IEEE P1363.2: Password-Based Cryptography
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Efficient Implementation of Elliptic Curve Cryptography in Reconfigurable Hardware
EFFICIENT IMPLEMENTATION OF ELLIPTIC CURVE CRYPTOGRAPHY IN RECONFIGURABLE HARDWARE by E-JEN LIEN Submitted in partial fulfillment of the requirements for the degree of Master of Science Thesis Advisor: Dr. Swarup Bhunia Department of Electrical Engineering and Computer Science CASE WESTERN RESERVE UNIVERSITY May, 2012 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of _____________________________________________________E-Jen Lien candidate for the ______________________degreeMaster of Science *. Swarup Bhunia (signed)_______________________________________________ (chair of the committee) Christos Papachristou ________________________________________________ Frank Merat ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ (date) _______________________03/19/2012 *We also certify that written approval has been obtained for any proprietary material contained therein. To my family ⋯ Contents List of Tables iii List of Figures v Acknowledgements vi List of Abbreviations vii Abstract viii 1 Introduction 1 1.1 Research objectives . .1 1.2 Thesis Outline . .3 1.3 Contributions . .4 2 Background and Motivation 6 2.1 MBC Architecture . .6 2.2 Application Mapping to MBC . .7 2.3 FPGA . .9 2.4 Mathematical Preliminary . 10 2.5 Elliptic Curve Cryptography . 10 2.6 Motivation . 16 i 3 Design Principles and Methodology 18 3.1 Curves over Prime Field . 18 3.2 Curves over Binary Field . 25 3.3 Software Code for ECC . 31 3.4 RTL code for FPGA design . 31 3.5 Input Data Flow Graph (DFG) for MBC . 31 4 Implementation of ECC 32 4.1 Software Implementation . 32 4.1.1 Prime Field . 33 4.1.2 Binary Field . 34 4.2 Implementation in FPGA . 35 4.2.1 Prime Field . 36 4.2.2 Binary Field . -
A High-Speed Constant-Time Hardware Implementation of Ntruencrypt SVES
A High-Speed Constant-Time Hardware Implementation of NTRUEncrypt SVES Farnoud Farahmand, Malik Umar Sharif, Kevin Briggs, Kris Gaj Department of Electrical and Computer Engineering, George Mason University, Fairfax, VA, U.S.A. fffarahma, msharif2, kbriggs2, [email protected] process a year later. Among the candidates, there are new, Abstract—In this paper, we present a high-speed constant- substantially modified versions of NTRUEncrypt. However, in time hardware implementation of NTRUEncrypt Short Vector an attempt to characterize an already standardized algorithm, Encryption Scheme (SVES), fully compliant with the IEEE 1363.1 Standard Specification for Public Key Cryptographic Techniques in this paper, we focus on the still unbroken version of the Based on Hard Problems over Lattices. Our implementation algorithm published in 2008. We are not aware of any previous follows an earlier proposed Post-Quantum Cryptography (PQC) high-speed hardware implementation of the entire NTRUEn- Hardware Application Programming Interface (API), which crypt SVES scheme reported in the scientific literature or facilitates its fair comparison with implementations of other available commercially. Our implementation is also unique in PQC schemes. The paper contains the detailed flow and block diagrams, timing analysis, as well as results in terms of latency (in that it is the first implementation of any PQC scheme following clock cycles), maximum clock frequency, and resource utilization our newly proposed PQC Hardware API [3]. As such, it in modern high-performance Field Programmable Gate Arrays provides a valuable reference for any future implementers of (FPGAs). Our design takes full advantage of the ability to paral- PQC schemes, which is very important in the context of the lelize the major operation of NTRU, polynomial multiplication, in ongoing NIST standard candidate evaluation process. -
Speke Cycle Route
