DOCSLIB.ORG

Selecting Elliptic Curves for Cryptography: an Efficiency And

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Selecting Elliptic Curves for Cryptography: an Efficiency And Noname manuscript No. (will be inserted by the editor) and 1:24 times faster than the new Weierstrass curves at the 128-, 192- and 256-bit security levels, respectively. Finally, we discuss how these curves behave in a real- world protocol by considering different scalar multipli- cation scenarios in the transport layer security (TLS) Selecting Elliptic Curves for protocol. The proposed curves and the results of the Cryptography: An Efficiency analysis are intended to contribute to the recent efforts towards recommending new elliptic curves for Internet and Security Analysis standards. Joppe W. Bos · Craig Keywords Elliptic curves, Weierstrass form, twisted Costello · Patrick Edwards form, secure scalar multiplication, constant- Longa · Michael time execution, transport layer security (TLS) protocol. Naehrig Received: date / Accepted: date 1 Introduction The first release of a cryptographic standard specify- Abstract We select a set of elliptic curves for cryp- ing elliptic curves for use in practice dates back to tography and analyze our selection from a performance 2000 [21]. Nowadays, roughly one out of ten systems and security perspective. This analysis complements re- on the publicly observable Internet offers cipher suites cent curve proposals that suggest (twisted) Edwards in the Secure Shell (SSH) and Transport Layer Security curves by also considering the Weierstrass model. Work- (TLS) protocols that contain elliptic-curve-based cryp- ing with both Montgomery-friendly and pseudo-Merse- tographic algorithms [16]. Most elliptic curve standards nne primes allows us to consider more possibilities which recommend curves for different perceived security lev- help to improve the overall efficiency of base field arith- els that are either defined over prime fields or binary metic. Our Weierstrass curves are backwards compati- extension fields; on the Internet, however, the deployed ble with current implementations of prime order NIST curves are mostly defined over prime fields [16]. This curves, while providing improved efficiency and stronger can be partially explained by the increasing skepticism security properties. We choose algorithms and explicit towards the security of elliptic curves defined over bi- formulas to demonstrate that our curves support cons- nary extension fields (justified by recent progress on tant-time, exception-free scalar multiplications, thereby solving the discrete logarithm problem on such curves offering high practical security in cryptographic appli- [26]). Therefore, in this work, we only consider elliptic cations. Our implementation shows that variable-base curves defined over prime fields. scalar multiplication on the new Weierstrass curves at Recently, part of the cryptographic community has the 128-bit security level is about 1:4 times faster than been looking for alternatives to the currently deployed the recent implementation record on the corresponding elliptic curves that may offer better performance and NIST curve. For practitioners who are willing to use a provide stronger overall security (see for example an different curve model and sacrifice a few bits of security, evaluation of recent curve candidates in [12]). Most no- we present a collection of twisted Edwards curves with tably, the TLS working group has issued a formal re- particularly efficient arithmetic that are up to 1:42, 1:26 quest to the Crypto Forum Research Group (CFRG) asking for recommendations for new elliptic curves. The Joppe W. Bos urge to change curves has been fueled by the recently NXP Semiconductors, Leuven, Belgium leaked NSA documents, which suggest the existence of E-mail: [email protected] a back door in the Dual Elliptic Curve Deterministic Craig Costello · Patrick Longa · Michael Naehrig Random Bit Generator [56]. Although cryptographers Microsoft Research, Redmond, USA have suspected this at least as early as in 2007 [53], Craig Costello these recent revelations have accelerated a controversy E-mail: [email protected] on whether the widely deployed NIST curves [58] should Patrick Longa be replaced by curves with a verifiably deterministic E-mail: [email protected] generation. Besides such security concerns, there has Michael Naehrig been significant progress related to both efficiency and E-mail: [email protected] security since the initial standardization of elliptic curve 2 Joppe W. Bos et al. cryptography. Notable examples are algorithms protected posal projects (either because they are overlooked or do against certain side-channel attacks, different “special” not fit the requirements set by the project). Our goal prime shapes which allow faster modular arithmetic, is to rigorously analyze all of these different aspects and a larger set of curve models from which to choose. from both a security and efficiency perspective, in hope For example, in 2007, Edwards [25] discovered an in- that this paper helps practitioners better understand teresting normal form for elliptic curves, now called (and correctly implement) the choices