DOCSLIB.ORG

On the Energy Consumption of Quantum-Resistant Cryptographic Software Implementations Suitable for Wireless Sensor Networks

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
On the Energy Consumption of Quantum-Resistant Cryptographic Software Implementations Suitable for Wireless Sensor Networks On the Energy Consumption of Quantum-resistant Cryptographic Software Implementations Suitable for Wireless Sensor Networks Michael Heigl1;2, Laurin Doerr1;2, Martin Schramm2 and Dalibor Fiala1 1Department of Computer Science and Engineering, University of West Bohemia, Pilsen 301 00, Czech Republic 2Institute ProtectIT, Deggendorf Institute of Technology, 94469 Deggendorf, Germany Keywords: Wireless Sensor Networks, Post-quantum Cryptography, Energy Consumption. Abstract: For an effective protection of the communication in Wireless Sensor Networks (WSN) facing e.g. threats by quantum computers in the near future, it is necessary to examine the applicability of quantum-resistant mechanisms in this field. It is the aim of this article to survey possible candidate schemes utilizable on sensor nodes and to compare the energy consumption of a selection of freely-available software implementations using a WSN-ready Texas Instruments CC1350 LaunchPad ARM® Cortex®-M3 microcontroller board. 1 INTRODUCTION itary area, cryptographic schemes are inevitable to preserve the protection goals confidentiality, integrity The set consisting of base stations and multiple tiny and authenticity. The application of these schemes on autonomous devices interconnected via an ad-hoc the other side still imposes several limitations since communication is called WSN. Nowadays, they have the known resource issues and other constraints pre- permeated many technological areas mainly driven by sented in (Sen, 2013) inhibit the deployment in WSN. the Internet of Things (IoT). The sensor nodes are Furthermore, with the advent of quantum comput- composed of a microcontroller, a radio transceiver, ers, quantum computation will have a tremendous im- a power supply (typically battery-powered), memory pact on a major field of cryptography not only erupt- and one or more sensors to collect data from the im- ing WSN-security. It has the potential to break or mediate environment and transmit it wirelessly. Ap- weaken asymmetric schemes including the Elliptic- plication areas are boosted by the IoT ranging from Curve Diffie-Hellman (ECDH) key exchange often simple measurements of environmental data such as applied in the embedded domain. temperature or smoke towards IoT-enabled Smart Thus, in this work possible state-of-the-art cryp- Cars (Bartolomeu et al., 2018). tographic schemes are proposed which are resistant The ever-increasing and more advanced attack to the power of quantum computers. A selection of capabilities and strategies pose an enormous chal- freely-available software implementation candidates lenge and demand IT-security for WSN in the near are integrated on a WSN-ready microcontroller board future. The sophistication of attacks utilizing dis- and evaluated in terms of their applicability in WSN. tributed, cloud or even quantum computation (Sen, The remainder of this paper is structured as follows: 2013) forces classical IT-security to change into sus- Section 2 discusses the threats from quantum comput- tainable cyber resilience. However, the application of ers towards cryptographic schemes. A state-of-the-art viable cryptographic schemes vital for holistic secu- review on cryptographic mechanisms with regard to rity solutions are often seen as an undesirable over- quantum-resistance for WSN is provided in Section 3. head cost and therefore neglected in the design of Details on the measurement setup and integration of a WSN. Due to the inherent resource limitations in selection of freely-available software implementation terms of memory size, processing speed as well as candidates on the Texas Instruments CC1350 Launch- energy consumption, attacks towards WSN are man- Pad microcontroller board are presented in Section 4. ifold (Costa et al., 2017). Because of the open com- The evaluation in Section 5 deals with energy con- munication nature of the wireless radio channel, at- sumption measurements with respect to fundamental tackers can easily eavesdrop on, intercept, inject and cryptographic components and discusses their com- forge the exchanged information. Especially when putational and communication cost. A short conclu- it comes to the transmission of confidential informa- sion and a glance at the future work of the ongoing tion, for instance measurements in the medical or mil- research work finalizes the article in Section 6. 