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We demonstrate that the framework of bounded quantum reference frames has application to building quantum-public-key cryptographic protocols and proving their security. Thus, the framework we introduce can be seen as a public-key analogue of the framework of Bartlett et al. (Phys. Rev. A 70, 032307), where a private shared reference frame is shown to have cryptographic application. The protocol we present in this paper is an identification scheme, which, like a digital signature scheme, is a type of authentication scheme. We prove that our protocol is both reusable and secure under the honest-verifier assumption. Thus, we also demonstrate that secure reusable quantum-public-key authentication is possible to some extent.

Josh and Kurt talk about public key cryptography

Advances in communication technology have seen strong interest in digital data transmission. However, illegal data access has become more easy and prevalent in wireless and general communication networks. In order to protect the valuable data from illegal access, different kinds of cryptographic systems have been proposed. In this paper, a new integrating channel coding and cryptography design communication systems is proposed. So we use cryptography as an error detection tool. In order to preserve the advantages of encryption and to improve its disadvantages, we place the encryptor before the encoder. The hamming encoder is used to select the generator matrix to be used as a block code to form the new system .In this the security of common cryptographic primitive i.e a key stream generator based on LFSR can be strengthened by using the properties of a physical layer.So, a passive eaves dropping will experience great difficulty in cracking the LFSR based cryptography system as the computational complexity of discovering the secret key increases to large extent. The analysis indicates that the proposed design possesses the following feature. Its security is higher than the conventional one with the channel encoder only. Privacy is more due to unknown random codes. As the applied codes are unknown to a hostile user, this means that it is hardly possible to detect the message of another user. Anti-jam performance is good. It overcomes the disadvantage of Chaos based cryptography system as input data is not extended and hence bandwidth is not wasted. Moreover, the computer simulation shows that the proposed system has a good ability in error detection especially when the SNR per bit is moderate high, and the detection ability is enhanced when the increased length of Hamming code is employed.

Cryptography is a method used to establish secure data communication. The goal of cryptography is to send data to satisfy the criteria of confidentiality, data integrity, authentication and non-repudiation. In line with the goals, the performance metrics is the important evaluation criteria to be analyzed. This paper presents the review of performance metrics of Public Key Cryptography (PKC) that had been analyzed based on the PKC scheme from the previous researchers‟ effort since the last four decades. It also displayed the research pattern in different performance metrics over the years. The aim of this paper is to identify the key performance metrics which addressed by the researchers in previous studies. Finally, the critical concern of this paper which shows the overall PKC performance metrics also presented in this paper.

Abstract Security in the world of the internet has become very important in all aspects of social life. One of the methods of securing the information on the internet is public-key cryptography or asymmetric cryptography. Public key cryptography is not only a process of encrypting information, it also provides confidentiality, data integrity and authentication. RSA and ElGamal are two very important public-key cryptosystems. These two cryptosystems are also used for digital signature scheme because of their high level of security. In this paper, we discussed RSA algorithm in details with example. RSA is one of the most widely used public-key cryptography in various application. Then we discussed the ElGamal algorithm in details with example. ElGamal public-key cryptography is also used in many applications nowadays. In the next section, we discussed digital signature using RSA algorithm and ElGamal algorithm as digital signature is one of the important application of public-key cryptography. Therefore, Reader will have a good understanding of public-key cryptography. In this paper we have also included a relative study between RSA and ElGamal.

This paper proposes an image encryption technique using three stages algorithms based on hyper-chaotic maps. In the first scenario, bit-level scrambling (BLS) using a 2D coupled chaotic map (2D-CCM) is used to encrypt the bits of the basic colour image. In the second strategy, the scrambled bit level is XORed with pseudo random bit generator (PRBG). The PRBG is designed using a combination of chaotic maps, including, logistic map (LM), sine map (SM), 5D chaotic map (5D-CM), enhanced quadratic map (EQM), and 2D henon SM (2D-HSM). The pubic key based on the Chebyshev polynomial chaotic map is used as the final phase of the encryption algorithms. The performance analysis of the proposed image encryption technique is validated through various criteria such as fundamental space analysis, correlation coefficient, entropy, the number of pixels changes rate (NPCR), and unified average-changing intensity (UACI). Also, the obtained results are compared with other recent studies. The simulation results demonstrated that the proposed technique has robust security and it provides the image with high protection against various attacks.