that lie in front the Edwards model, which was introduced to crypto- of them. Abandoning a set of standard curves demands graphic applications by Bernstein and Lange [11]. A a judicious selection of new curves, since this cannot be generalization of this curve model, known as the twisted done too frequently if widespread adoption is desired. Edwards model [7], facilitates the most efficient curve In that light, it is our opinion that one should consider arithmetic [35]. Such (twisted) Edwards curves also have all of the options available. For example, in contrast other attractive properties: they may be selected to sup- to [12,3], our selection includes prime order Weierstrass port a complete addition law and are compatible with curves. Just as the almost-prime order twisted Edwards the Montgomery model, which supports efficient Mont- curves have their practical advantages, we argue that gomery ladder computations [47]. However, twisted Ed- there are also benefits to choosing prime order Weier- wards curves cannot have a prime number of rational strass curves: the absence of small torsion simplifies the points over the base field, and they are therefore incom- point/input validation process, and (over a prime field patible with the prime-order Weierstrass curves used in of fixed length) does not sacrifice any bits of security all of the current cryptographic standards [21,48,58]. with respect to attacks on the underlying elliptic curve discrete logarithm problem (ECDLP). In addition, such Related Work. The NIST curves [58] have been in- curves are backwards compatible with current imple- cluded in numerous standards (e.g. [21,48]) and are mentations supporting NIST curves over prime fields deployed in many security protocols. The most recent (i.e., no changes are required in protocols), and could speed record on the NIST curve which aims to provide be integrated into existing implementations by simply 128-bit security is due to Gueron and Krasnov [31]. changing the curve constant and (in some cases) field Alternatives to the NIST curves have been suggested arithmetic1. by the German working group Brainpool [24]; their We investigate the selection of prime moduli that curve choices followed additional security requirements, allow efficient modular arithmetic. As in [5,35,42,15, one of which demands verifiably pseudo-random curve 12,3], we study pseudo-Mersenne primes of the form generation. Another alternative curve has been pro- 2α − γ, but also primes of the form 2α(2β − γ) − 1 that posed by Bernstein [5]; this is a Montgomery curve, can be used to accelerate Montgomery arithmetic [46] called Curve25519, which allows efficient computation as used in [32,15]. Following the deterministic selec- of ECDH using the Montgomery ladder at the 128-bit tion requirement from [12], we pick two primes of each security level. It was later shown by Bernstein et al. [9] shape for a given targeted security level: one prime is that a twisted Edwards curve, birationally equivalent to selected to be slightly smaller than the other, which Curve25519, can be used for efficient elliptic curve sig- sacrifices a small amount of ECDLP security in favor of nature generation and verification. Recently, Bernstein enhanced performance. Note that, as explained in Sec- and Lange started a project to select and analyze se- tion 2, for practical considerations we require all primes cure elliptic curves for use in cryptography: see [12] for to be congruent to 3 modulo 4. These primes are used to a list of the security assessments the project performs construct cryptographically suitable curves focusing on and the requirements it imposes. A range of curves, tar- (arguably) the two most relevant curve models: short geting different security levels, is also presented in [12]. Weierstrass curves with the curve parameter a set to Following this, several new curves satisfying the require- −3 and twisted Edwards curves with the curve param- ments from [12], which facilitate both the twisted Ed- eter a set to −1. The prime order Weierstrass curves wards and Montgomery form, were proposed by Aranha give full ECDLP security over prime fields of a fixed et al. [3]. bitlength, while offering good practical performance. On the other hand, the twisted Edwards curves sacrifice Motivation and Rationale. The new curves presented a small amount of ECDLP security but facilitate the in [12,3] are all efficient and secure elliptic curves ready fastest realization of curve arithmetic [35]. Both types to be used in cryptography. This prompts the question of curves are selected in a deterministic fashion (see Sec- as to why we should perform an efficiency and secu- rity analysis for a set of new curves. It is our opinion 1 Cryptographic libraries with support for generic-prime that not all options for prime fields and elliptic curve field arithmetic (e.g., using Montgomery arithmetic) are fully models have been considered in the recent curve pro- compatible with the proposed curves. Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis 3 tion 3 for the full details) and offer twist-security [5], a friendly primes whose bitlengths match those of the property which is useful in certain scenarios.
