166 research outputs found

    Comments and Improvements on Chameleon Hashing Without Key Exposure Based on Factoring

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    In this paper, we present some security flaws of the key-exposure free chameleon hash scheme based on factoring \cite{GWX07}. Besides, we propose an improved chameleon hash scheme without key exposure based on factoring which enjoys all the desired security notions of chameleon hashing

    Digital Signcryption

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    Signcryption is a new cryptographic primitive which simultaneously provides both confidentiality and authenticity. Previously, these two goals had been considered separately, with encryption schemes providing confidentiality and signature schemes providing authenticity. In cases where both were required, the encryption and signature operations were simply sequentially composed. In 1997, Zheng demonstrated that by combining both goals into a single primitive, it is possible to achieve significant savings both in computational and communication overhead. Since then, a wide variety of signcryption schemes have been proposed. In this thesis, we present a number of the proposed signcryption schemes in terms of a common framework. For the most part, the material has been previously presented in various research papers, but some previously omitted proofs have been filled in here. We begin by giving a formal definition of the signcryption primitive, complete with a security model. Then we look at some of the various proposed signcryption schemes, and consider their relative advantages and disadvantages. Finally, we look ahead at what future progress might be made in the field

    A unified framework for trapdoor-permutation-based sequential aggregate signatures

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    We give a framework for trapdoor-permutation-based sequential aggregate signatures (SAS) that unifies and simplifies prior work and leads to new results. The framework is based on ideal ciphers over large domains, which have recently been shown to be realizable in the random oracle model. The basic idea is to replace the random oracle in the full-domain-hash signature scheme with an ideal cipher. Each signer in sequence applies the ideal cipher, keyed by the message, to the output of the previous signer, and then inverts the trapdoor permutation on the result. We obtain different variants of the scheme by varying additional keying material in the ideal cipher and making different assumptions on the trapdoor permutation. In particular, we obtain the first scheme with lazy verification and signature size independent of the number of signers that does not rely on bilinear pairings. Since existing proofs that ideal ciphers over large domains can be realized in the random oracle model are lossy, our schemes do not currently permit practical instantiation parameters at a reasonable security level, and thus we view our contribution as mainly conceptual. However, we are optimistic tighter proofs will be found, at least in our specific application.https://eprint.iacr.org/2018/070.pdfAccepted manuscrip

    Certifying Trapdoor Permutations, Revisited

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    The modeling of trapdoor permutations has evolved over the years. Indeed, finding an appropriate abstraction that bridges between the existing candidate constructions and the needs of applications has proved to be challenging. In particular, the notions of certifying permutations (Bellare and Yung, 96), enhanced and doubly enhanced trapdoor permutations (Goldreich, 04, 08, 11, Goldreich and Rothblum, 13) were added to bridge the gap between the modeling of trapdoor permutations and needs of applications. We identify an additional gap in the current abstraction of trapdoor permutations: Previous works implicitly assumed that it is easy to recognize elements in the domain, as well as uniformly sample from it, even for illegitimate function indices. We demonstrate this gap by using the (Bitansky-Paneth-Wichs, 16) doubly-enhanced trapdoor permutation family to instantiate the Feige-Lapidot-Shamir (FLS) paradigm for constructing non-interactive zero-knowledge (NIZK) protocols, and show that the resulting proof system is unsound. To close the gap, we propose a general notion of certifiably injective doubly enhanced trapdoor functions (DECITDFs), which provides a way of certifying that a given key defines an injective function over the domain defined by it, even when that domain is not efficiently recognizable and sampleable. We show that DECITDFs suffice for instantiating the FLS paradigm; more generally, we argue that certifiable injectivity is needed whenever the generation process of the function is not trusted. We then show two very different ways to construct DECITDFs: One is via the traditional method of RSA/Rabin with the Bellare-Yung certification mechanism, and the other using indistinguishability obfuscation and injective pseudorandom generators. In particular the latter is the first candidate injective trapdoor function, from assumptions other than factoring, that suffices for the FLS paradigm. Finally we observe that a similar gap appears also in other paths proposed in the literature for instantiating the FLS paradigm, specifically via verifiable pseudorandom generators and verifiable pseudorandom functions. Closing the gap there can be done in similar ways to the ones proposed here

    Trapdoor commitment schemes and their applications

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    Informally, commitment schemes can be described by lockable steely boxes. In the commitment phase, the sender puts a message into the box, locks the box and hands it over to the receiver. On one hand, the receiver does not learn anything about the message. On the other hand, the sender cannot change the message in the box anymore. In the decommitment phase the sender gives the receiver the key, and the receiver then opens the box and retrieves the message. One application of such schemes are digital auctions where each participant places his secret bid into a box and submits it to the auctioneer. In this thesis we investigate trapdoor commitment schemes. Following the abstract viewpoint of lockable boxes, a trapdoor commitment is a box with a tiny secret door. If someone knows the secret door, then this person is still able to change the committed message in the box, even after the commitment phase. Such trapdoors turn out to be very useful for the design of secure cryptographic protocols involving commitment schemes. In the first part of the thesis, we formally introduce trapdoor commitments and extend the notion to identity-based trapdoors, where trapdoors can only be used in connection with certain identities. We then recall the most popular constructions of ordinary trapdoor protocols and present new solutions for identity-based trapdoors. In the second part of the thesis, we show the usefulness of trapdoors in commitment schemes. Deploying trapdoors we construct efficient non-malleable commitment schemes which basically guarantee indepency of commitments. Furthermore, applying (identity-based) trapdoor commitments we secure well-known identification protocols against a new kind of attack. And finally, by means of trapdoors, we show how to construct composable commitment schemes that can be securely executed as subprotocols within complex protocols

    The Interpolating Random Spline Cryptosystem and the Chaotic-Map Public-Key Cryptosystem

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    The feasibility of implementing the interpolating cubic spline function as encryption and decryption transformations is presented. The encryption method can be viewed as computing a transposed polynomial. The main characteristic of the spline cryptosystem is that the domain and range of encryption are defined over real numbers, instead of the traditional integer numbers. Moreover, the spline cryptosystem can be implemented in terms of inexpensive multiplications and additions. Using spline functions, a series of discontiguous spline segments can execute the modular arithmetic of the RSA system. The similarity of the RSA and spline functions within the integer domain is demonstrated. Furthermore, we observe that such a reformulation of RSA cryptosystem can be characterized as polynomials with random offsets between ciphertext values and plaintext values. This contrasts with the spline cryptosystems, so that a random spline system has been developed. The random spline cryptosystem is an advanced structure of spline cryptosystem. Its mathematical indeterminacy on computing keys with interpolants no more than 4 and numerical sensitivity to the random offset t( increases its utility. This article also presents a chaotic public-key cryptosystem employing a one-dimensional difference equation as well as a quadratic difference equation. This system makes use of the El Gamal’s scheme to accomplish the encryption process. We note that breaking this system requires the identical work factor that is needed in solving discrete logarithm with the same size of moduli
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