This paper proposes an image encryption technique using three stages algorithms based on hyper-chaotic maps. In the first scenario, bit-level scrambling (BLS) using a 2D coupled chaotic map (2D-CCM) is used to encrypt the bits of the basic colour image. In the second strategy, the scrambled bit level is XORed with pseudo random bit generator (PRBG). The PRBG is designed using a combination of chaotic maps, including, logistic map (LM), sine map (SM), 5D chaotic map (5D-CM), enhanced quadratic map (EQM), and 2D henon SM (2D-HSM). The pubic key based on the Chebyshev polynomial chaotic map is used as the final phase of the encryption algorithms. The performance analysis of the proposed image encryption technique is validated through various criteria such as fundamental space analysis, correlation coefficient, entropy, the number of pixels changes rate (NPCR), and unified average-changing intensity (UACI). Also, the obtained results are compared with other recent studies. The simulation results demonstrated that the proposed technique has robust security and it provides the image with high protection against various attacks.

with the growth of technological advancements, the threats dealt by a user grow exponentially. Hence security has become a critical issue in data storage and transmission. As traditional cryptographic systems are now vulnerable to attacks, the concept of using DNA Cryptography has been identified as a possible technology that brings forward a new hope for unbreakable algorithms. This paper analyzes the different approaches on DNA based Cryptography

This document supplements RFC 3279. It describes the conventions for using the RSA Probabilistic Signature Scheme (RSASSA-PSS) signature algorithm, the RSA Encryption Scheme - Optimal Asymmetric Encryption Padding (RSAES-OAEP) key transport algorithm and additional one-way hash functions with the Public-Key Cryptography Standards (PKCS) #1 version 1.5 signature algorithm in the Internet X.509 Public Key Infrastructure (PKI). Encoding formats, algorithm identifiers, and parameter formats are specified. [STANDARDS-TRACK]

First Edition (version 1.0) published online on 14 March 2009 This book is a collection of my essays presenting the methods to create big and yet memorizable secrets with its key sizes beyond 128 bits till 512 bits to realize various key size requirements of information engineering applications in general and MePKC (Memorizable Public-Key Cryptography) in particular. In addition to the discussed topics, there are original and novel idea conceptions proposed as follows: (i) methods and systems to realize memorizable symmetric key the secret till resistance to quantum computer attack; (ii) methods and systems to realize memorizable public-key cryptography (MePKC); (iii) methods and systems to improve security strength of other cryptographic, information-hiding, and non-cryptographic applications of secret beyond 128 bits; (iv) method and system to harden the identification of embedded data in steganography although stego-data has been detected; (v) method and system to transfer fund electronically over a remote network using MePKC; (vi) method and system to license software electronically over a remote network using MePKC; (vii) methods and systems to authenticate human-computer and human-human communications at a local station or over a remote network using MePKC; (viii) method and system to use digital certificate with more than one asymmetric key pair for different protection periods and password throttling; (ix) method and system to use three-tier MePKC digital certificates for ladder authentication; (x) method and system to store, manage, and download voice and video calls of mobile phone and wired phone at online distributed servers; (xi) method and system of multipartite electronic commerce transactions; as well as (xii) method and system to boost up the trust level of MePKC digital certificate by using more than one certification authority (CA) and/or introducer of trust of web. Other than that, there are some imperative feature enhancements as follows: (i) hack-proof data storage using innovated DIP switch; (ii) MePKC digital timestamping scheme to prove idea originality of intellectual properties (IP); and (ii) limited first-to-invent patent filing system. Due to the relatively high research costs invested by the author, for refund, as well as for building up a fund for further maintenance, research and development, any original and novel idea conceptions from the author in this book is only free of usage for public interests, press report, private study, research, and teaching throughout the World, with the condition that proper originality citation for source references has been clearly shown. Yet for any commercial usage, prior consent has to be obtained from the author or his successor(s). For more details on the conditions to use the novel copyrighted ideas in this literary work, please refer to the websites [W1-W6] as follows: [W1] Kok-Wah LEE @ XpreeLi's website: http://www.xpreeli.com [W2] Author's copyrighted works: http://www.xpreeli.com/personal/kwlee_copyright.htm [W3] Author's exclusion list for self-defence: http://www.xpreeli.com/personal/exclusion_list.htm [W4] Copyrighted idea unit for licensing cost: http://www.xpreeli.com/personal/copyright_unit.htm [W5] Copyright leasing application (PDF): http://www.xpreeli.com/mydoc/copyright_licensing_form.pdf [W6] Copyright leasing application (DOC): http://www.xpreeli.com/mydoc/copyright_licensing_form.doc © Kok-Wah Lee @ Xpree Jinhua Li, 14 March 2009 Email (h): [email protected] Email (o): [email protected] URL (h): www.geocities.com/xpree/ URL (o): www.xpreeli.com All rights reserved E. & O. E., + E. (Errors and Omissions Exempted, plus Estimations)

