A Thesis: A CRYPTOGRAPHIC STUDY OF SOME DIGITAL SIGNATURE SCHEMES.

In this thesis, we propose some directed signature schemes. In addition, we have discussed their applications in different situations. In this thesis, we would like to discuss the security aspects during the design process of the proposed directed digital signature schemes. The security of the most digital signature schemes widely use in practice is based on the two difficult problems, viz; the problem of factoring integers (The RSA scheme) and the problem of finding discrete logarithms over finite fields (The ElGamal scheme). The proposed works in this thesis is divided into seven chapters

Improvements and Generalisations of Signcryption Schemes

In this work, we study the cryptographic primitive: signcryption, which combines the functionalities of digital signatures and public-key encryption. We first propose two generic transforms from meta-ElGamal signature schemes to signcryption schemes. These constructions can be thought of as generalisations of the signcryption schemes by Zheng and Gamage et al. Our results show that a large class of signcryption schemes arc outsider IND-CCA2 secure and insider UF-CMA secure. As a by-product, we also show that the meta-EIGamal signature schemes, for which no previous formal security proofs have been shown, arc UF-CMA secure. \Ve then propose a modification of one of the transforms in order to achieve insider IXD-CCA2 security in addition to insider UF-CMA security. This modification COStS just one extra exponential operation. In particular, we can apply this modification to the Zheng signcryption scheme to make it fully insider secure. Finally, we propose a generic transform from a two-key signcryption scheme to a one-key signcryption scheme while preserving both confidentiality and unforgeability. Our result shows that if we have an insider I)JD•CCA2 and CFC1A secure two-key signcryption scheme, then it can be turned into an insider IND-CCA2 and CF•CMA secure one• key signcryption scheme. We also show that an insider IND•CCA2 and UF-CMA secure one• key signcryption scheme induces a secure combined public• key scheme; that is, a combination of a signature scheme and a public• key encryption scheme that can securely share the same key pair. Combining previous results suggests that we can obtain a large class of insider secure one-key signcryption schemes from meta-ElGamal signature schemes, and that each of them can induce a secure combined public-key scheme.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Advances in signatures, encryption, and E-Cash from bilinear groups

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 147-161).We present new formal definitions, algorithms, and motivating applications for three natural cryptographic constructions. Our constructions are based on a special type of algebraic group called bilinear groups. 1. Re-Signatures: We present the first public key signature scheme where a semi-trusted proxy, given special information, can translate Alice's signature on a message into Bob's signature on the same message. The special information, however, allows nothing else, i.e., the proxy cannot translate from Bob to Alice, nor can it sign on behalf of either Alice or Bob. We show that a path through a graph can be cheaply authenticated using this scheme, with applications to electronic passports. 2. Re-Encryption: We present the first public key cryptosystem where a semi-trusted proxy, given special information, can translate an encryption of a message under Alice's key into an encryption of the same message under Bob's key. Again, the special information allows nothing else, i.e. the proxy cannot translate from Bob to Alice, decrypt on behalf of either Alice or Bob, or learn anything else about the message. We apply this scheme to create a new mechanism for secure distributed storage.(cont.) 3. Compact; E-Cash with Tracing and Bounded-Anonymity: We present an offline e-cash system where 2 coins can be stored in O(e + k) bits and withdrawn or spent in 0(f + k) time, where k is the security parameter. The best previously known schemes required at least one of these complexities to be 0(2t . k). In our system, a user's transactions are anonymous and unlinkable, unless she performs a forbidden action, such as double-spending a coin. Performing a forbidden action reveals the identity of the user, and optionally allows to trace all of her past transactions. We provide solutions without using a trusted party. We argue why features of our system are likely to be crucial to the adoption of any e-cash system.by Susan Hohenberger.Ph.D