72 Heigl, M., Doerr, L., Schramm, M. and Fiala, D. On the Energy Consumption of Quantum-resistant Cryptographic Software Implementations Suitable for Wireless Sensor Networks. DOI: 10.5220/0007835600720083 In Proceedings of the 16th International Joint Conference on e-Business and Telecommunications (ICETE 2019), pages 72-83 ISBN: 978-989-758-378-0 Copyright c 2019 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved On the Energy Consumption of Quantum-resistant Cryptographic Software Implementations Suitable for Wireless Sensor Networks 2 QUANTUM NERVOUSNESS 3 CRYPTOGRAPHY FOR WSN Quantum computing is founded on the microscopic The protection of communicated data in WSN to physical phenomena of quantum mechanics. Instead achieve the stated security goals is mainly founded on of using bits with observed states 0 and 1 on contem- hash functions, symmetric-key and asymmetric-key porary computers, quantum computers are based on algorithms composed of the following crucial com- quantum bits (qubits). Qubits are particles that can ponents: message authentication, message encryption exist in both states simultaneously, by the effect of / decryption, key exchange, digital signature. Es- superposition, and are able to exploit true parallelism pecially with the threat of quantum computers to- due to quantum entanglement (Jozsa, 1997). In the wards asymmetric cryptography, practical alternatives era of having first viable quantum computers, the so- for contemporary schemes in WSN such as ECDH or called quantum nervousness begins and represents a DSA must be researched. new type of threat for cryptography in general. Post-quantum cryptography (PQC) refers to cryp- Shor’s algorithm (Shor, 1997) makes use of the tographic schemes that can function on classical quantum Fourier transform to extract the required in- non-quantum machines but promise to withstand formation from the superposition of quantum states the impact of Shor’s or Grover’s algorithm run- which allows to break all contemporary asymmet- ning on quantum-accelerated computers. Several ric cryptography such as RSA, DSA or Elliptic- different families of PQC are presented in (Bern- Curve Cryptography (ECC) based schemes. Espe- stein et al., 2009) including hash-based, code- cially ECC is widely deployed in IoT-environments based, lattice-based, multivariate-quadratic-equations due to the more efficient arithmetic, low memory and secret-key cryptography. Supersingular elliptic- usage, shorter key sizes and lower CPU consump- curve isogeny cryptography is much closer to classi- tion compared to RSA or DSA (Mani and Nishamol, cal ECDH-schemes, but it is very young and not well 2013). Even if asymmetric cryptography with ade- researched (Bogomolec and Gerhard, 2018). quate key sizes (BSI, 2018) is considered very safe Recommendations for cryptographic schemes to today, the underlying mathematical problems such as be used in the quantum-era, not intended for embed- efficient integer factorization e.g. in RSA or the cal- ded domains, are provided by (PQCRYPTO, 2015). culation of the discrete logarithm e.g. in ECC can be Even if some PQC software implementations aimed solved with Shor’s algorithm in a reasonable amount for low-cost devices exist (Xu et al., 2018), a major of time if a powerful quantum computer can be uti- demerit is the poor resource-efficiency especially in lized. Even if such efficient machines are currently terms of communication overhead of most of the post- far from being practically feasible, the NIST states quantum schemes compared to contemporary cryp- that a quantum computer capable of breaking RSA- tography which makes them hardly applicable on 2048 or ECC-256 in a matter of hours could be built resource-constrained devices. Another uncertainty by 2030 (NIST, 2016). with PQC is that there could be a currently unknown A breakthrough has recently been announced by algorithm that breaks even such schemes in the near Google regarding its 72-qubit capable Bristlecone future. Thus, a combination with contemporarily used paving the way for large scale quantum comput- mechanisms could be a possible tradeoff. An exam- ers (Kelly, 2018). Those will also affect symmet- ple is Google’s CECPQ1 which is a key exchange that ric cryptography such as AES. Even if Grover’s