This document updates RFC 5480 to specify semantics for the keyEncipherment and dataEncipherment key usage bits when used in certificates that support Elliptic Curve Cryptography.

Kerberos is one of the advanced security system that helps prevent people from stealing information that gets sent across the network from one computer to another. Usually, these people are after your password. The Kerberos security system, guards electronic transmissions that get sent across the Internet. It does this by scrambling the information -- encrypting it -- so that only the computer that is supposed to receive the information can unscramble it, or say decrypt it. In addition, it makes sure that your password itself never gets sent across the wire: only a scrambled "key" to your password. To make a certain addition to the Kerberos Protocol we add the public key Cryptography for the phases of the Kerberos Authentication System. This would help in a more secure and a password attack free system. There would also be addition of the current location of the user requesting the service to the Data provided by the user which would add to more authentication and security.

The objective of this paper is to build the neutrosophic version of the RSA crypto-algorithm, where we use the foundations of fusion neutrosophic number theory such as neutrosophic phi-Euler's function, neutrosophic congruencies, and neutrosophic inverses to build novel algorithms for cryptography depending of famous RSA algorithm.

This paper proposes an image encryption technique using three stages algorithms based on hyper-chaotic maps. In the first scenario, bit-level scrambling (BLS) using a 2D coupled chaotic map (2D-CCM) is used to encrypt the bits of the basic colour image. In the second strategy, the scrambled bit level is XORed with pseudo random bit generator (PRBG). The PRBG is designed using a combination of chaotic maps, including, logistic map (LM), sine map (SM), 5D chaotic map (5D-CM), enhanced quadratic map (EQM), and 2D henon SM (2D-HSM). The pubic key based on the Chebyshev polynomial chaotic map is used as the final phase of the encryption algorithms. The performance analysis of the proposed image encryption technique is validated through various criteria such as fundamental space analysis, correlation coefficient, entropy, the number of pixels changes rate (NPCR), and unified average-changing intensity (UACI). Also, the obtained results are compared with other recent studies. The simulation results demonstrated that the proposed technique has robust security and it provides the image with high protection against various attacks.

This paper proposes an image encryption technique using three stages algorithms based on hyper-chaotic maps. In the first scenario, bit-level scrambling (BLS) using a 2D coupled chaotic map (2D-CCM) is used to encrypt the bits of the basic colour image. In the second strategy, the scrambled bit level is XORed with pseudo random bit generator (PRBG). The PRBG is designed using a combination of chaotic maps, including, logistic map (LM), sine map (SM), 5D chaotic map (5D-CM), enhanced quadratic map (EQM), and 2D henon SM (2D-HSM). The pubic key based on the Chebyshev polynomial chaotic map is used as the final phase of the encryption algorithms. The performance analysis of the proposed image encryption technique is validated through various criteria such as fundamental space analysis, correlation coefficient, entropy, the number of pixels changes rate (NPCR), and unified average-changing intensity (UACI). Also, the obtained results are compared with other recent studies. The simulation results demonstrated that the proposed technique has robust security and it provides the image with high protection against various attacks.

