Faster pairings on special Weierstrass curves

This paper presents efficient formulas for computing cryptographic pairings on the curve y 2 = c x 3 + 1 over fields of large characteristic. We provide examples of pairing-friendly elliptic curves of this form which are of interest for efficient pairing implementations.

How to extract and expand randomness : a summary and explanation of existing results

We examine the use of randomness extraction and expansion in key agreement (KA) pro- tocols to generate uniformly random keys in the standard model. Although existing works provide the basic theorems necessary, they lack details or examples of appropriate cryptographic primitives and/or parameter sizes. This has lead to the large amount of min-entropy needed in the (non-uniform) shared secret being overlooked in proposals and efficiency comparisons of KA protocols. We therefore summa- rize existing work in the area and examine the security levels achieved with the use of various extractors and expanders for particular parameter sizes. The tables presented herein show that the shared secret needs a min-entropy of at least 292 bits (and even more with more realistic assumptions) to achieve an overall security level of 80 bits using the extractors and expanders we consider. The tables may be used to �nd the min-entropy required for various security levels and assumptions. We also �nd that when using the short exponent theorems of Gennaro et al., the short exponents may need to be much longer than they suggested.

Modeling and Verification of Privacy Enhancing Protocols

Privacy enhancing protocols (PEPs) are a family of protocols that allow secure exchange and management of sensitive user information. They are important in preserving users’ privacy in today’s open environment. Proof of the correctness of PEPs is necessary before they can be deployed. However, the traditional provable security approach, though well established for verifying cryptographic primitives, is not applicable to PEPs. We apply the formal method of Coloured Petri Nets (CPNs) to construct an executable specification of a representative PEP, namely the Private Information Escrow Bound to Multiple Conditions Protocol (PIEMCP). Formal semantics of the CPN specification allow us to reason about various security properties of PIEMCP using state space analysis techniques. This investigation provides us with preliminary insights for modeling and verification of PEPs in general, demonstrating the benefit of applying the CPN-based formal approach to proving the correctness of PEPs.

Analysis of authenticated encryption stream ciphers

Authenticated Encryption (AE) is the cryptographic process of providing simultaneous confidentiality and integrity protection to messages. AE is potentially more efficient than applying a two-step process of providing confidentiality for a message by encrypting the message and in a separate pass, providing integrity protection by generating a Message Authentication Code (MAC) tag. This paper presents results on the analysis of three AE stream ciphers submitted to the recently completed eSTREAM competition. We classify the ciphers based on the methods the ciphers use to provide authenticated encryption and discuss possible methods for mounting attacks on these ciphers.

Multi-factor password-authenticated key exchange

We consider a new form of authenticated key exchange which we call multi-factor password-authenticated key exchange, where session establishment depends on successful authentication of multiple short secrets that are complementary in nature, such as a long-term password and a one-time response, allowing the client and server to be mutually assured of each other's identity without directly disclosing private information to the other party. Multi-factor authentication can provide an enhanced level of assurance in higher-security scenarios such as online banking, virtual private network access, and physical access because a multi-factor protocol is designed to remain secure even if all but one of the factors has been compromised. We introduce a security model for multi-factor password-authenticated key exchange protocols, propose an efficient and secure protocol called MFPAK, and provide a security argument to show that our protocol is secure in this model. Our security model is an extension of the Bellare-Pointcheval-Rogaway security model for password-authenticated key exchange and accommodates an arbitrary number of symmetric and asymmetric authentication factors.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

Fixed argument pairings

A common scenario in many pairing-based cryptographic protocols is that one argument in the pairing is fixed as a long term secret key or a constant parameter in the system. In these situations, the runtime of Miller's algorithm can be significantly reduced by storing precomputed values that depend on the fixed argument, prior to the input or existence of the second argument. In light of recent developments in pairing computation, we show that the computation of the Miller loop can be sped up by up to 37 if precomputation is employed, with our method being up to 19.5 faster than the previous precomputation techniques.

Quantum coins

One of the earliest cryptographic applications of quantum information was to create quantum digital cash that could not be counterfeited. In this paper, we describe a new type of quantum money: quantum coins, where all coins of the same denomination are represented by identical quantum states. We state desirable security properties such as anonymity and unforgeability and propose two candidate quantum coin schemes: one using black box operations, and another using blind quantum computation.

