On the provable security of an efficient RSA-based pseudorandom generator

Pseudorandom Generators (PRGs) based on the RSA inversion (one-wayness) problem have been extensively studied in the literature over the last 25 years. These generators have the attractive feature of provable pseudorandomness security assuming the hardness of the RSA inversion problem. However, despite extensive study, the most efficient provably secure RSA-based generators output asymptotically only at most O(logn) bits per multiply modulo an RSA modulus of bitlength n, and hence are too slow to be used in many practical applications. To bring theory closer to practice, we present a simple modification to the proof of security by Fischlin and Schnorr of an RSA-based PRG, which shows that one can obtain an RSA-based PRG which outputs Ω(n) bits per multiply and has provable pseudorandomness security assuming the hardness of a well-studied variant of the RSA inversion problem, where a constant fraction of the plaintext bits are given. Our result gives a positive answer to an open question posed by Gennaro (J. of Cryptology, 2005) regarding finding a PRG beating the rate O(logn) bits per multiply at the cost of a reasonable assumption on RSA inversion.

an improved smart card based password authentication scheme with provable security

Password authentication has been adopted as one of the most commonly used solutions in network environment to protect resources from unauthorized access. Recently, Lee–Kim–Yoo [S.W. Lee, H.S. Kim, K.Y. Yoo, Improvement of Chien et al.'s remote user authentication scheme using smart cards, Computer Standards & Interfaces 27 (2) (2005) 181–183] and Lee-Chiu [N.Y. Lee, Y.C. Chiu, Improved remote authentication scheme with smart card, Computer Standards & Interfaces 27 (2) (2005) 177–180] respectively proposed a smart card based password authentication scheme. We show that these two schemes are both subject to forgery attacks provided that the information stored in the smart card is disclosed by the adversary. We also propose an improved scheme with formal security proof.

Provable Security for Cryptocurrencies

The past several years have seen the surprising and rapid rise of Bitcoin and other “cryptocurrencies.” These are decentralized peer-to-peer networks that allow users to transmit money, tocompose financial instruments, and to enforce contracts between mutually distrusting peers, andthat show great promise as a foundation for financial infrastructure that is more robust, efficientand equitable than ours today. However, it is difficult to reason about the security of cryptocurrencies. Bitcoin is a complex system, comprising many intricate and subtly-interacting protocol layers. At each layer it features design innovations that (prior to our work) have not undergone any rigorous analysis. Compounding the challenge, Bitcoin is but one of hundreds of competing cryptocurrencies in an ecosystem that is constantly evolving. The goal of this thesis is to formally reason about the security of cryptocurrencies, reining in their complexity, and providing well-defined and justified statements of their guarantees. We provide a formal specification and construction for each layer of an abstract cryptocurrency protocol, and prove that our constructions satisfy their specifications. The contributions of this thesis are centered around two new abstractions: “scratch-off puzzles,” and the “blockchain functionality” model. Scratch-off puzzles are a generalization of the Bitcoin “mining” algorithm, its most iconic and novel design feature. We show how to provide secure upgrades to a cryptocurrency by instantiating the protocol with alternative puzzle schemes. We construct secure puzzles that address important and well-known challenges facing Bitcoin today, including wasted energy and dangerous coalitions. The blockchain functionality is a general-purpose model of a cryptocurrency rooted in the “Universal Composability” cryptography theory. We use this model to express a wide range of applications, including transparent “smart contracts” (like those featured in Bitcoin and Ethereum), and also privacy-preserving applications like sealed-bid auctions. We also construct a new protocol compiler, called Hawk, which translates user-provided specifications into privacy-preserving protocols based on zero-knowledge proofs.

Security of Two-Party Identity-Based Key Agreement

Identity-based cryptography has become extremely fashionable in the last few years. As a consequence many proposals for identity-based key establishment have emerged, the majority in the two party case. We survey the currently proposed protocols of this type, examining their security and efficiency. Problems with some published protocols are noted.