Load more

Recommended publications
  • Cryptography in Modern World
    Cryptography in Modern World Julius O. Olwenyi, Aby Tino Thomas, Ayad Barsoum* St. Mary’s University, San Antonio, TX (USA) Emails: [email protected], [email protected], [email protected] Abstract — Cryptography and Encryption have been where a letter in plaintext is simply shifted 3 places down used for secure communication. In the modern world, the alphabet [4,5]. cryptography is a very important tool for protecting information in computer systems. With the invention ABCDEFGHIJKLMNOPQRSTUVWXYZ of the World Wide Web or Internet, computer systems are highly interconnected and accessible from DEFGHIJKLMNOPQRSTUVWXYZABC any part of the world. As more systems get interconnected, more threat actors try to gain access The ciphertext of the plaintext “CRYPTOGRAPHY” will to critical information stored on the network. It is the be “FUBSWRJUASLB” in a Caesar cipher. responsibility of data owners or organizations to keep More recent derivative of Caesar cipher is Rot13 this data securely and encryption is the main tool used which shifts 13 places down the alphabet instead of 3. to secure information. In this paper, we will focus on Rot13 was not all about data protection but it was used on different techniques and its modern application of online forums where members could share inappropriate cryptography. language or nasty jokes without necessarily being Keywords: Cryptography, Encryption, Decryption, Data offensive as it will take those interested in those “jokes’ security, Hybrid Encryption to shift characters 13 spaces to read the message and if not interested you do not need to go through the hassle of converting the cipher. I. INTRODUCTION In the 16th century, the French cryptographer Back in the days, cryptography was not all about Blaise de Vigenere [4,5], developed the first hiding messages or secret communication, but in ancient polyalphabetic substitution basically based on Caesar Egypt, where it began; it was carved into the walls of cipher, but more difficult to crack the cipher text.
    [Show full text]
  • A Review on Elliptic Curve Cryptography for Embedded Systems
    International Journal of Computer Science & Information Technology (IJCSIT), Vol 3, No 3, June 2011 A REVIEW ON ELLIPTIC CURVE CRYPTOGRAPHY FOR EMBEDDED SYSTEMS Rahat Afreen 1 and S.C. Mehrotra 2 1Tom Patrick Institute of Computer & I.T, Dr. Rafiq Zakaria Campus, Rauza Bagh, Aurangabad. (Maharashtra) INDIA [email protected] 2Department of C.S. & I.T., Dr. B.A.M. University, Aurangabad. (Maharashtra) INDIA [email protected] ABSTRACT Importance of Elliptic Curves in Cryptography was independently proposed by Neal Koblitz and Victor Miller in 1985.Since then, Elliptic curve cryptography or ECC has evolved as a vast field for public key cryptography (PKC) systems. In PKC system, we use separate keys to encode and decode the data. Since one of the keys is distributed publicly in PKC systems, the strength of security depends on large key size. The mathematical problems of prime factorization and discrete logarithm are previously used in PKC systems. ECC has proved to provide same level of security with relatively small key sizes. The research in the field of ECC is mostly focused on its implementation on application specific systems. Such systems have restricted resources like storage, processing speed and domain specific CPU architecture. KEYWORDS Elliptic curve cryptography Public Key Cryptography, embedded systems, Elliptic Curve Digital Signature Algorithm ( ECDSA), Elliptic Curve Diffie Hellman Key Exchange (ECDH) 1. INTRODUCTION The changing global scenario shows an elegant merging of computing and communication in such a way that computers with wired communication are being rapidly replaced to smaller handheld embedded computers using wireless communication in almost every field. This has increased data privacy and security requirements.