www.LetsTravelWise.org 1253 330 0151 Telephone: need. might you else 090305/IS/TM/08O9/P anything and times, the through you talk will bike. by easily more Speke around get and person local a – 33 22 200 0871 travel to way wiser a is cycling how shows leaflet This future. our and us on Traveline call want, for move wise a is out them trying Merseyside, in options of lots have We Updated you train or bus which out find To Getting around Speke on your bike your on Speke around Getting September journey. each making of way Manchester. best the about think to need all we cities big other in seen pollution and and Widnes Warrington, in stations 2011. congestion the avoid to want we If slower. getting is travel car meaning Cycle Speke Cycle for outwards and Centre City the in MA. rapidly, rising is Merseyside in car by made being trips of number the Central Liverpool and Street Lime but journeys, their of many or all for TravelWise already are people Most Liverpool towards stations rail Cross Hunts and Parkway South Liverpool from both operate trains Line City and Northern Frequent Centre. City car. a without journeys make the to Parkway South Liverpool from minutes 15 to 10 about takes only It to everyone for easier it make to aim we Merseytravel, and Authorities Local Merseyside the by Funded sharing. car and transport public cycling, trains. Merseyside walking, more – travel sustainable more encourage to aims TravelWise all on free go Bikes problem. a be can parking where Centre City Liverpool into travelling when or workplace, your or school to get to easier it makes www.transpenninetrail.org.uk Web: This way. -
FIDO Technical Glossary
Client to Authenticator Protocol (CTAP) Implementation Draft, February 27, 2018 This version: https://fidoalliance.org/specs/fido-v2.0-id-20180227/fido-client-to-authenticator-protocol-v2.0-id- 20180227.html Previous Versions: https://fidoalliance.org/specs/fido-v2.0-ps-20170927/ Issue Tracking: GitHub Editors: Christiaan Brand (Google) Alexei Czeskis (Google) Jakob Ehrensvärd (Yubico) Michael B. Jones (Microsoft) Akshay Kumar (Microsoft) Rolf Lindemann (Nok Nok Labs) Adam Powers (FIDO Alliance) Johan Verrept (VASCO Data Security) Former Editors: Matthieu Antoine (Gemalto) Vijay Bharadwaj (Microsoft) Mirko J. Ploch (SurePassID) Contributors: Jeff Hodges (PayPal) Copyright © 2018 FIDO Alliance. All Rights Reserved. Abstract This specification describes an application layer protocol for communication between a roaming authenticator and another client/platform, as well as bindings of this application protocol to a variety of transport protocols using different physical media. The application layer protocol defines requirements for such transport protocols. Each transport binding defines the details of how such transport layer connections should be set up, in a manner that meets the requirements of the application layer protocol. Table of Contents 1 Introduction 1.1 Relationship to Other Specifications 2 Conformance 3 Protocol Structure 4 Protocol Overview 5 Authenticator API 5.1 authenticatorMakeCredential (0x01) 5.2 authenticatorGetAssertion (0x02) 5.3 authenticatorGetNextAssertion (0x08) 5.3.1 Client Logic 5.4 authenticatorGetInfo (0x04) -
White-Box Implementation of the Identity-Based Signature Scheme in the IEEE P1363 Standard for Public Key Cryptography
IEICE TRANS. INF. & SYST., VOL.E103–D, NO.2 FEBRUARY 2020 188 INVITED PAPER Special Section on Security, Privacy, Anonymity and Trust in Cyberspace Computing and Communications White-Box Implementation of the Identity-Based Signature Scheme in the IEEE P1363 Standard for Public Key Cryptography Yudi ZHANG†,††, Debiao HE†,††a), Xinyi HUANG†††,††††, Ding WANG††,†††††, Kim-Kwang Raymond CHOO††††††, Nonmembers, and Jing WANG†,††, Student Member SUMMARY Unlike black-box cryptography, an adversary in a white- box security model has full access to the implementation of the crypto- graphic algorithm. Thus, white-box implementation of cryptographic algo- rithms is more practical. Nevertheless, in recent years, there is no white- box implementation for public key cryptography. In this paper, we propose Fig. 1 A typical DRM architecture the first white-box implementation of the identity-based signature scheme in the IEEE P1363 standard. Our main idea is to hide the private key to multiple lookup tables, so that the private key cannot be leaked during the algorithm executed in the untrusted environment. We prove its security in both black-box and white-box models. We also evaluate the performance gram. However, the adversary does not have the permis- of our white-box implementations, in order to demonstrate utility for real- sion to access the internal process of the program’s execu- world applications. tion. In practice, an adversary can also observe and mod- key words: white-box implementation, white-box security, IEEE P1363, ify the algorithm’s implementation to obtain the internal de- identity-based signature, key extraction tails, such as the secret key. -
