Key Agreement Protocol Based on EC-MQV Algorithm for Cooperative Wireless
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Public Key Cryptography And
PublicPublic KeyKey CryptographyCryptography andand RSARSA Raj Jain Washington University in Saint Louis Saint Louis, MO 63130 [email protected] Audio/Video recordings of this lecture are available at: http://www.cse.wustl.edu/~jain/cse571-11/ Washington University in St. Louis CSE571S ©2011 Raj Jain 9-1 OverviewOverview 1. Public Key Encryption 2. Symmetric vs. Public-Key 3. RSA Public Key Encryption 4. RSA Key Construction 5. Optimizing Private Key Operations 6. RSA Security These slides are based partly on Lawrie Brown’s slides supplied with William Stallings’s book “Cryptography and Network Security: Principles and Practice,” 5th Ed, 2011. Washington University in St. Louis CSE571S ©2011 Raj Jain 9-2 PublicPublic KeyKey EncryptionEncryption Invented in 1975 by Diffie and Hellman at Stanford Encrypted_Message = Encrypt(Key1, Message) Message = Decrypt(Key2, Encrypted_Message) Key1 Key2 Text Ciphertext Text Keys are interchangeable: Key2 Key1 Text Ciphertext Text One key is made public while the other is kept private Sender knows only public key of the receiver Asymmetric Washington University in St. Louis CSE571S ©2011 Raj Jain 9-3 PublicPublic KeyKey EncryptionEncryption ExampleExample Rivest, Shamir, and Adleman at MIT RSA: Encrypted_Message = m3 mod 187 Message = Encrypted_Message107 mod 187 Key1 = <3,187>, Key2 = <107,187> Message = 5 Encrypted Message = 53 = 125 Message = 125107 mod 187 = 5 = 125(64+32+8+2+1) mod 187 = {(12564 mod 187)(12532 mod 187)... (1252 mod 187)(125 mod 187)} mod 187 Washington University in -
Ch 13 Digital Signature
1 CH 13 DIGITAL SIGNATURE Cryptography and Network Security HanJung Mason Yun 2 Index 13.1 Digital Signatures 13.2 Elgamal Digital Signature Scheme 13.3 Schnorr Digital Signature Scheme 13.4 NIST Digital Signature Algorithm 13.6 RSA-PSS Digital Signature Algorithm 3 13.1 Digital Signature - Properties • It must verify the author and the date and time of the signature. • It must authenticate the contents at the time of the signature. • It must be verifiable by third parties, to resolve disputes. • The digital signature function includes authentication. 4 5 6 Attacks and Forgeries • Key-Only attack • Known message attack • Generic chosen message attack • Directed chosen message attack • Adaptive chosen message attack 7 Attacks and Forgeries • Total break • Universal forgery • Selective forgery • Existential forgery 8 Digital Signature Requirements • It must be a bit pattern that depends on the message. • It must use some information unique to the sender to prevent both forgery and denial. • It must be relatively easy to produce the digital signature. • It must be relatively easy to recognize and verify the digital signature. • It must be computationally infeasible to forge a digital signature, either by constructing a new message for an existing digital signature or by constructing a fraudulent digital signature for a given message. • It must be practical to retain a copy of the digital signature in storage. 9 Direct Digital Signature • Digital signature scheme that involves only the communication parties. • It must authenticate the contents at the time of the signature. • It must be verifiable by third parties, to resolve disputes. • Thus, the digital signature function includes the authentication function. -
Implementation and Performance Evaluation of XTR Over Wireless Network
Implementation and Performance Evaluation of XTR over Wireless Network By Basem Shihada [email protected] Dept. of Computer Science 200 University Avenue West Waterloo, Ontario, Canada (519) 888-4567 ext. 6238 CS 887 Final Project 19th of April 2002 Implementation and Performance Evaluation of XTR over Wireless Network 1. Abstract Wireless systems require reliable data transmission, large bandwidth and maximum data security. Most current implementations of wireless security algorithms perform lots of operations on the wireless device. This result in a large number of computation overhead, thus reducing the device performance. Furthermore, many current implementations do not provide a fast level of security measures such as client authentication, authorization, data validation