al- concatenates the results of an X25519 and NewHope gorithm (Grover, 1996) has been initially intended to key exchange. X25519 is a Diffie-Hellman-based key search unsorted databases, it can be applied to crack exchange applying Curve25519. symmetric ciphers. However, the impact is far less The following sections discuss the cryptographic than with Shor’s algorithm since currently it is as- key components with respect to the application in sumed that doubling the key length mitigates its harm. WSN by stating contemporary applied schemes and According to the authors of (Amy et al., 2016), cryp- possible PQC-alternatives. With respect to the secu- tographic hash functions are not affected by quan- rity level, schemes providing 128-bit will be consid- tum computers. They state that both SHA-256 and ered, since the 112-bit security level should be phased SHA3-256 need around 2166 logical
Load more

Recommended publications
  • Etsi Gr Qsc 001 V1.1.1 (2016-07)
    ETSI GR QSC 001 V1.1.1 (2016-07) GROUP REPORT Quantum-Safe Cryptography (QSC); Quantum-safe algorithmic framework 2 ETSI GR QSC 001 V1.1.1 (2016-07) Reference DGR/QSC-001 Keywords algorithm, authentication, confidentiality, security ETSI 650 Route des Lucioles F-06921 Sophia Antipolis Cedex - FRANCE Tel.: +33 4 92 94 42 00 Fax: +33 4 93 65 47 16 Siret N° 348 623 562 00017 - NAF 742 C Association à but non lucratif enregistrée à la Sous-Préfecture de Grasse (06) N° 7803/88 Important notice The present document can be downloaded from: http://www.etsi.org/standards-search The present document may be made available in electronic versions and/or in print. The content of any electronic and/or print versions of the present document shall not be modified without the prior written authorization of ETSI. In case of any existing or perceived difference in contents between such versions and/or in print, the only prevailing document is the print of the Portable Document Format (PDF) version kept on a specific network drive within ETSI Secretariat. Users of the present document should be aware that the document may be subject to revision or change of status. Information on the current status of this and other ETSI documents is available at https://portal.etsi.org/TB/ETSIDeliverableStatus.aspx If you find errors in the present document, please send your comment to one of the following services: https://portal.etsi.org/People/CommiteeSupportStaff.aspx Copyright Notification No part may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm except as authorized by written permission of ETSI.
    [Show full text]
  • Handling the State of Hash-Based Signatures
    Let Live and Let Die — Handling the State of Hash-based Signatures Stefan-Lukas Gazdag1, Denis Butin2, and Johannes Buchmann2 1 genua mbh, Germany [email protected] 2 TU Darmstadt, Germany {dbutin,buchmann}@cdc.informatik.tu-darmstadt.de Abstract. Real-world use of digital signatures currently relies on algo­ rithms that will be broken once quantum computers become available. Quantum-safe alternatives exist; in particular, hash-based schemes offer adequate performance and security and are seen as a fitting solution for post-quantum signatures. Unfortunately, they are not used at large because practical hurdles have not yet been overcome. In particular, their reliance on one-time signing keys makes it necessary to carefully keep track of a key index. We present strategies for handling the state of hash- based signatures for different use cases, ranging from infrequent software update authentication to high-frequency TLS connection initialization. Keywords: Digital signatures, Hash-based, Integration 1 Motivation Digital signatures are massively used online, notably for authentication, integrity checking and non-repudiation. The digital signature algorithms most commonly used in practice — RSA, DSA and ECDSA — rely on hardness assumptions about number theoretic problems, namely composite integer factorisation and the computation of discrete logarithms. In light of Shor’s [19] algorithm, these arithmetical problems would be broken in the presence of quantum computing. While quantum computers are not yet available, their development is occurring at a swift pace [18]. However, post-quantum cryptography [3] provides a variety of quantum-resistant alternatives to classical digital signature schemes. Hash- based (or Merkle) signatures are one of the most promising of these alternatives and have received a lot of attention lately.