Applied batch cryptography

The material presented in this thesis may be viewed as comprising two key parts, the first part concerns batch cryptography specifically, whilst the second deals with how this form of cryptography may be applied to security related applications such as electronic cash for improving efficiency of the protocols. The objective of batch cryptography is to devise more efficient primitive cryptographic protocols. In general, these primitives make use of some property such as homomorphism to perform a computationally expensive operation on a collective input set. The idea is to amortise an expensive operation, such as modular exponentiation, over the input. Most of the research work in this field has concentrated on its employment as a batch verifier of digital signatures. It is shown that several new attacks may be launched against these published schemes as some weaknesses are exposed. Another common use of batch cryptography is the simultaneous generation of digital signatures. There is significantly less previous work on this area, and the present schemes have some limited use in practical applications. Several new batch signatures schemes are introduced that improve upon the existing techniques and some practical uses are illustrated. Electronic cash is a technology that demands complex protocols in order to furnish several security properties. These typically include anonymity, traceability of a double spender, and off-line payment features. Presently, the most efficient schemes make use of coin divisibility to withdraw one large financial amount that may be progressively spent with one or more merchants. Several new cash schemes are introduced here that make use of batch cryptography for improving the withdrawal, payment, and deposit of electronic coins. The devised schemes apply both to the batch signature and verification techniques introduced, demonstrating improved performance over the contemporary divisible based structures. The solutions also provide an alternative paradigm for the construction of electronic cash systems. Whilst electronic cash is used as the vehicle for demonstrating the relevance of batch cryptography to security related applications, the applicability of the techniques introduced extends well beyond this.

Compliant cryptologic protocols

Literally, the word compliance suggests conformity in fulfilling official requirements. The thesis presents the results of the analysis and design of a class of protocols called compliant cryptologic protocols (CCP). The thesis presents a notion for compliance in cryptosystems that is conducive as a cryptologic goal. CCP are employed in security systems used by at least two mutually mistrusting sets of entities. The individuals in the sets of entities only trust the design of the security system and any trusted third party the security system may include. Such a security system can be thought of as a broker between the mistrusting sets of entities. In order to provide confidence in operation for the mistrusting sets of entities, CCP must provide compliance verification mechanisms. These mechanisms are employed either by all the entities or a set of authorised entities in the system to verify the compliance of the behaviour of various participating entities with the rules of the system. It is often stated that confidentiality, integrity and authentication are the primary interests of cryptology. It is evident from the literature that authentication mechanisms employ confidentiality and integrity services to achieve their goal. Therefore, the fundamental services that any cryptographic algorithm may provide are confidentiality and integrity only. Since controlling the behaviour of the entities is not a feasible cryptologic goal,the verification of the confidentiality of any data is a futile cryptologic exercise. For example, there exists no cryptologic mechanism that would prevent an entity from willingly or unwillingly exposing its private key corresponding to a certified public key. The confidentiality of the data can only be assumed. Therefore, any verification in cryptologic protocols must take the form of integrity verification mechanisms. Thus, compliance verification must take the form of integrity verification in cryptologic protocols. A definition of compliance that is conducive as a cryptologic goal is presented as a guarantee on the confidentiality and integrity services. The definitions are employed to provide a classification mechanism for various message formats in a cryptologic protocol. The classification assists in the characterisation of protocols, which assists in providing a focus for the goals of the research. The resulting concrete goal of the research is the study of those protocols that employ message formats to provide restricted confidentiality and universal integrity services to selected data. The thesis proposes an informal technique to understand, analyse and synthesise the integrity goals of a protocol system. The thesis contains a study of key recovery,electronic cash, peer-review, electronic auction, and electronic voting protocols. All these protocols contain message format that provide restricted confidentiality and universal integrity services to selected data. The study of key recovery systems aims to achieve robust key recovery relying only on the certification procedure and without the need for tamper-resistant system modules. The result of this study is a new technique for the design of key recovery systems called hybrid key escrow. The thesis identifies a class of compliant cryptologic protocols called secure selection protocols (SSP). The uniqueness of this class of protocols is the similarity in the goals of the member protocols, namely peer-review, electronic auction and electronic voting. The problem statement describing the goals of these protocols contain a tuple,(I, D), where I usually refers to an identity of a participant and D usually refers to the data selected by the participant. SSP are interested in providing confidentiality service to the tuple for hiding the relationship between I and D, and integrity service to the tuple after its formation to prevent the modification of the tuple. The thesis provides a schema to solve the instances of SSP by employing the electronic cash technology. The thesis makes a distinction between electronic cash technology and electronic payment technology. It will treat electronic cash technology to be a certification mechanism that allows the participants to obtain a certificate on their public key, without revealing the certificate or the public key to the certifier. The thesis abstracts the certificate and the public key as the data structure called anonymous token. It proposes design schemes for the peer-review, e-auction and e-voting protocols by employing the schema with the anonymous token abstraction. The thesis concludes by providing a variety of problem statements for future research that would further enrich the literature.