and data encryption. XTR is an abbreviation of Efficient and Compact Subgroup Trace Representation (ECSTR). Developed by Arjen Lenstra & Eric Verheul and considered a new public key cryptographic security system that merges high level of security GF(p6) with less number of computation GF(p2). The claim here is that XTR has less communication requirements, and significant computation advantages, which indicate that XTR is suitable for the small computing devices such as, wireless devices, wireless internet, and general wireless applications. The hoping result is a more flexible and powerful secure wireless network that can be easily used for application deployment. This project presents an implementation and performance evaluation to XTR public key cryptographic system over wireless network. The goal of this project is to develop an efficient and portable secure wireless network, which perform a variety of wireless applications in a secure manner. The project literately surveys XTR mathematical and theoretical background as well as system implementation and deployment over wireless network. -
Key Improvements to XTR
To appear in Advances in Cryptology|Asiacrypt 2000, Lecture Notes in Computer Science 1976, Springer-Verlag 2000, 220-223. Key improvements to XTR Arjen K. Lenstra1, Eric R. Verheul2 1 Citibank, N.A., Technical University Eindhoven, 1 North Gate Road, Mendham, NJ 07945-3104, U.S.A., [email protected] 2 PricewaterhouseCoopers, GRMS Crypto Group, Goudsbloemstraat 14, 5644 KE Eindhoven, The Netherlands, Eric.Verheul@[nl.pwcglobal.com, pobox.com] Abstract. This paper describes improved methods for XTR key rep- resentation and parameter generation (cf. [4]). If the ¯eld characteristic is properly chosen, the size of the XTR public key for signature appli- cations can be reduced by a factor of three at the cost of a small one time computation for the recipient of the key. Furthermore, the para- meter set-up for an XTR system can be simpli¯ed because the trace of a proper subgroup generator can, with very high probability, be com- puted directly, thus avoiding the probabilistic approach from [4]. These non-trivial extensions further enhance the practical potential of XTR. 1 Introduction In [1] it was shown that conjugates of elements of a subgroup of GF(p6)¤ of order 2 dividing Á6(p) = p ¡ p + 1 can be represented using 2 log2(p) bits, as opposed to the 6 log2(p) bits that would be required for their traditional representation. In [4] an improved version of the method from [1] was introduced that achieves the same communication advantage at a much lower computational cost. The resulting representation method is referred to as XTR, which stands for E±cient and Compact Subgroup Trace Representation. -
Efficient Encryption on Limited Devices
Rochester Institute of Technology RIT Scholar Works Theses 2006 Efficient encryption on limited devices Roderic Campbell Follow this and additional works at: https://scholarworks.rit.edu/theses Recommended Citation Campbell, Roderic, "Efficient encryption on limited devices" (2006). Thesis. Rochester Institute of Technology. Accessed from This Master's Project is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. Masters Project Proposal: Efficient Encryption on Limited Devices Roderic Campbell Department of Computer Science Rochester Institute of Technology Rochester, NY, USA [email protected] June 24, 2004 ________________________________________ Chair: Prof. Alan Kaminsky Date ________________________________________ Reader: Prof. Hans-Peter Bischof Date ________________________________________ Observer: Prof. Leonid Reznik Date 1 1 Summary As the capstone of my Master’s education, I intend to perform a comparison of Elliptic Curve Cryptography(ECC) and The XTR Public Key System to the well known RSA encryption algorithm. The purpose of such a project is to provide a further understanding of such types of encryption, as well as present an analysis and recommendation for the appropriate technique for given circumstances. This comparison will be done by developing a series of tests on which to run identical tasks using each of the previously mentioned algorithms. Metrics such as running time, maximum and average memory usage will be measured as applicable. There are four main goals of Crypto-systems: Confidentiality, Data Integrity, Authentication and Non-repudiation[5]. This implementation deals only with confidentiality of symmetric key exchange. -