    [Show full text]
  • 2 XII December 2014
    2 XII December 2014 www.ijraset.com Volume 2 Issue XII, December 2014 ISSN: 2321-9653 International Journal for Research in Applied Science & Engineering Technology (IJRASET) Privacy in Data Storage and MultiOwner Authentication with Load Balancing in Cloud Computing Thulasibai.U1, Arul prem.G2, Deepika.J3 Sri Venkateshwara College of Engineering and Technology, India Abstract: Using Cloud Storage, users can remotely store their data and enjoy the on-demand high quality applications and services from a shared pool of configurable computing resources, without the encumbrance of local data storage and maintenance. the data integrity protection in Cloud Computing a formidable task, especially for users with constrained computing resources. Moreover, users should be able to just use the cloud storage as if it is local, without worrying about the need to verify its integrity. Thus, enabling public audit ability for cloud storage is of critical prominence so that users can resort to a Third Party Auditor (TPA) to check the integrity of outsourced data and be worry-free. To securely introduce an effective TPA, the auditing process should bring in no new vulnerabilities towards user data privacy, and introduce no additional online burden to user. In this project, we propose a secure cloud storage system supporting privacy-preserving public auditing. We further extend our result to enable the TPA to perform audits for multiple users simultaneously and efficiently. Extensive security and performance analysis show the proposed schemes are provably secure and highly efficient. Keyword: Cloud Storage Security, batch auditing, Tpa, load balancing, Rdpc I. INTRODUCTION Cloud computing is recognized as an alternative to traditional information technology due to its intrinsic resource-sharing and low-maintenance characteristics.
    [Show full text]
  • Question 1.1. What Is the RSA Laboratories' Frequently Asked
    Copyright © 1996, 1998 RSA Data Security, Inc. All rights reserved. RSA BSAFE Crypto-C, RSA BSAFE Crypto-J, PKCS, S/WAN, RC2, RC4, RC5, MD2, MD4, and MD5 are trade- marks or registered trademarks of RSA Data Security, Inc. Other products and names are trademarks or regis- tered trademarks of their respective owners. For permission to reprint or redistribute in part or in whole, send e-mail to [email protected] or contact your RSA representative. RSA Laboratories’ Frequently Asked Questions About Today’s Cryptography, v4.0 2 Table of Contents Table of Contents............................................................................................ 3 Foreword......................................................................................................... 8 Section 1: Introduction .................................................................................... 9 Question 1.1. What is the RSA Laboratories’ Frequently Asked Questions About Today’s Cryptography? ................................................................................................................ 9 Question 1.2. What is cryptography? ............................................................................................10 Question 1.3. What are some of the more popular techniques in cryptography? ................... 11 Question 1.4. How is cryptography applied? ............................................................................... 12 Question 1.5. What are cryptography standards? ......................................................................
    [Show full text]
  • Survey of One Time Signature Schemes on Cloud Computing
    ISSN(Online): 2320-9801 ISSN (Print): 2320-9798 International Journal of Innovative Research in Computer and Communication Engineering (An ISO 3297: 2007 Certified Organization) Vol. 3, Issue 4, April 2015 Survey of One Time Signature Schemes on Cloud Computing Revatthy Krishnamurthy1, K.P. Kaliyamurthie2 1M.Tech Scholar, Department of Computer Science & Engineering, Bharath University, Chennai, India 2Professor, Department of Computer Science & Engineering, Bharath University, Chennai, India. ABSTRACT : Cloud computing is a technology and large - scale computing resources to effectively integrate, and the resources are computed based on cryptographic secure hash functions. The biggest problem of one time signature scheme is the key management. An efficient key management is needed to make one-time signature scheme and the Merkle signature schemes feasible. This paper presents detailed study on one-time signature and Merkle signature schemes. KEYWORDS: Cloud computing, one-time signature scheme, Merkle signature scheme, Key generation. I. INTRODUCTION Cloud is a large group of interconnected computers, which is a major change in how we store information and run application. Cloud computing is used for many bigdata applications and it is cost effective. Data storage and sharing services in the cloud with three entities such as the cloud, the third party Auditor (TPA), and users who participate as a group includes one original user and a number of group users. The original user is an original owner of data, and shares data in the cloud with other users [2]. A single message using a given piece of private or public information. The conventional signature schemes like RSA, the same key pair can be used to authenticate large number of documents.