    [Show full text]
  • Choosing Key Sizes for Cryptography
    information security technical report 15 (2010) 21e27 available at www.sciencedirect.com www.compseconline.com/publications/prodinf.htm Choosing key sizes for cryptography Alexander W. Dent Information Security Group, University Of London, Royal Holloway, UK abstract After making the decision to use public-key cryptography, an organisation still has to make many important decisions before a practical system can be implemented. One of the more difficult challenges is to decide the length of the keys which are to be used within the system: longer keys provide more security but mean that the cryptographic operation will take more time to complete. The most common solution is to take advice from information security standards. This article will investigate the methodology that is used produce these standards and their meaning for an organisation who wishes to implement public-key cryptography. ª 2010 Elsevier Ltd. All rights reserved. 1. Introduction being compromised by an attacker). It also typically means a slower scheme. Most symmetric cryptographic schemes do The power of public-key cryptography is undeniable. It is not allow the use of keys of different lengths. If a designer astounding in its simplicity and its ability to provide solutions wishes to offer a symmetric scheme which provides different to many seemingly insurmountable organisational problems. security levels depending on the key size, then the designer However, the use of public-key cryptography in practice is has to construct distinct variants of a central design which rarely as simple as the concept first appears. First one has to make use of different pre-specified key lengths.
    [Show full text]
  • Cryptographic Control Standard, Version
    Nuclear Regulatory Commission Office of the Chief Information Officer Computer Security Standard Office Instruction: OCIO-CS-STD-2009 Office Instruction Title: Cryptographic Control Standard Revision Number: 2.0 Issuance: Date of last signature below Effective Date: October 1, 2017 Primary Contacts: Kathy Lyons-Burke, Senior Level Advisor for Information Security Responsible Organization: OCIO Summary of Changes: OCIO-CS-STD-2009, “Cryptographic Control Standard,” provides the minimum security requirements that must be applied to the Nuclear Regulatory Commission (NRC) systems which utilize cryptographic algorithms, protocols, and cryptographic modules to provide secure communication services. This update is based on the latest versions of the National Institute of Standards and Technology (NIST) Guidance and Federal Information Processing Standards (FIPS) publications, Committee on National Security System (CNSS) issuances, and National Security Agency (NSA) requirements. Training: Upon request ADAMS Accession No.: ML17024A095 Approvals Primary Office Owner Office of the Chief Information Officer Signature Date Enterprise Security Kathy Lyons-Burke 09/26/17 Architecture Working Group Chair CIO David Nelson /RA/ 09/26/17 CISO Jonathan Feibus 09/26/17 OCIO-CS-STD-2009 Page i TABLE OF CONTENTS 1 PURPOSE ............................................................................................................................. 1 2 INTRODUCTION ..................................................................................................................
    [Show full text]
  • SHA-3 and the Hash Function Keccak
    Christof Paar Jan Pelzl SHA-3 and The Hash Function Keccak An extension chapter for “Understanding Cryptography — A Textbook for Students and Practitioners” www.crypto-textbook.com Springer 2 Table of Contents 1 The Hash Function Keccak and the Upcoming SHA-3 Standard . 1 1.1 Brief History of the SHA Family of Hash Functions. .2 1.2 High-level Description of Keccak . .3 1.3 Input Padding and Generating of Output . .6 1.4 The Function Keccak- f (or the Keccak- f Permutation) . .7 1.4.1 Theta (q)Step.......................................9 1.4.2 Steps Rho (r) and Pi (p).............................. 10 1.4.3 Chi (c)Step ........................................ 10 1.4.4 Iota (i)Step......................................... 11 1.5 Implementation in Software and Hardware . 11 1.6 Discussion and Further Reading . 12 1.7 Lessons Learned . 14 Problems . 15 References ......................................................... 17 v Chapter 1 The Hash Function Keccak and the Upcoming SHA-3 Standard This document1 is a stand-alone description of the Keccak hash function which is the basis of the upcoming SHA-3 standard. The description is consistent with the approach used in our book Understanding Cryptography — A Textbook for Students and Practioners [11]. If you own the book, this document can be considered “Chap- ter 11b”. However, the book is most certainly not necessary for using the SHA-3 description in this document. You may want to check the companion web site of Understanding Cryptography for more information on Keccak: www.crypto-textbook.com. In this chapter you will learn: A brief history of the SHA-3 selection process A high-level description of SHA-3 The internal structure of SHA-3 A discussion of the software and hardware implementation of SHA-3 A problem set and recommended further readings 1 We would like to thank the Keccak designers as well as Pawel Swierczynski and Christian Zenger for their extremely helpful input to this document.