DRAFT Special Publication 800-56A, Recommendation for Pair-Wise Key
The attached DRAFT document (provided here for historical purposes) has been superseded by the following publication: Publication Number: NIST Special Publication (SP) 800-56A Revision 2 Title: Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography Publication Date: 05/13/2013 • Final Publication: https://doi.org/10.6028/NIST.SP.800-56Ar2 (which links to http://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Ar2.pdf). • Information on other NIST Computer Security Division publications and programs can be found at: http://csrc.nist.gov/ The following information was posted with the attached DRAFT document: Aug 20, 2012 SP 800-56 A Rev.1 DRAFT Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography (Draft Revision) NIST announces the release of draft revision of Special Publication 800-56A, Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography. SP 800-56A specifies key-establishment schemes based on the discrete logarithm problem over finite fields and elliptic curves, including several variations of Diffie-Hellman and MQV key establishment schemes. The revision is made on the March 2007 version. The main changes are listed in Appendix D. Please submit comments to 56A2012rev-comments @ nist.gov with "Comments on SP 800-56A (Revision)" in the subject line. The comment period closes on October 31, 2012. NIST Special Publication 800-56A Recommendation for Pair-Wise August 2012 Key-Establishment Schemes Using Discrete Logarithm Cryptography (Draft Revision) Elaine Barker, Lily Chen, Miles Smid and Allen Roginsky C O M P U T E R S E C U R I T Y Abstract This Recommendation specifies key-establishment schemes based on the discrete logarithm problem over finite fields and elliptic curves, including several variations of Diffie-Hellman and MQV key establishment schemes. -
Guidelines on Cryptographic Algorithms Usage and Key Management
EPC342-08 Version 7.0 4 November 2017 [X] Public – [ ] Internal Use – [ ] Confidential – [ ] Strictest Confidence Distribution: Publicly available GUIDELINES ON CRYPTOGRAPHIC ALGORITHMS USAGE AND KEY MANAGEMENT Abstract This document defines guidelines on cryptographic algorithms usage and key management. Document Reference EPC342-08 Issue Version 7.0 Date of Issue 22 November 2017 Reason for Issue Maintenance of document Produced by EPC Authorised by EPC Document History This document was first produced by ECBS as TR 406, with its latest ECBS version published in September 2005. The document has been handed over to the EPC which is responsible for its yearly maintenance. DISCLAIMER: Whilst the European Payments Council (EPC) has used its best endeavours to make sure that all the information, data, documentation (including references) and other material in the present document are accurate and complete, it does not accept liability for any errors or omissions. EPC will not be liable for any claims or losses of any nature arising directly or indirectly from use of the information, data, documentation or other material in the present document. Conseil Européen des Paiements AISBL– Cours Saint-Michel 30A – B 1040 Brussels Tel: +32 2 733 35 33 – Fax: +32 2 736 49 88 Enterprise N° 0873.268.927 – www.epc-cep.eu – [email protected] © 2016 Copyright European Payments Council (EPC) AISBL: Reproduction for non-commercial purposes is authorised, with acknowledgement of the source Table of Content MANAGEMENT SUMMARY ............................................................. 5 1 INTRODUCTION .................................................................... 7 1.1 Scope of the document ...................................................... 7 1.2 Document structure .......................................................... 7 1.3 Recommendations ............................................................ 8 1.4 Implementation best practices ......................................... -
The RSA Algorithm