    [Show full text]
  • Lecture 17 March 28, 2019
    Outline Lamport Signatures Merkle Signatures Passwords CPSC 367: Cryptography and Security Michael J. Fischer Lecture 17 March 28, 2019 CPSC 367, Lecture 17 1/23 Outline Lamport Signatures Merkle Signatures Passwords Lamport One-Time Signatures Merkle Signatures Authentication Using Passwords Authentication problem Passwords authentication schemes CPSC 367, Lecture 17 2/23 Outline Lamport Signatures Merkle Signatures Passwords Lamport One-Time Signatures CPSC 367, Lecture 17 3/23 Outline Lamport Signatures Merkle Signatures Passwords Overview of Lamport signatures Leslie Lamport devised a digital signature scheme based on hash functions rather than on public key cryptography. Its drawback is that each key pair can be used to sign only one message. We describe how Alice uses it to sign a 256-bit message. As wtih other signature schemes, it suffices to sign the hash of the actual message. CPSC 367, Lecture 17 4/23 Outline Lamport Signatures Merkle Signatures Passwords How signing works The private signing key consists of a sequence r = (r 1;:::; r 256) of k k pairs( r0 ; r1 ) of random numbers,1 ≤ k ≤ 256. th Let m be a 256-bit message. Denote by mk the k bit of m. The signature of m is the sequence of numbers s = (s1;:::; s256), where sk = r k : mk k k Thus, one element from the pair( r0 ; r1 ) is used to sign mk , so k k k k s = r0 if mk = 0 and s = r1 if mk = 1. CPSC 367, Lecture 17 5/23 Outline Lamport Signatures Merkle Signatures Passwords How verification works The public verification key consists of the sequence 1 256 k k k k v = (v ;:::; v ) of pairs( v0 ; v1 ), where vj = H(rj ), and H is any one-way function (such as a cryptographically strong hash function).
    [Show full text]
  • Performance Evaluation of Post-Quantum Public-Key Cryptography in Smart Mobile Devices Noureddine Chikouche, Abderrahmen Ghadbane
    Performance Evaluation of Post-quantum Public-Key Cryptography in Smart Mobile Devices Noureddine Chikouche, Abderrahmen Ghadbane To cite this version: Noureddine Chikouche, Abderrahmen Ghadbane. Performance Evaluation of Post-quantum Public- Key Cryptography in Smart Mobile Devices. 17th Conference on e-Business, e-Services and e-Society (I3E), Oct 2018, Kuwait City, Kuwait. pp.67-80, 10.1007/978-3-030-02131-3_9. hal-02274171 HAL Id: hal-02274171 https://hal.inria.fr/hal-02274171 Submitted on 29 Aug 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License Performance Evaluation of Post-Quantum Public-Key Cryptography in Smart Mobile Devices Noureddine Chikouche1;2[0000−0001−9653−6608] and Abderrahmen Ghadbane2 1 Laboratory of Pure and Applied Mathematics, University of M'sila, Algeria 2 Computer Science Department, University of M'sila, Algeria Abstract. The classical public-key schemes are based on number the- ory, such as integer factorization and discrete logarithm. In 1994, P.W. Shor proposed an algorithm to solve these problems in polynomial time using quantum computers. Recent advancements in quantum computing open the door to the possibility of developing quantum computers so- phisticated enough to solve these problems.