This publication presents a state-of-the-art survey of public key cryptography circa 1988-1990. In doing so, it covers a number of different topics including: the theory of public key cryptography, comparisons to conventional (secret-key) cryptography, a largely self contained summary of relevant mathematics, a survey of major existing public key systems an exploration of digital signatures and hash functions, a survey of public key implementations in networks, an introduction to zero-knowledge protocols and probabilistic encryption, and an exploitation of security issues and key sizes.

Up to now, for efficiency reasons cryptographic algorithm has been written in an imperative language. But to get acquaintance with a functional programming language a question arises: functional programming offers some new for secure communication or not? This article investigates this question giving an overview on some cryptography algorithms and presents how the RSA encryption in the functional language Clean can be implemented and how can be measured the efficiency of a certain application.

We introduce a generalized Anshel-Anshel-Goldfeld (AAG) key establishment protocol (KEP) for magmas. This leads to the foundation of non-associative public-key cryptography (PKC), generalizing the concept of non-commutative PKC. We show that left selfdistributive systems appear in a natural special case of a generalized AAG-KEP for magmas, and we propose, among others instances, concrete realizations using $f$-conjugacy in groups and shifted conjugacy in braid groups. We discuss the advantages of our schemes compared with the classical AAG-KEP based on conjugacy in braid groups.

This document specifies the syntax and semantics for the Subject Public Key Information field in certificates that support Elliptic Curve Cryptography. This document updates Sections 2.3.5 and 5, and the ASN.1 module of "Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile", RFC 3279. [STANDARDS-TRACK]

Spies used to meet in the park to exchange code words, now things have moved on - Robert Miles explains the principle of Public/Private Key Cryptography note1: Yes, it should have been 'Obi Wan' not 'Obi One' :) note2: The string of 'garbage' text in the two examples should have been different to illustrate more clearly that there are two different systems in use. http://www.facebook.com/computerphile https://twitter.com/computer_phile This video was filmed and edited by Sean Riley. Computer Science at the University of Nottingham: http://bit.ly/nottscomputer Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels Source: https://www.youtube.com/watch?v=GSIDS_lvRv4 Uploader: Computerphile

A homomorphic public key crypto-scheme based on the Boolean Satisfiability Problem is proposed. The public key is a SAT formula satisfied by the private key. Probabilistic encryption generates functions implied to be false by the public key XOR the message bits. A zero-knowledge proof is used to provide signatures.

A homomorphic public key crypto-scheme based on the Boolean Satisfiability Problem is proposed. The public key is a SAT formula satisfied by the private key. Probabilistic encryption generates functions implied to be false by the public key XOR the message bits. A zero-knowledge proof is used to provide signatures.

A generalization of the original Diffie-Hellman key exchange in $(\Z/p\Z)^*$ found a new depth when Miller and Koblitz suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compute the sizes of these orbits in general and also if there exists a square root attack in general. In Section 2 a concrete practical semigroup action built from simple semirings is presented. It will require further research to analyse this system.

A generalization of the original Diffie-Hellman key exchange in $(\Z/p\Z)^*$ found a new depth when Miller and Koblitz suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compute the sizes of these orbits in general and also if there exists a square root attack in general. In Section 2 a concrete practical semigroup action built from simple semirings is presented. It will require further research to analyse this system.

This standard specifies two challenge-response protocols by which entities in a computer system may authenticate their identities to one another. These may be used during session initiation, and at any other time that entity authentication is necessary. Depending on which protocol is implemented, either one or both entities involved may be authenticated. The defined protocols are derived from an international standard for entity authentication based on public key cryptography, which uses digital signatures and random number challenges.

In this survey, we describe a general key exchange protocol based on semidirect product of (semi)groups (more specifically, on extensions of (semi)groups by automorphisms), and then focus on practical instances of this general idea. This protocol can be based on any group or semigroup, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when this protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. The focus then shifts to selecting an optimal platform (semi)group, in terms of security and efficiency. We show, in particular, that one can get a variety of new security assumptions by varying an automorphism used for a (semi)group extension.

This document updates the Public Key Cryptography for Initial Authentication in Kerberos (PKINIT) standard (RFC 4556) to remove protocol structures tied to specific cryptographic algorithms. The PKINIT key derivation function is made negotiable, and the digest algorithms for signing the pre-authentication data and the client's X.509 certificates are made discoverable.