The RSA Algorithm Evgeny Milanov 3 June 2009 In 1978, Ron Rivest, Adi Shamir, and Leonard Adleman introduced a cryptographic algorithm, which was essentially to replace the less secure National Bureau of Standards (NBS) algorithm. Most impor- tantly, RSA implements a public-key cryptosystem, as well as digital signatures. RSA is motivated by the published works of Diffie and Hellman from several years before, who described the idea of such an algorithm, but never truly developed it. Introduced at the time when the era of electronic email was expected to soon arise, RSA implemented two important ideas: 1. Public-key encryption. This idea omits the need for a \courier" to deliver keys to recipients over another secure channel before transmitting the originally-intended message. In RSA, encryption keys are public, while the decryption keys are not, so only the person with the correct decryption key can decipher an encrypted message. Everyone has their own encryption and decryption keys. The keys must be made in such a way that the decryption key may not be easily deduced from the public encryption key. 2. Digital signatures. The receiver may need to verify that a transmitted message actually origi- nated from the sender (signature), and didn't just come from there (authentication). This is done using the sender's decryption key, and the signature can later be verified by anyone, using the corresponding public encryption key. Signatures therefore cannot be forged. Also, no signer can later deny having signed the message. This is not only useful for electronic mail, but for other electronic transactions and transmissions, such as fund transfers. -
Hash, DH and RSA
CSE468/598 Computer Network Security Hash, DH and RSA Short Version Chun-Jen Chung Arizona State University CSE468/598 Computer Network Security Outline . Background . Hash Functions . Public key cryptography (PKC) • DH • RSA . Summary 2 CSE468/598 Computer Network Security Background CSE468/598 Computer Network Security Crypto algorithms review Encryption Authentication Hash functions Symmetric Asymmetric SHA-1 MD5 MAC Secret key: Public key: (message authentication code) DES, 3DES, AES RSA, ECC HMAC Digital Signature (secret key) (public key) Key management Manual Secret key Exchange: Public key Exchange: operation Diffie-Hellman Certificate Authority on PKI CSE468/598 Computer Network Security Introduction to Hash Functions CSE468/598 Computer Network Security Hash Algorithms Message of hash H A fixed-length arbitrary length Math transformation short message . Also known as • (Cryptographic) Hash functions • Message digests • One-way transformations • One-way functions . Length of H(m) much shorter than length of m . Usually fixed lengths: 128 or 160 bits . Example algorithms • MD5 (Message-Digest) – 128 bits output • SHA-1 (secure hash algorithm) : 160 bits output • SHA-2: 256/224, 512/384 CSE468/598 Computer Network Security Hash Algorithms (cont’d) Image from scanner All files of a floppy disk All files of a hard disk User password 8 bytes 512 K bytes 1.4 M bytes 80Giga bytes One way hash One way hash One way hash One way hash (SHA-1) (SHA-1) (SHA-1) (SHA-1) 43 B0 4C 54 3B 73 BF 4C 34 3B 54 3B 4C 34 3B 32 2B 23 70 7A 67 A2 23 3F 7D 67 A2 45 23 76 62 3C D3 AF A2 2B 4F 43 B0 4C 36 2B 7A 2B 49 3F 76 D2 37 F6 45 67 A2 23 3F 54 3B 49 28 67 3C D3 AF 27 4A 44 47 8F 93 D2 7D 43 B0 4C 19 A2 23 8F 7D 36 Hash value 20 bytes Hash value 20 bytes Hash value 20 bytes Hash value 20 bytes (160 bits) CSE468/598 Computer Network Security Applications of Hash Functions . -
Public Key Infrastructure Configuration Guide
Public Key Infrastructure Configuration Guide Americas Headquarters Cisco Systems, Inc. 170 West Tasman Drive San Jose, CA 95134-1706 USA http://www.cisco.com Tel: 408 526-4000 800 553-NETS (6387) Fax: 408 527-0883 THE SPECIFICATIONS AND INFORMATION REGARDING THE PRODUCTS IN THIS MANUAL ARE SUBJECT TO CHANGE WITHOUT NOTICE. ALL STATEMENTS, INFORMATION, AND RECOMMENDATIONS IN THIS MANUAL ARE BELIEVED TO BE ACCURATE BUT ARE PRESENTED WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED. USERS MUST TAKE FULL RESPONSIBILITY FOR THEIR APPLICATION OF ANY PRODUCTS. THE SOFTWARE LICENSE AND LIMITED WARRANTY FOR THE ACCOMPANYING PRODUCT ARE SET FORTH IN THE INFORMATION PACKET THAT SHIPPED WITH THE PRODUCT AND ARE INCORPORATED HEREIN BY THIS REFERENCE. IF YOU ARE UNABLE TO LOCATE THE SOFTWARE LICENSE OR LIMITED WARRANTY, CONTACT YOUR CISCO REPRESENTATIVE FOR A COPY. The Cisco