    [Show full text]
  • Flexible Signatures: Making Authentication Suitable for Real-Time Environments
    Flexible Signatures: Making Authentication Suitable for Real-Time Environments Duc V. Le1, Mahimna Kelkar2 ?, and Aniket Kate1 1 Purdue University fle52,[email protected] 2 Cornell University [email protected] Abstract. This work introduces the concept of flexible signatures. In a flexible signature scheme, the verification algorithm quantifies the va- lidity of a signature based on the number of computations performed, such that the signature's validation (or confidence) level in [0; 1] improves as the algorithm performs more computations. Importantly, the defini- tion of flexible signatures does not assume the resource restriction to be known in advance, a significant advantage when the verification process is hard stopped by a system interrupt. Prominent traditional signature schemes such as RSA, (EC)DSA seem unsuitable towards building flexi- ble signatures because rigid all-or-nothing guarantees offered by the tra- ditional cryptographic primitives have been particularly unattractive in these unpredictably resource-constrained environments. In this work, we find the use of the Lamport-Diffie one-time signature and Merkle authentication tree to be suitable for building flexible signatures. We present a flexible signature construction based on these hash-based primitives and prove its security with concrete security analysis. We also perform a thorough validity-level analysis demonstrating an attractive computation-vs-validity trade-off offered by our construction: a security 2 level of 80 bits can be ensured by performing only around 3 rd of the total hash computations for our flexible signature construction with a Merkle tree of height 20. Finally, we have implemented our constructions in a resource-constrained environment on a Raspberry Pi.
    [Show full text]
  • A Comparative Analysis of Post-Quantum Hash-Based Signature Algorithm
    Eötvös Loránd University Faculty of Informatics A Comparative Analysis of Post-Quantum Hash-based Signature Algorithm Mr. Péter Ligeti Kimsukha Selvi S Assistant Professor at ELTE Computer Science Mr. Andreas Peter Associate Professor at University of Twente Mr. Áron Szabó IT Security Consultant at E-Group ICT Software Budapest, 2020. STATEMENT OF THESIS SUBMISSION AND ORIGINALITY I hereby confirm the submission of the Master Thesis Work on the Com- puter Science MSc course with author and title: Name of Student: ......................................................Kimsukha Selvi Sivasubramanian Code of Student: ......................................................G2T460 Title of Thesis: ......................................................A Comparative Analysis of Post-Quantum Hash-based Signature Algorithm Supervisor: ......................................................Mr.Péter Ligeti ......................................................Assistant Professor at Eötvös Loránd University, Faculty of Informatics. In consciousness of my full legal and disciplinary responsibility I hereby claim that the submitted thesis work is my own original intellectual prod- uct, the use of referenced literature is done according to the general rules of copyright. I understand that in the case of thesis works the following acts are consid- ered plagiarism: • literal quotation without quotation marks and reference; • citation of content without reference; • presenting others’ published thoughts as own thoughts. Budapest, student Acknowledgement I would like to express my gratitude to my supervisors Mr.Péter Ligeti and Mr.Áron Szabó from E-Group for their guidance and support while I was working on my thesis. I would also like to thank my friends Ann Mariam and Veeraraghavan for reading my draft version and for providing valuable feedback, and my family for supporting me during my studies. Thank you all. i CONTENTS Contents 1 Introduction 1 2 Preliminaries 4 2.1 Digital Signatures .
    [Show full text]
  • Lecture 17 November 1, 2017
    Outline Hashed Data Structures Lamport Signatures Merkle Signatures Passwords CPSC 467: Cryptography and Computer Security Michael J. Fischer Lecture 17 November 1, 2017 CPSC 467, Lecture 17 1/42 Outline Hashed Data Structures Lamport Signatures Merkle Signatures Passwords Hashed Data Structures Motivation: Peer-to-peer file sharing networks Hash lists Hash Trees Lamport One-Time Signatures Merkle Signatures Authentication Using Passwords Authentication problem Passwords authentication schemes Secure password storage Dictionary attacks CPSC 467, Lecture 17 2/42 Outline Hashed Data Structures Lamport Signatures Merkle Signatures Passwords Hashed Data Structures CPSC 467, Lecture 17 3/42 Outline Hashed Data Structures Lamport Signatures Merkle Signatures Passwords P2P Peer-to-peer networks One real-world application of hash functions is to peer-to-peer file-sharing networks. The goal of a P2P network is to improve throughput when sending large files to large numbers of clients. It operates by splitting the file into blocks and sending each block separately through the network along possibly different paths to the client. Rather than fetching each block from the master source, a block can be received from any node (peer) that happens to have the needed block. The problem is to validate blocks received from untrusted peers. CPSC 467, Lecture 17 4/42 Outline Hashed Data Structures Lamport Signatures Merkle Signatures Passwords P2P Integrity checking An obvious approach is for a trusted master node to send each client a hash of the entire file. When all blocks have been received, the client reassembles the file, computes its hash, and checks that it matches the hash received from the master.