Elliptic Curve Cryptography on Modern Processor Architectures

Abstract Elliptic Curve Cryptography (ECC) has been adopted by the US National Security Agency (NSA) in Suite "B" as part of its "Cryptographic Modernisation Program ". Additionally, it has been favoured by an entire host of mobile devices due to its superior performance characteristics. ECC is also the building block on which the exciting field of pairing/identity based cryptography is based. This widespread use means that there is potentially a lot to be gained by researching efficient implementations on modern processors such as IBM's Cell Broadband Engine and Philip's next generation smart card cores. ECC operations can be thought of as a pyramid of building blocks, from instructions on a core, modular operations on a finite field, point addition & doubling, elliptic curve scalar multiplication to application level protocols. In this thesis we examine an implementation of these components for ECC focusing on a range of optimising techniques for the Cell's SPU and the MIPS smart card. We show significant performance improvements that can be achieved through of adoption of EC

Biometric Cryptosystems : Authentication, Encryption and Signature for Biometric Identities

Biometrics have been used for secure identification and authentication for more than two decades since biometric data is unique, non-transferable, unforgettable, and always with us. Recently, biometrics has pervaded other aspects of security applications that can be listed under the topic of ``Biometric Cryptosystems''. Although the security of some of these systems is questionable when they are utilized alone, integration with other technologies such as digital signatures or Identity Based Encryption (IBE) schemes results in cryptographically secure applications of biometrics. It is exactly this field of biometric cryptosystems that we focused in this thesis. In particular, our goal is to design cryptographic protocols for biometrics in the framework of a realistic security model with a security reduction. Our protocols are designed for biometric based encryption, signature and remote authentication. We first analyze the recently introduced biometric remote authentication schemes designed according to the security model of Bringer et al.. In this model, we show that one can improve the database storage cost significantly by designing a new architecture, which is a two-factor authentication protocol. This construction is also secure against the new attacks we present, which disprove the claimed security of remote authentication schemes, in particular the ones requiring a secure sketch. Thus, we introduce a new notion called ``Weak-identity Privacy'' and propose a new construction by combining cancelable biometrics and distributed remote authentication in order to obtain a highly secure biometric authentication system. We continue our research on biometric remote authentication by analyzing the security issues of multi-factor biometric authentication (MFBA). We formally describe the security model for MFBA that captures simultaneous attacks against these systems and define the notion of user privacy, where the goal of the adversary is to impersonate a client to the server. We design a new protocol by combining bipartite biotokens, homomorphic encryption and zero-knowledge proofs and provide a security reduction to achieve user privacy. The main difference of this MFBA protocol is that the server-side computations are performed in the encrypted domain but without requiring a decryption key for the authentication decision of the server. Thus, leakage of the secret key of any system component does not affect the security of the scheme as opposed to the current biometric systems involving cryptographic techniques. We also show that there is a tradeoff between the security level the scheme achieves and the requirement for making the authentication decision without using any secret key. In the second part of the thesis, we delve into biometric-based signature and encryption schemes. We start by designing a new biometric IBS system that is based on the currently most efficient pairing based signature scheme in the literature. We prove the security of our new scheme in the framework of a stronger model compared to existing adversarial models for fuzzy IBS, which basically simulates the leakage of partial secret key components of the challenge identity. In accordance with the novel features of this scheme, we describe a new biometric IBE system called as BIO-IBE. BIO-IBE differs from the current fuzzy systems with its key generation method that not only allows for a larger set of encryption systems to function for biometric identities, but also provides a better accuracy/identification of the users in the system. In this context, BIO-IBE is the first scheme that allows for the use of multi-modal biometrics to avoid collision attacks. Finally, BIO-IBE outperforms the current schemes and for small-universe of attributes, it is secure in the standard model with a better efficiency compared to its counterpart. Another contribution of this thesis is the design of biometric IBE systems without using pairings. In fact, current fuzzy IBE schemes are secure under (stronger) bilinear assumptions and the decryption of each message requires pairing computations almost equal to the number of attributes defining the user. Thus, fuzzy IBE makes error-tolerant encryption possible at the expense of efficiency and security. Hence, we design a completely new construction for biometric IBE based on error-correcting codes, generic conversion schemes and weakly secure anonymous IBE schemes that encrypt a message bit by bit. The resulting scheme is anonymous, highly secure and more efficient compared to pairing-based biometric IBE, especially for the decryption phase. The security of our generic construction is reduced to the security of the anonymous IBE scheme, which is based on the Quadratic Residuosity assumption. The binding of biometric features to the user's identity is achieved similar to BIO-IBE, thus, preserving the advantages of its key generation procedure