IEEE P1363.3 Standard Specifications for Public Key Cryptography
IEEE P1363.3 D1 IBKAS January 29, 2008 IEEE P1363.3 Standard Specifications for Public Key Cryptography: Identity Based Key Agreement Scheme (IBKAS) Abstract. This document specifies pairing based, identity based, and authenticated key agreement techniques. One of the advantages of Identity Based key agreement techniques is that there is no public key transmission and verification needed. Contents 1. DEFINITIONS ......................................................................................................................................... 2 2. TYPES OF CRYPTOGRAPHIC TECHNIQUES ................................................................................ 2 2.1 GENERAL MODEL .................................................................................................................................. 2 2.2 PRIMITIVES............................................................................................................................................ 2 2.3 SCHEMES ............................................................................................................................................... 3 2.4 ADDITIONAL METHODS ......................................................................................................................... 3 2.5 TABLE SUMMARY.................................................................................................................................. 3 3. PRIMITIVES FOR IDENTITY BASED KEY AGREEMENT PROBLEM...................................... 4 3.1 PRIMITIVES BORROWED FROM -
Analysing and Patching SPEKE in ISO/IEC
1 Analysing and Patching SPEKE in ISO/IEC Feng Hao, Roberto Metere, Siamak F. Shahandashti and Changyu Dong Abstract—Simple Password Exponential Key Exchange reported. Over the years, SPEKE has been used in several (SPEKE) is a well-known Password Authenticated Key Ex- commercial applications: for example, the secure messaging change (PAKE) protocol that has been used in Blackberry on Blackberry phones [11] and Entrust’s TruePass end-to- phones for secure messaging and Entrust’s TruePass end-to- end web products. It has also been included into international end web products [16]. SPEKE has also been included into standards such as ISO/IEC 11770-4 and IEEE P1363.2. In the international standards such as IEEE P1363.2 [22] and this paper, we analyse the SPEKE protocol as specified in the ISO/IEC 11770-4 [24]. ISO/IEC and IEEE standards. We identify that the protocol is Given the wide usage of SPEKE in practical applications vulnerable to two new attacks: an impersonation attack that and its inclusion in standards, we believe a thorough allows an attacker to impersonate a user without knowing the password by launching two parallel sessions with the victim, analysis of SPEKE is both necessary and important. In and a key-malleability attack that allows a man-in-the-middle this paper, we revisit SPEKE and its variants specified in (MITM) to manipulate the session key without being detected the original paper [25], the IEEE 1363.2 [22] and ISO/IEC by the end users. Both attacks have been acknowledged by 11770-4 [23] standards. -
Education in Uganda
0E-14103 Bulletin 1964, No. 32 Education in Uganda by DAVID SCANLON Professor of International Education Teachers College, Columbia University In U.S.DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE Office of Education Foreword ASTRIKINGrTHENOMENON of the last few years has been the mounting interest among citizens of the United States in the developing areas of the worldparticularly per- haps the area of middle Africa.Since 1960 most of the coun- tries in this area have gained their independence and are confronting the great problems of nation building and economic development. The entireregionshowsbotha popular enthusiasm for education and a conviction