This document describes protocol extensions (hereafter called PKINIT) to the Kerberos protocol specification. These extensions provide a method for integrating public key cryptography into the initial authentication exchange, by using asymmetric-key signature and/or encryption algorithms in pre-authentication data fields. [STANDARDS-TRACK]

This document defines a mechanism to enable in-band transmission of Online Certificate Status Protocol (OCSP) responses in the Kerberos network authentication protocol. These responses are used to verify the validity of the certificates used in Public Key Cryptography for Initial Authentication in Kerberos (PKINIT), which is the Kerberos Version 5 extension that provides for the use of public key cryptography. [STANDARDS-TRACK]

This document describes how to further extend the Public Key Cryptography for Initial Authentication in Kerberos (PKINIT) extension (defined in RFC 4556) to exchange an opaque data blob that a Key Distribution Center (KDC) can validate to ensure that the client is currently in possession of the private key during a PKINIT Authentication Service (AS) exchange.

Third Edition (draft version 3.0) publicly archived online on 02 May 2011 This book is copyright protected by the Copyright Acts in Malaysia, USA, and international treaties. It aims to build a safer electronic society for more friendly environment on Earth planet. Kok-Wah Lee @ Xpree Li the author cum inventor proposes four major novel components: (i) 2D (two-dimensional) key input method, system, and device to support big and yet memorizable secret beyond 128 bits; (ii) multihash key to generate multiple slave keys for both offline and online accounts from a master key, preferably a big secret from 2D key method; (iii) MePKC (Memorizable Public Key Cryptography) and its applications using fully memorizable private key from 2D key directly or slave key of multihash key indirectly; and (iv) anti-hacking data storage using improved DIP (Dual In-Line Package) switch to securely store original plaintext and decrypted ciphertext from virtual hacking via the computer communication networks. For more development on the preparation of this book mainly for the acquisition of a normal doctorate degree, i.e. Ph.D. degree, in engineering field in Malaysia, please refer to [L1]: [L1] Kok-Wah Lee's degree study: http://www.xpreeli.com/homepage/study.htm For more details on the conditions to use the novel copyrighted ideas in this literary work, please refer to the websites [W1-W6] as follows: [W1] Kok-Wah LEE @ XpreeLi's website: http://www.xpreeli.com [W2] Author's copyrighted works: http://www.xpreeli.com/personal/kwlee_copyright.htm [W3] Author's exclusion list for self-defence: http://www.xpreeli.com/personal/exclusion_list.htm [W4] Copyrighted idea unit for licensing cost: http://www.xpreeli.com/personal/copyright_unit.htm [W5] Copyright leasing application (PDF): http://www.xpreeli.com/mydoc/copyright_licensing_form.pdf [W6] Copyright leasing application (DOC): http://www.xpreeli.com/mydoc/copyright_licensing_form.doc For any commercial usage, prior written consent has to be obtained from the author or his successor(s). © Kok-Wah Lee @ Xpree Jinhua Li, 02 May 2011 10.30am GMT +0800 NRIC (Malaysia): 750821-08-5447 Email (h): [email protected] Email (o): [email protected] URL (o): www.xpreeli.com All rights reserved. E. & O. E., + E. (Errors and Omissions Exempted, plus Estimations)