Verifiable Encryption from MPC-in-the-Head

Verifiable encryption (VE) is a protocol where one can provide assurance that an encrypted plaintext satisfies certain properties. It is an important buiding block in cryptography with many useful applications, such as key escrow, group signatures, optimistic fair exchange, etc. However, a majority of previous VE schemes are restricted to instantiation with specific public-key encryption schemes or relations. In this work, we propose a novel framework that realizes VE protocols using the MPC-in-the-head zero-knowledge proof systems (Ishai et al. STOC 2007). Our generic compiler can turn a large class of MPC-in-the-head ZK proofs into secure VE protocols for any CPA secure public-key encryption (PKE) schemes with the undeniability property, a notion that essentially guarantees binding of encryption when used as a commitment scheme. Our framework is versatile: because the circuit proven by the MPC-in-the-head prover is decoupled from a complex encryption function, the prover’s work can be focused on proving properties (i.e. relation) about the encrypted data, not the proof of plaintext knowledge. Hence, our approach allows for instantiation with various combinations of properties about encrypted data and encryption functions. As concrete applications we describe new approaches to verifiably encrypting discrete logarithms in any prime order group and AES private keys

Design and Analysis of Opaque Signatures

Digital signatures were introduced to guarantee the authenticity and integrity of the underlying messages. A digital signature scheme comprises the key generation, the signature, and the verification algorithms. The key generation algorithm creates the signing and the verifying keys, called also the signer’s private and public keys respectively. The signature algorithm, which is run by the signer, produces a signature on the input message. Finally, the verification algorithm, run by anyone who knows the signer’s public key, checks whether a purported signature on some message is valid or not. The last property, namely the universal verification of digital signatures is undesirable in situations where the signed data is commercially or personally sensitive. Therefore, mechanisms which share most properties with digital signatures except for the universal verification were invented to respond to the aforementioned need; we call such mechanisms “opaque signatures”. In this thesis, we study the signatures where the verification cannot be achieved without the cooperation of a specific entity, namely the signer in case of undeniable signatures, or the confirmer in case of confirmer signatures; we make three main contributions. We first study the relationship between two security properties important for public key encryption, namely data privacy and key privacy. Our study is motivated by the fact that opaque signatures involve always an encryption layer that ensures their opacity. The properties required for this encryption vary according to whether we want to protect the identity (i.e. the key) of the signer or hide the validity of the signature. Therefore, it would be convenient to use existing work about the encryption scheme in order to derive one notion from the other. Next, we delve into the generic constructions of confirmer signatures from basic cryptographic primitives, e.g. digital signatures, encryption, or commitment schemes. In fact, generic constructions give easy-to-understand and easy-to-prove schemes, however, this convenience is often achieved at the expense of efficiency. In this contribution, which constitutes the core of this thesis, we first analyze the already existing constructions; our study concludes that the popular generic constructions of confirmer signatures necessitate strong security assumptions on the building blocks, which impacts negatively the efficiency of the resulting signatures. Next, we show that a small change in these constructionsmakes these assumptions drop drastically, allowing as a result constructions with instantiations that compete with the dedicated realizations of these signatures. Finally, we revisit two early undeniable signatures which were proposed with a conjectural security. We disprove the claimed security of the first scheme, and we provide a fix to it in order to achieve strong security properties. Next, we upgrade the second scheme so that it supports a iii desirable feature, and we provide a formal security treatment of the new scheme: we prove that it is secure assuming new reasonable assumptions on the underlying constituents