implementation of TCP header compression is an adaptation of a program developed by the University of California, Berkeley (UCB) as part of UCB's public domain version of the UNIX operating system. All rights reserved. Copyright © 1981, Regents of the University of California. NOTWITHSTANDING ANY OTHER WARRANTY HEREIN, ALL DOCUMENT FILES AND SOFTWARE OF THESE SUPPLIERS ARE PROVIDED “AS IS" WITH ALL FAULTS. CISCO AND THE ABOVE-NAMED SUPPLIERS DISCLAIM ALL WARRANTIES, EXPRESSED OR IMPLIED, INCLUDING, WITHOUT LIMITATION, THOSE OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT OR ARISING FROM A COURSE OF DEALING, USAGE, OR TRADE PRACTICE. IN NO EVENT SHALL CISCO OR ITS SUPPLIERS BE LIABLE FOR ANY INDIRECT, SPECIAL, CONSEQUENTIAL, OR INCIDENTAL DAMAGES, INCLUDING, WITHOUT LIMITATION, LOST PROFITS OR LOSS OR DAMAGE TO DATA ARISING OUT OF THE USE OR INABILITY TO USE THIS MANUAL, EVEN IF CISCO OR ITS SUPPLIERS HAVE BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. -
On Robust Key Agreement Based on Public Key Authentication Feng Hao Thales E-Security, Cambridge, UK [email protected]
1 On Robust Key Agreement Based on Public Key Authentication Feng Hao Thales E-Security, Cambridge, UK [email protected] Abstract—This paper discusses public-key authenticated key Elliptic Curve Cryptography (ECC) [10]. Using ECC essen- agreement protocols. First, we critically analyze several authen- tially replaces the underlying (multiplicative) cyclic group ticated key agreement protocols and uncover various theoretical with another (additive) cyclic group defined over some elliptic and practical flaws. In particular, we present two new attacks on the HMQV protocol, which is currently being standardized curve. The essence of the protocol remains unchanged. by IEEE P1363. The first attack presents a counterexample to The acute problem with the Diffie-Hellman key agreement invalidate the basic authentication in HMQV. The second attack is that it is unauthenticated [2]. While secure against passive is applicable to almost all past schemes, despite that many of attackers, the protocol is inherently vulnerable to active attacks them have formal security proofs. These attacks highlight the such as the man-in-the-middle attack [6]. This is a serious lim- difficulty to design a crypto protocol correctly and suggest the caution one should always take. itation, which for many years has been motivating researchers We further point out that many of the design errors are caused to find a solution [3]–[5], [7], [9], [11], [13], [20]. by sidestepping an important engineering principle, namely To add authentication, we must start with assuming some “Do not assume that a message you receive has a particular shared secret. In general, there are two approaches. -
The Whole Is Less Than the Sum of Its Parts: Constructing More Efficient Lattice-Based Akes Rafael Del Pino, Vadim Lyubashevsky, David Pointcheval
The Whole is Less Than the Sum of Its Parts: Constructing More Efficient Lattice-Based AKEs Rafael del Pino, Vadim Lyubashevsky, David Pointcheval To cite this version: Rafael del Pino, Vadim Lyubashevsky, David Pointcheval. The Whole is Less Than the Sum of Its Parts: Constructing More Efficient Lattice-Based AKEs. SCN 2016 - 10th International Conference Security and Cryptography for Networks, Aug 2016, Amalfi, Italy. pp.273 - 291, 10.1007/978-3-319- 44618-9_15. hal-01378005 HAL Id: hal-01378005 https://hal.inria.fr/hal-01378005 Submitted on 8 Oct 2016 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. The Whole is Less than the Sum of its Parts: Constructing More Efficient Lattice-Based AKEs? Rafael del Pino1;2;3, Vadim Lyubashevsky4, and David Pointcheval3;2;1 1 INRIA, Paris 2 Ecole´ Normale Sup´erieure,Paris 3 CNRS 4 IBM Research Zurich Abstract. Authenticated Key Exchange (AKE) is the backbone of internet security protocols such as TLS and IKE. A recent announcement by standardization bodies calling for a shift to quantum-resilient crypto has resulted in several AKE proposals from the research community. Be- cause AKE can be generically constructed by combining a digital signature scheme with public key encryption (or a KEM), most of these proposals focused on optimizing the known KEMs and left the authentication part to the generic combination with digital signatures.