    [Show full text]
  • Eurocrypt 2013 Athens, Greece, May 28Th, 2013
    Keccak Guido Bertoni1 Joan Daemen1 Michaël Peeters2 Gilles Van Assche1 1STMicroelectronics 2NXP Semiconductors Eurocrypt 2013 Athens, Greece, May 28th, 2013 1 / 57 Symmetric crypto: what textbooks and intro’s say Symmetric cryptographic primitives: Block ciphers Stream ciphers Hash functions And their modes-of-use Picture by GlasgowAmateur 2 / 57 Outline 1 The sponge construction 2 Inside Keccak 3 Outside Keccak (using sponge and duplex) 4 Keccak towards the SHA-3 standard 5 Further inside Keccak 3 / 57 The sponge construction Outline 1 The sponge construction 2 Inside Keccak 3 Outside Keccak (using sponge and duplex) 4 Keccak towards the SHA-3 standard 5 Further inside Keccak 4 / 57 The sponge construction Our beginning: RadioGatún Initiative to design hash/stream function (late 2005) rumours about NIST call for hash functions forming of Keccak Team starting point: fixing Panama [Daemen, Clapp, FSE 1998] RadioGatún [Keccak team, NIST 2nd hash workshop 2006] more conservative than Panama arbitrary output length primitive expressing security claim for arbitrary output length primitive Sponge functions [Keccak team, Ecrypt hash, 2007] … closest thing to a random oracle with a finite state … Sponge construction calling random permutation 5 / 57 The sponge construction The sponge construction More general than a hash function: arbitrary-length output Calls a b-bit permutation f, with b = r + c r bits of rate c bits of capacity (security parameter) 6 / 57 The sponge construction Generic security of the sponge construction Theorem (Indifferentiability of the sponge construction) The sponge construction calling a random permutation, S0[F], is 2 (tD, tS, N, e)-indifferentiable from a random oracle, for any tD, tS = O(N ), c e e ≈ N N < 2 and for any with > fP(N) 2c+1 .
    [Show full text]
  • Broad View of Cryptographic Hash Functions
    IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 4, No 1, July 2013 ISSN (Print): 1694-0814 | ISSN (Online): 1694-0784 www.IJCSI.org 239 Broad View of Cryptographic Hash Functions 1 2 Mohammad A. AlAhmad , Imad Fakhri Alshaikhli 1 Department of Computer Science, International Islamic University of Malaysia, 53100 Jalan Gombak Kuala Lumpur, Malaysia, 2 Department of Computer Science, International Islamic University of Malaysia, 53100 Jalan Gombak Kuala Lumpur, Malaysia Abstract Cryptographic hash function is a function that takes an arbitrary length as an input and produces a fixed size of an output. The viability of using cryptographic hash function is to verify data integrity and sender identity or source of information. This paper provides a detailed overview of cryptographic hash functions. It includes the properties, classification, constructions, attacks, applications and an overview of a selected dedicated cryptographic hash functions. Keywords-cryptographic hash function, construction, attack, classification, SHA-1, SHA-2, SHA-3. Figure 1. Classification of cryptographic hash function 1. INTRODUCTION CRHF usually deals with longer length hash values. An A cryptographic hash function H is an algorithm that takes an unkeyed hash function is a function for a fixed positive integer n * arbitrary length of message as an input {0, 1} and produce a which has, as a minimum, the following two properties: n fixed length of an output called message digest {0, 1} 1) Compression: h maps an input x of arbitrary finite bit (sometimes called an imprint, digital fingerprint, hash code, hash length, to an output h(x) of fixed bit length n.