among leaders that education is a key to economic and social developmentan enthusiasm and conviction almost unsurpassed anywhere else in the world. It is not, surprising, then, that during recent years an increas- ing number of Africans have come to study in the United States and hundreds of Americans have traveled in the opposite direc- tion to teach in African schools or otherwise help develop Afri- can educational systems.Administrators of American insti- tutions having African students, teachers of comparative education and social studies, persons engaged in programs for educational assistance in Africa, and others, have reflected a demand for basic information on the educational systems of that continent.This bulletin on education in Uganda is one response to the need. The author, Professor of International Education at Teachers College, Columbia University, spent several months in Uganda during academic year 1960-61 lecturing at the Institute of Edu- cation, Makerere College.During this period he consulted with educators, visited educational institutions, and gathered materials for the present study. -
The Martini Synch
The Martini Synch Darko Kirovski, Michael Sinclair, and David Wilson Microsoft Research Contact: {darkok,sinclair,dbwilson}@microsoft.com Technical Report MSR-TR-2007-123 September 2007 Microsoft Research One Microsoft Way Redmond, WA 98052, USA http://research.microsoft.com The Martini Synch Darko Kirovski, Michael Sinclair, and David Wilson Microsoft Research Abstract. Device pairing is a significant problem for a large class of increasingly popular resource-constrained wireless protocols such as BlueTooth. The objective of pairing is to establish a secure wireless communication channel between two specific devices without a public-key infrastructure, a secure near-field communi- cation channel, or electrical contact. We use a surprising user-device interaction as a solution to this problem. By adding an accelerometer, a device can sense its motion in a Cartesian space relative to the inertial space. The idea is to have two devices in a fixed, relative position to each other. Then, the joint object is moved randomly in 3D for several seconds. The unique motion generates approximately the same distinct signal at the accelerometers. The difference between the signals in the two inertially conjoined sensors should be relatively small under normal motion induced manually. The objective is to derive a deterministic key at both sides with maximized entropy that will be used as a private key for symmetric encryption. Currently, our prototype produces between 10–15 bits of entropy per second of usual manual motion using off-the-shelf components. Keywords: device pairing, key exchange, fuzzy hashing, error correction. 1 INTRODUCTION Establishing a secure session is one of the least efficiently resolved problems with mod- ern low-cost wireless protocols such as BlueTooth [1]. -
Eurocrypt'2000 Conference Report
Eurocrypt'2000 Conference Report May 15–18, 2000 Bruges Richard Graveman Telcordia Technologies Morristown, NJ USA [email protected] Welcome This was the nineteenth annual Eurocrypt conference. Thirty-nine out of 150 papers were accepted, and there were two invited talks along with the traditional rump session. About 480 participants from 39 countries were present. Bart Preneel was Program Chair. The Proceedings were published by Springer Verlag as Advances in Cryptology— Eurocrypt'98, Lecture Notes in Computer Science, Volume 1807, Bart Preneel, editor. Session 1: Factoring and Discrete Logarithm, Chair: Bart Preneel Factorization of a 512-bit RSA Modulus, Stefania Cavallar (CWI, The Netherlands), Bruce Dodson (Lehigh University, USA), Arjen K. Lenstra (Citibank, USA), Walter Lioen (CWI, The Netherlands), Peter L. Montgomery (Microsoft Research, USA and CWI, The Netherlands), Brian Murphy (The Australian National University, Australia), Herman te Riele (CWI, The Netherlands), Karen Aardal (Utrecht University, The Netherlands), Jeff Gilchrist (Entrust Technologies Ltd., Canada), Gérard Guillerm (École Polytechnique, France), Paul Leyland (Microsoft Research Ltd., UK), Joël Marchand (École Polytechnique/CNRS, France), François Morain (École Polytechnique, France), Alec Muffett (Sun Microsystems, UK), Chris and Craig Putnam (USA), Paul Zimmermann (Inria Lorraine and Loria, France) The authors factored the RSA challenge number RSA-512 with the general number field sieve (NFS). The algorithm has four steps: polynomial selection, sieving, linear algebra, and square root extraction. For N known to be composite, two irreducible polynomials with a common root mod N are needed. f1 (of degree 5 in this case) should have many roots modulo small primes as well as being as small as possible. -