Third Edition (draft version 3.0) publicly archived online on 02 May 2011 This book is copyright protected by the Copyright Acts in Malaysia, USA, and international treaties. It aims to build a safer electronic society for more friendly environment on Earth planet. Kok-Wah Lee @ Xpree Li the author cum inventor proposes four major novel components: (i) 2D (two-dimensional) key input method, system, and device to support big and yet memorizable secret beyond 128 bits; (ii) multihash key to generate multiple slave keys for both offline and online accounts from a master key, preferably a big secret from 2D key method; (iii) MePKC (Memorizable Public Key Cryptography) and its applications using fully memorizable private key from 2D key directly or slave key of multihash key indirectly; and (iv) anti-hacking data storage using improved DIP (Dual In-Line Package) switch to securely store original plaintext and decrypted ciphertext from virtual hacking via the computer communication networks. For more development on the preparation of this book mainly for the acquisition of a normal doctorate degree, i.e. Ph.D. degree, in engineering field in Malaysia, please refer to [L1]: [L1] Kok-Wah Lee's degree study: http://www.xpreeli.com/homepage/study.htm For more details on the conditions to use the novel copyrighted ideas in this literary work, please refer to the websites [W1-W6] as follows: [W1] Kok-Wah LEE @ XpreeLi's website: http://www.xpreeli.com [W2] Author's copyrighted works: http://www.xpreeli.com/personal/kwlee_copyright.htm [W3] Author's exclusion list for self-defence: http://www.xpreeli.com/personal/exclusion_list.htm [W4] Copyrighted idea unit for licensing cost: http://www.xpreeli.com/personal/copyright_unit.htm [W5] Copyright leasing application (PDF): http://www.xpreeli.com/mydoc/copyright_licensing_form.pdf [W6] Copyright leasing application (DOC): http://www.xpreeli.com/mydoc/copyright_licensing_form.doc For any commercial usage, prior written consent has to be obtained from the author or his successor(s). © Kok-Wah Lee @ Xpree Jinhua Li, 02 May 2011 10.30am GMT +0800 NRIC (Malaysia): 750821-08-5447 Email (h): [email protected] Email (o): [email protected] URL (o): www.xpreeli.com All rights reserved. E. & O. E., + E. (Errors and Omissions Exempted, plus Estimations)

This paper presents several Public Key Cryptography (PKC) algorithms based on the perspective of researchers‟ effort since it was invented in the last four decades. The categories of the algorithms had been analyzed which are Discrete Logarithm, Integer Factorization, Coding Theory, Elliptic Curve, Lattices, Digital Signature and Hybrid algorithms. This paper reviewed the previous schemes in different PKC algorithms. The aim of this paper is to present the comparative trends of PKC algorithms based on number of research for each algorithm in last four decades, the roadmap of PKC algorithms since they were invented and the most chosen algorithms among previous researchers. Finally, the strength and drawback of proposed schemes and algorithms also presented in this paper.

We employ the methods of statistical physics to study the performance of Gallager type error-correcting codes. In this approach, the transmitted codeword comprises Boolean sums of the original message bits selected by two randomly-constructed sparse matrices. We show that a broad range of these codes potentially saturate Shannon's bound but are limited due to the decoding dynamics used. Other codes show sub-optimal performance but are not restricted by the decoding dynamics. We show how these codes may also be employed as a practical public-key cryptosystem and are of competitive performance to modern cyptographical methods.

The conjugacy search problem in a group G is the problem of recovering an x in G from given g in G and h=x^{-1}gx. This problem is in the core of several recently suggested public key exchange protocols, most notably the one due to Anshel, Anshel, and Goldfeld, and the one due to Ko, Lee at al. In this note, we make two observations that seem to have eluded most people's attention. The first observation is that solving the conjugacy search problem is not necessary for an adversary to get the common secret key in the Ko-Lee protocol. It is sufficient to solve an apparently easier problem of finding x, y in G such that h=ygx for given g, h in G. Another observation is that solving the conjugacy search problem is not sufficient for an adversary to get the common secret key in the Anshel-Anshel-Goldfeld protocol.

Public-key cryptosystems are suggested based on invariants of groups. We give also an overview of the known cryptosystems which involve groups.

Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al. exploited the conjugacy search problem in groups, which is a ramification of the discrete logarithm problem. However, it is a prevalent opinion now that the conjugacy search problem alone is unlikely to provide sufficient level of security no matter what particular group is chosen as a platform. In this paper we employ another problem (we call it the decomposition problem), which is more general than the conjugacy search problem, and we suggest to use R. Thompson's group as a platform. This group is well known in many areas of mathematics, including algebra, geometry, and analysis. It also has several properties that make it fit for cryptographic purposes. In particular, we show here that the word problem in Thompson's group is solvable in almost linear time.

Briefing on cryptography, PKI and other encryption technologies.

Having discussed symmetric (private) key ciphers during the last two weeks, this week Leo and Steve examine asymmetric key cryptography, commonly known as "Public Key Cryptography".  They begin by examining the first public key cryptosystem, known as the Diffie-Hellman Key Exchange, invented in 1976. Then they describe the operation of general purpose public key cryptosystems such as the one invented by RSA.