    [Show full text]
  • Security Analysis of SHA-256 and Sisters
    Security Analysis of SHA-256 and Sisters Henri Gilbert1 and Helena Handschuh2 1 France T´el´ecom R&D, FTRD/DTL/SSR 38-40 Rue du G´en´eral Leclerc, F-92131 Issy-Les Moulineaux [email protected] 2 GEMPLUS, Security Technologies Department 34 Rue Guynemer, F-92447 Issy-les-Moulineaux [email protected] Abstract. This paper studies the security of SHA-256, SHA-384 and SHA-512 against collision attacks and provides some insight into the security properties of the basic building blocks of the structure. It is concluded that neither Chabaud and Joux’s attack, nor Dobbertin-style attacks apply. Differential and linear attacks also don’t apply on the underlying structure. However we show that slightly simplified versions of the hash functions are surprisingly weak : whenever symmetric con- stants and initialization values are used throughout the computations, and modular additions are replaced by exclusive or operations, sym- metric messages hash to symmetric digests. Therefore the complexity of collision search on these modified hash functions potentially becomes as low as one wishes. 1 Introduction A cryptographic hash function can be informally defined as an easy to compute but hard to invert function which maps a message of arbitrary length into a fixed length (m-bit) hash value, and satisfies the property that finding a collision, i.e. two messages with the same hash value, is computationally infeasible. Most collision resistant hash function candidates proposed so far are based upon the iterated use of a so-called compression function, which maps a fixed-length (m+ n-bit) input value into a shorter fixed-length m-bit output value.
    [Show full text]
  • Modified SHA1: a Hashing Solution to Secure Web Applications Through Login Authentication
    36 International Journal of Communication Networks and Information Security (IJCNIS) Vol. 11, No. 1, April 2019 Modified SHA1: A Hashing Solution to Secure Web Applications through Login Authentication Esmael V. Maliberan Graduate Studies, Surigao del Sur State University, Philippines Abstract: The modified SHA1 algorithm has been developed by attack against the SHA-1 hash function, generating two expanding its hash value up to 1280 bits from the original size of different PDF files. The research study conducted by [9] 160 bit. This was done by allocating 32 buffer registers for presented a specific freestart identical pair for SHA-1, i.e. a variables A, B, C and D at 5 bytes each. The expansion was done by collision within its compression function. This was the first generating 4 buffer registers in every round inside the compression appropriate break of the SHA-1, extending all 80 out of 80 function for 8 times. Findings revealed that the hash value of the steps. This attack was performed for only 10 days of modified algorithm was not cracked or hacked during the experiment and testing using powerful online cracking tool, brute computation on a 64-GPU. Thus, SHA1 algorithm is not force and rainbow table such as Cracking Station and Rainbow anymore safe in login authentication and data transfer. For Crack and bruteforcer which are available online thus improved its this reason, there were enhancements and modifications security level compared to the original SHA1. being developed in the algorithm in order to solve these issues [10, 11]. [12] proposed a new approach to enhance Keywords: SHA1, hashing, client-server communication, MD5 algorithm combined with SHA compression function modified SHA1, hacking, brute force, rainbow table that produced a 256-bit hash code.
    [Show full text]
  • An Introduction to Cryptographic Security Methods and Their Role in Securing Low Resource Computing Devices
    An Introduction to Cryptographic Security Methods and Their Role in Securing Low Resource Computing Devices An Overview of Public-key Cryptosystems based on RSA, Diffie-Hellman and the Next Generation of Public Key Cryptographic Security for Low-Resource Computing Devices - the Algebraic Eraser™ SecureRF Corporation 100 Beard Sawmill Road Suite 350 Shelton, CT 06484 203-227-3151 [email protected] www.SecureRF.com An Introduction to Cryptographic Security Methods and Their Role in Securing Low-Resource Computing Devices 1. Introduction: The need for secure communications dates back to antiquity. Whether we are looking at the 5000 year old cylinder seals of ancient Mesopotamia, which were used for authentication, or the Caesar cipher, which was used to protect military messages, a theme quickly emerges: information needs to be secured. There are two distinct paradigms for approaching security. One is the symmetric or private key path, which can be viewed as a descendant of the very early attempts at security. Any such system assumes that, if two individuals wish to communicate securely, they must both possess a unique common secret key, which is used for both encryption and decryption. While many such systems have evolved over time, it is this very assumption, and the difficulties of sharing and distributing the common key and keeping it a secret, that leads to their vulnerability and the need for a new paradigm. By the early 1970’s a significantly new and different perspective on security began to take shape contributing to the emergence of public-key cryptography. Public-key cryptosystems themselves fall into two categories: the Diffie-Hellman protocol published by Whitfield Diffie and Martin Hellman in 1976, and the RSA protocol, as publicly described by Ron Rivest, Adi Shamir, and Leonard Adleman in 1978.