    [Show full text]
  • The Impact of Quantum Computing on Present Cryptography
    (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 9, No. 3, 2018 The Impact of Quantum Computing on Present Cryptography Vasileios Mavroeidis, Kamer Vishi, Mateusz D. Zych, Audun Jøsang Department of Informatics, University of Oslo, Norway Email(s): fvasileim, kamerv, mateusdz, josangg@ifi.uio.no Abstract—The aim of this paper is to elucidate the impli- challenge of building a true quantum computer. Furthermore, cations of quantum computing in present cryptography and we introduce two important quantum algorithms that can to introduce the reader to basic post-quantum algorithms. In have a huge impact in asymmetric cryptography and less in particular the reader can delve into the following subjects: present symmetric, namely Shor’s algorithm and Grover’s algorithm cryptographic schemes (symmetric and asymmetric), differences respectively. Finally, post-quantum cryptography is presented. between quantum and classical computing, challenges in quantum Particularly, an emphasis is given on the analysis of quantum computing, quantum algorithms (Shor’s and Grover’s), public key encryption schemes affected, symmetric schemes affected, the im- key distribution and some mathematical based solutions such pact on hash functions, and post quantum cryptography. Specif- as lattice-based cryptography, multivariate-based cryptography, ically, the section of Post-Quantum Cryptography deals with hash-based signatures, and code-based cryptography. different quantum key distribution methods and mathematical- based solutions, such as the BB84 protocol, lattice-based cryptog- II. PRESENT CRYPTOGRAPHY raphy, multivariate-based cryptography, hash-based signatures and code-based cryptography. In this chapter we explain briefly the role of symmetric algorithms, asymmetric algorithms and hash functions in mod- Keywords—quantum computers; post-quantum cryptography; Shor’s algorithm; Grover’s algorithm; asymmetric cryptography; ern cryptography.
    [Show full text]
  • SPHINCS $^+ $ Post-Quantum Digital Signature Scheme with Streebog
    SPHINCS+ post-quantum digital signature scheme with Streebog hash function E.O. Kiktenko1,2, A.A. Bulychev1, P.A. Karagodin1,2, N.O. Pozhar1,2, M.N. Anufriev1,2 and A.K. Fedorov1,2 a)Corresponding author: [email protected] (E.O.K.) b)Corresponding author: [email protected] (A.K.F.) 1Russian Quantum Center, Skolkovo, Moscow 143025, Russia 2QApp, Skolkovo, Moscow 143025, Russia Abstract. Many commonly used public-key cryptosystems will become insecure once a scalable quantum computer is built. New cryptographic schemes that can guarantee protection against attacks with quantum computers, so-called post-quantum algorithms, have emerged in recent decades. One of the most promising candidates for a post-quantum signature scheme is SPHINCS+, which is based on cryptographic hash functions. In this contribution, we analyze the use of the new Russian standardized hash function, known as Streebog, for the implementation of the SPHINCS+ signature scheme. We provide a performance comparison with SHA-256-based instantiation and give benchmarks for various sets of parameters. Introduction Public-key cryptography is a cornerstone of internet security. Quantum computers possess a threat to the widely deployed public-key cryptography schemes, whose security is based on the computational complexity of certain tasks, such as integer factorization and discrete logarithm. Shor’s quantum algorithm [1] and variational quantum factor- ing [2] would allow one to solve these tasks with a significant boost [3]. Quantum computers have less of an effect on symmetric cryptography since Shor’s algorithm does not apply for their cryptoanalysis. Nevertheless, Grover’s algorithm [4] would allow quantum computers a quadratic speedup in brute force attacks.
    [Show full text]