H. Krawczyk, IBM Reasearch R. Barnes, O. Friel, Cisco N. Sullivan
OPAQUE IN TLS 1.3 NICK SULLIVAN H. Krawczyk, IBM Reasearch CLOUDFLARE R. Barnes, O. Friel, Cisco @GRITTYGREASE N. Sullivan, Cloudflare MODERN PASSWORD-BASED AUTHENTICATION IN TLS OPAQUE IN TLS 1.3 A SHORT HISTORY ▸ Password-based authentication ▸ * without sending the password to the server ▸ SRP (Secure Remote Password) — RFC 2945 ▸ aPAKE (Augmented Password-Authenticated Key Exchange) ▸ Widely implemented, used in Apple iCloud, ProtonMail, etc. ▸ Dragonfly — RFC 8492 ▸ SPEKE (Simple password exponential key exchange) derived ▸ Independent submission OPAQUE IN TLS 1.3 SRP IN TLS (RFC 5054) ▸ Salt sent in the clear ▸ Leads to pre-computation attack on password database ▸ Unsatisfying security analysis ▸ Finite fields only, no ECC ▸ Awkward fit for TLS 1.3 ▸ Needs missing messages (challenges outlined in draft-barnes-tls-pake) ▸ Post-handshake requires renegotiation OPAQUE A new methodology for designing secure aPAKEs OPAQUE IN TLS 1.3 OPAQUE OVERVIEW ▸ Methodology to combine an authenticated key exchange (such as TLS 1.3) with an OPRF (Oblivious Pseudo-Random Function) to get a Secure aPAKE ▸ Desirable properties ▸ Security proof ▸ Secure against pre-computation attacks ▸ Efficient implementation based on ECC OPAQUE IN TLS 1.3 OPAQUE DEPENDENCIES OVERVIEW ▸ Underlying cryptographic work in CFRG ▸ OPAQUE (draft-krawczyk-cfrg-opaque) ▸ OPRF (draft-sullivan-cfrg-voprf) ▸ Hash-to-curve (draft-irtf-cfrg-hash-to-curve) EC-OPRF FUNDAMENTALS FUNDAMENTAL COMPONENTS / TERMINOLOGY ▸ The OPRF protocol allows the client to obtain a value based on the password and the server’s private key without revealing the password to the server ▸ OPRF(pwd) is used to encrypt an envelope containing OPAQUE keys ▸ The client’s TLS 1.3-compatible private key ▸ The server’s TLS 1.3-compatible public key EC-OPRF FUNDAMENTALS FUNDAMENTAL COMPONENTS / TERMINOLOGY ▸ Prime order group ▸ e.g. -
A Low-Power Design for an Elliptic Curve Digital Signature Chip
A Low-Power Design for an Elliptic Curve Digital Signature Chip Richard Schroeppel, Cheryl Beaver, Rita Gonzales, Russell Miller, and Timothy Draelos Sandia National Laboratories Albuquerque, NM 87185-0785 {rschroe, cbeaver, ragonza, rdmille, tjdrael}@sandia.gov Abstract. We present a VHDL design that incorporates optimizations intended to provide digital signature generation with as little power, space, and time as possible. These three primary objectives of power, size, and speed must be balanced along with other important goals, including flexibility of the hardware and ease of use. The highest-level function offered by our hardware design is Elliptic Curve Optimal El Gamal digital signature generation. Our parameters are defined over the finite field GF (2178), which gives security that is roughly equivalent to that provided by 1500-bit RSA signatures. Our optimizations include using the point-halving algorithm for elliptic curves, field towers to speed up the finite field arithmetic in general, and further enhancements of basic finite field arithmetic operations. The result is a synthesized VHDL digital signature design (using a CMOS 0.5µm,5V ,25◦C library) of 191,000 gates that generates a signature in 4.4 ms at 20 MHz. Keywords: Digital Signature, Elliptic Curve, ECDSA, Optimal El Gamal, Characteristic 2, Field Towers, Trinomial Basis, Quadratic Equa- tion, Qsolve, Almost-Inverse Algorithm, Point Halving, Signed Sliding Window, GF(289), GF(2178), Hardware, VHDL, Low Power 1 Introduction While the value of elliptic curve arithmetic in enabling public-key cryptography to serve in resource-constrained environments is well accepted, efforts in cre- ative implementations continue to bear fruit.