Security ceremonies : including humans in cryptographic protocols

Whether by using electronic banking, by using credit cards, or by synchronising a mobile telephone via Bluetooth to an in-car system, humans are a critical part in many cryptographic protocols daily. We reduced the gap that exists between the theory and the reality of the security of these cryptographic protocols involving humans, by creating tools and techniques for proofs and implementations of human-followable security. After three human research studies, we present a model for capturing human recognition; we provide a tool for generating values called Computer-HUman Recognisable Nonces (CHURNs); and we provide a model for capturing human perceptible freshness.

Formalising human recognition : a fundamental building block for security proofs

A fundamental part of many authentication protocols which authenticate a party to a human involves the human recognizing or otherwise processing a message received from the party. Examples include typical implementations of Verified by Visa in which a message, previously stored by the human at a bank, is sent by the bank to the human to authenticate the bank to the human; or the expectation that humans will recognize or verify an extended validation certificate in a HTTPS context. This paper presents general definitions and building blocks for the modelling and analysis of human recognition in authentication protocols, allowing the creation of proofs for protocols which include humans. We cover both generalized trawling and human-specific targeted attacks. As examples of the range of uses of our construction, we use the model presented in this paper to prove the security of a mutual authentication login protocol and a human-assisted device pairing protocol.

NTRUCCA : how to strengthen NTRUEncrypt to chosen-ciphertext security in the standard model

NTRUEncrypt is a fast and practical lattice-based public-key encryption scheme, which has been standardized by IEEE, but until recently, its security analysis relied only on heuristic arguments. Recently, Stehlé and Steinfeld showed that a slight variant (that we call pNE) could be proven to be secure under chosen-plaintext attack (IND-CPA), assuming the hardness of worst-case problems in ideal lattices. We present a variant of pNE called NTRUCCA, that is IND-CCA2 secure in the standard model assuming the hardness of worst-case problems in ideal lattices, and only incurs a constant factor overhead in ciphertext and key length over the pNE scheme. To our knowledge, our result gives the first IND-CCA2 secure variant of NTRUEncrypt in the standard model, based on standard cryptographic assumptions. As an intermediate step, we present a construction for an All-But-One (ABO) lossy trapdoor function from pNE, which may be of independent interest. Our scheme uses the lossy trapdoor function framework of Peikert and Waters, which we generalize to the case of (k − 1)-of-k-correlated input distributions.

Universal Hashing for Information-Theoretic Security

The information-theoretic approach to security entails harnessing the correlated randomness available in nature to establish security. It uses tools from information theory and coding and yields provable security, even against an adversary with unbounded computational power. However, the feasibility of this approach in practice depends on the development of efficiently implementable schemes. In this paper, we review a special class of practical schemes for information-theoretic security that are based on 2-universal hash families. Specific cases of secret key agreement and wiretap coding are considered, and general themes are identified. The scheme presented for wiretap coding is modular and can be implemented easily by including an extra preprocessing layer over the existing transmission codes.

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.

Automating computational proofs for public-key-based key exchange

We present an approach to automating computationally sound proofs of key exchange protocols based on public-key encryption. We show that satisfying the property called occultness in the Dolev-Yao model guarantees the security of a related key exchange protocol in a simple computational model. Security in this simpler model has been shown to imply security in a Bellare {Rogaway-like model. Furthermore, the occultness in the Dolev-Yao model can be searched automatically by a mechanisable procedure. Thus automated proofs for key exchange protocols in the computational model can be achieved. We illustrate the method using the well-known Lowe-Needham-Schroeder protocol.

Ceremony analysis : strengths and weaknesses

We investigate known security flaws in the context of security ceremonies to gain an understanding of the ceremony analysis process. The term security ceremonies is used to describe a system of protocols and humans which interact for a specific purpose. Security ceremonies and ceremony analysis is an area of research in its infancy, and we explore the basic principles involved to better understand the issues involved.We analyse three ceremonies, HTTPS, EMV and Opera Mini, and use the information gained from the experience to establish a list of typical flaws in ceremonies. Finally, we use that list to analyse a protocol proven secure for human use. This leads to a realisation of the strengths and weaknesses of ceremony analysis.