    [Show full text]
  • Physical Security of Elliptic Curve Cryptography Cédric Murdica
    Physical security of elliptic curve cryptography Cédric Murdica To cite this version: Cédric Murdica. Physical security of elliptic curve cryptography. Cryptography and Security [cs.CR]. Télécom ParisTech, 2014. English. NNT : 2014ENST0008. tel-01179584 HAL Id: tel-01179584 https://pastel.archives-ouvertes.fr/tel-01179584 Submitted on 23 Jul 2015 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. N°:N° : 20092 00 9 ENAMEN AM XXXXXX XX 2014-ENST-0008 EDITE ED 130 Doctorat ParisTech T H È S E pour obtenir le grade de docteur délivré par Télécom ParisTech Spécialité “ Électronique et Communications ” présentée et soutenue publiquement par Cédric MURDICA le 13 février 2014 Sécurité Physique de la Cryptographie sur Courbes Elliptiques Directeurs de thèse : Philippe HOOGVORST, David NACCACHE Co-encadrement de la thèse : Jean-Luc DANGER T Jury M. Pierre-Alain FOUQUE , Professeur, Université de Rennes I Président, Rapporteur H M. Jean-Sébastien CORON , Maître de Conférences, Université du Luxembourg Rapporteur M. Jean-Jacques QUISQUATER , Professeur, Université Catholique de Louvain Examinateur È M. Philippe NGUYEN , Directeur Technique, Secure-IC Examinateur M. Sylvain GUILLEY , Professeur Associé, Télécom ParisTech Invité S E Télécom ParisTech école de l’Institut Mines Télécom – membre de ParisTech 46, rue Barrault – 75634 Paris Cedex 13 – Tél.
    [Show full text]
  • Secure Hash Algorithm-3 Cryptographic Hash Functions
    Secure Hash Algorithm-3 Cryptographic Hash Functions SHA-3 is a cryptographic hash function (designed by Guido Bertoni, Joan Daemen, Michaël Peeters and Gilles Van Assche) A cryptographic hash function takes an arbitrary block of data (message) and returns a fixed-size bit string (hash value) H : {0, 1}* --> {0,1}n Hash functions provides integrity and has applications in digital signatures, message authentication codes,etc. Need for SHA-3 Widespread Hash functions before 2004: MD4, MD5, RIPE-MD, RIPE-MD160, SHA0, SHA1, SHA2 • 1991-1993: Den Boer and Bosselaers attack MD4 and MD5 • 1996: Dobbertin improves attacks on MD4 and MD5 • 1998: Chabaud and Joux attack SHA-0 • 2004: Joux et al. break SHA-0 • 2004: Wang et al. break MD5 • 2005: Lenstra et al., and Klima, make MD5 attack practical • 2005: Wang et al. theoretically break SHA-1 • 2006: De Cannière and Rechberger further break SHA-1 Cypto 2004 In the conference, Joux shows a surprising property in Merkle-Damgaard hashes ►Multicollisions ►Cascaded hashes don’t help security much Wang, Feng, Lai, and Yu found a collison attack on SHA-0 with complexity of 2^40. Attacks on MD4, MD5 and RIPEMD were also found. Biham/Chen announced new results in cryptanalyzing SHA-1, including a collision attack in a reduced-round version of SHA-1. Wang's algorithm was extended to find collision in SHA-1 in 2^63 steps in 2005. Need for SHA3 and the NIST competition Algorithm Ouput size Collision attack Second Preimage (in bits) preimage attack attack MD5 128 Yes (2^20.96) Yes (2^123.4) Yes (2^123.4) SHA-0
    [Show full text]