Having discussed symmetric (private) key ciphers during the last two weeks, this week Leo and Steve examine asymmetric key cryptography, commonly known as "Public Key Cryptography".  They begin by examining the first public key cryptosystem, known as the Diffie-Hellman Key Exchange, invented in 1976. Then they describe the operation of general purpose public key cryptosystems such as the one invented by RSA.

xiv, 542 pages : 24 cm

Third Edition of the book "Handbook of Surveillance Technologies" by J. K. Petersen lists Absolute Public Key Cryptography (US Patent:7088821) as one of key encryption techniques (PDF of the page available) along with AES-IA-8314, Blowfish, and others. Book Details ISBN 9781439873151, Published January 23, 2012 by Routledge, 1040 Pages 969 B/W Illustrations talks

Third Edition of the book "Handbook of Surveillance Technologies" by J. K. Petersen lists Absolute Public Key Cryptography (US Patent:7088821) as one of key encryption techniques (PDF of the page available) along with AES-IA-8314, Blowfish, and others. Book Details ISBN 9781439873151, Published January 23, 2012 by Routledge, 1040 Pages 969 B/W Illustrations talks

Third Edition of the book "Handbook of Surveillance Technologies" by J. K. Petersen lists Absolute Public Key Cryptography (US Patent:7088821) as one of key encryption techniques (PDF of the page available) along with AES-IA-8314, Blowfish, and others. Book Details ISBN 9781439873151, Published January 23, 2012 by Routledge, 1040 Pages 969 B/W Illustrations talks

To secure the transmission and distribution of complex keys in optical transformation-based image encryption networks, an original optical image encryption looks at based on hyper-chaos and public key cryptography can be employed. The original image is then encrypted in the specular domain using hyper-chaotic phase filters and double random phase encoding. To perform asymmetric, imagine encryption, public key encryption systems are used to assign and manage the hyper-chaotic system's setting values, system parameters, including the frequency diffraction system parameters. During the decryption process, the receiver generates hyper-chaotic random phase masks by decrypting the private keys in the public key cryptosystem and optically decrypts the encrypted image. Finally, the generated key stream is used to generate the final encryption image by performing an end-to-end circular modulus diffusion operation on all rows and columns. In addition, the key sequence has been connected to the plain image, which could notify the user to the chosen plaintext and known plaintext attack.

To secure the transmission and distribution of complex keys in optical transformation-based image encryption networks, an original optical image encryption looks at based on hyper-chaos and public key cryptography can be employed. The original image is then encrypted in the specular domain using hyper-chaotic phase filters and double random phase encoding. To perform asymmetric, imagine encryption, public key encryption systems are used to assign and manage the hyper-chaotic system's setting values, system parameters, including the frequency diffraction system parameters. During the decryption process, the receiver generates hyper-chaotic random phase masks by decrypting the private keys in the public key cryptosystem and optically decrypts the encrypted image. Finally, the generated key stream is used to generate the final encryption image by performing an end-to-end circular modulus diffusion operation on all rows and columns. In addition, the key sequence has been connected to the plain image, which could notify the user to the chosen plaintext and known plaintext attack.

The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new homomorphic public-key cryptosystem. They rely on difficulty of the conjugacy and membership problems for subgroups of a given group. To support these and other known cryptographic schemes we present a general technique to produce a family of instances being matrix groups (over finite commutative rings) which play a role for these schemes similar to the groups $Z\_n^*$ in the existing cryptographic constructions like RSA or discrete logarithm.

We discuss cryptographic applications of single-qubit rotations from the perspective of trapdoor one-way functions and public-key encryption. In particular, we present an asymmetric cryptosystem whose security relies on fundamental principles of quantum physics. A quantum public key is used for the encryption of messages while decryption is possible by means of a classical private key only. The trapdoor one-way function underlying the proposed cryptosystem maps integer numbers to quantum states of a qubit and its inversion can be infeasible by virtue of the Holevo's theorem.

Thesis advisor, Chyan Yang

Cryptography FAQ 06/10 Public Key.