-key cryptography and hash functions. However, the fast progress of quantum computing has opened the possibility of performing attacks based on Grover's and Shor's algorithms in the near future. Such algorithms threaten both public-key cryptography and hash functions, forcing to redesign blockchains to make use of cryptosystems that withstand quantum attacks, thus creating which are known as post-quantum, quantum-proof, quantum-safe or quantum-resistant cryptosystems. For such a purpose, this article first studies current state of the art on post-quantum cryptosystems and how they can be applied to blockchains and DLTs. Moreover, the most relevant post-quantum blockchain systems are studied, as well as their main challenges. Furthermore, extensive comparisons are provided on the characteristics and performance of the most promising post-quantum public-key encryption and digital signature schemes for blockchains. Thus, this article seeks to provide a broad view and useful guidelines on post-quantum blockchain security to future blockchain researchers and developers.10.13039/501100010801-Xunta de Galicia (Grant Number: ED431G2019/01) 10.13039/501100011033-Agencia Estatal de Investigación (Grant Number: TEC2016-75067-C4-1-R and RED2018-102668-T) 10.13039/501100008530-European Regional Development FundXunta de Galicia; ED431G2019/0

Cryptography from tensor problems

We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler

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

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

New Directions in Multivariate Public Key Cryptography

Most public key cryptosystems used in practice are based on integer factorization or discrete logarithms (in finite fields or elliptic curves). However, these systems suffer from two potential drawbacks. First, they must use large keys to maintain security, resulting in decreased efficiency. Second, if large enough quantum computers can be built, Shor\u27s algorithm will render them completely insecure. Multivariate public key cryptosystems (MPKC) are one possible alternative. MPKC makes use of the fact that solving multivariate polynomial systems over a finite field is an NP-complete problem, for which it is not known whether there is a polynomial algorithm on quantum computers. The main goal of this work is to show how to use new mathematical structures, specifically polynomial identities from algebraic geometry, to construct new multivariate public key cryptosystems. We begin with a basic overview of MPKC and present several significant cryptosystems that have been proposed. We also examine in detail some of the most powerful attacks against MPKCs. We propose a new framework for constructing multivariate public key cryptosystems and consider several strategies for constructing polynomial identities that can be utilized by the framework. In particular, we have discovered several new families of polynomial identities. Finally, we propose our new cryptosystem and give parameters for which it is secure against known attacks on MPKCs

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 $m$ Boolean multivariate quadratic equations in $n$ variables} (\MQb); a central problem in post-quantum cryptography. When $n=m$, under a natural algebraic assumption, we present a Las-Vegas quantum algorithm solving \MQb{} that requires the evaluation of, on average, $O(2^{0.462n})$ quantum gates. To our knowledge this is the fastest algorithm for solving \MQb{}

Towards Green Computing Oriented Security: A Lightweight Postquantum Signature for IoE

[EN] Postquantum cryptography for elevating security against attacks by quantum computers in the Internet of Everything (IoE) is still in its infancy. Most postquantum based cryptosystems have longer keys and signature sizes and require more computations that span several orders of magnitude in energy consumption and computation time, hence the sizes of the keys and signature are considered as another aspect of security by green design. To address these issues, the security solutions should migrate to the advanced and potent methods for protection against quantum attacks and offer energy efficient and faster cryptocomputations. In this context, a novel security framework Lightweight Postquantum ID-based Signature (LPQS) for secure communication in the IoE environment is presented. The proposed LPQS framework incorporates a supersingular isogeny curve to present a digital signature with small key sizes which is quantum-resistant. To reduce the size of the keys, compressed curves are used and the validation of the signature depends on the commutative property of the curves. The unforgeability of LPQS under an adaptively chosen message attack is proved. Security analysis and the experimental validation of LPQS are performed under a realistic software simulation environment to assess its lightweight performance considering embedded nodes. It is evident that the size of keys and the signature of LPQS is smaller than that of existing signature-based postquantum security techniques for IoE. It is robust in the postquantum environment and efficient in terms of energy and computations.This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University. Jeddah. under grant No. (DF-457-156-1441).Rani, R.; Kumar, S.; Kaiwartya, O.; Khasawneh, AM.; Lloret, J.; Al-Khasawneh, MA.; Mahmoud, M.... (2021). Towards Green Computing Oriented Security: A Lightweight Postquantum Signature for IoE. Sensors. 21(5):1-20. https://doi.org/10.3390/s2105188312021