Design and analysis of group key exchange protocols

A group key exchange (GKE) protocol allows a set of parties to agree upon a common secret session key over a public network. In this thesis, we focus on designing efficient GKE protocols using public key techniques and appropriately revising security models for GKE protocols. For the purpose of modelling and analysing the security of GKE protocols we apply the widely accepted computational complexity approach. The contributions of the thesis to the area of GKE protocols are manifold. We propose the first GKE protocol that requires only one round of communication and is proven secure in the standard model. Our protocol is generically constructed from a key encapsulation mechanism (KEM). We also suggest an efficient KEM from the literature, which satisfies the underlying security notion, to instantiate the generic protocol. We then concentrate on enhancing the security of one-round GKE protocols. A new model of security for forward secure GKE protocols is introduced and a generic one-round GKE protocol with forward security is then presented. The security of this protocol is also proven in the standard model. We also propose an efficient forward secure encryption scheme that can be used to instantiate the generic GKE protocol. Our next contributions are to the security models of GKE protocols. We observe that the analysis of GKE protocols has not been as extensive as that of two-party key exchange protocols. Particularly, the security attribute of key compromise impersonation (KCI) resilience has so far been ignored for GKE protocols. We model the security of GKE protocols addressing KCI attacks by both outsider and insider adversaries. We then show that a few existing protocols are not secure against KCI attacks. A new proof of security for an existing GKE protocol is given under the revised model assuming random oracles. Subsequently, we treat the security of GKE protocols in the universal composability (UC) framework. We present a new UC ideal functionality for GKE protocols capturing the security attribute of contributiveness. An existing protocol with minor revisions is then shown to realize our functionality in the random oracle model. Finally, we explore the possibility of constructing GKE protocols in the attribute-based setting. We introduce the concept of attribute-based group key exchange (AB-GKE). A security model for AB-GKE and a one-round AB-GKE protocol satisfying our security notion are presented. The protocol is generically constructed from a new cryptographic primitive called encapsulation policy attribute-based KEM (EP-AB-KEM), which we introduce in this thesis. We also present a new EP-AB-KEM with a proof of security assuming generic groups and random oracles. The EP-AB-KEM can be used to instantiate our generic AB-GKE protocol.

Signal authentication and integrity schemes for next generation global navigation satellite systems

This paper describes a number of techniques for GNSS navigation message authentication. A detailed analysis of the security facilitated by navigation message authentication is given. The analysis takes into consideration the risk of critical applications that rely on GPS including transportation, finance and telecommunication networks. We propose a number of cryptographic authentication schemes for navigation data authentication. These authentication schemes provide authenticity and integrity of the navigation data to the receiver. Through software simulation, the performance of the schemes is quantified. The use of software simulation enables the collection of authentication performance data of different data channels, and the impact of various schemes on the infrastructure and receiver. Navigation message authentication schemes have been simulated at the proposed data rates of Galileo and GPS services, for which the resulting performance data is presented. This paper concludes by making recommendations for optimal implementation of navigation message authentication for Galileo and next generation GPS systems.

Requirements for enhancing trust, security and integrity of GNSS location services

The paper describes a number of requirements for enhancing the trust of location acquisition from Satellite Navigation Systems, particularly for those applications where the location is monitored through a remote GNSS receiver. We discuss how the trust of a location acquisition could be propagated to an application through the use of a proposed tamper-­resistant GNSS receiver which quantifies the trust of a location solution from the signaling used (ie. P(Y) code, Galileo SOL, PRS, CS) and provides a cryptographic proof of this to a remote application. The tamper­-resistance state of the receiver is also included in this cryptographic proof.

Reinforcing bad behaviour : the misuse of security indicators on popular websites

Before making a security or privacy decision, Internet users should evaluate several security indicators in their browser, such as the use of HTTPS (indicated via the lock icon), the domain name of the site, and information from extended validation certificates. However, studies have shown that human subjects infrequently employ these indicators, relying on other indicators that can be spoofed and convey no cryptographic assurances. We identify four simple security indicators that accurately represent security properties of the connection and then examine 125 popular websites to determine if the sites' designs result in correctly displayed security indicators during login. In the vast majority of cases, at least some security indicators are absent or suboptimal. This suggests users are becoming habituated to ignoring recommended security indicators.

Linearity within the SMS4 Block Cipher

We present several new observations on the SMS4 block cipher, and discuss their cryptographic significance. The crucial observation is the existence of fixed points and also of simple linear relationships between the bits of the input and output words for each component of the round functions for some input words. This implies that the non-linear function T of SMS4 does not appear random and that the linear transformation provides poor diffusion. Furthermore, the branch number of the linear transformation in the key scheduling algorithm is shown to be less than optimal. The main security implication of these observations is that the round function is not always non-linear. Due to this linearity, it is possible to reduce the number of effective rounds of SMS4 by four. We also investigate the susceptibility of SMS4 to further cryptanalysis. Finally, we demonstrate a successful differential attack on a slightly modified variant of SMS4. These findings raise serious questions on the security provided by SMS4.