Automated proof for formal indistinguishability and its applications

Bana et al. proposed the relation formal indistinguishability (FIR), i.e. an equivalence between two terms built from an abstract algebra. Later Ene et al. extended it to cover active adversaries and random oracles. This notion enables a framework to verify computational indistinguishability while still offering the simplicity and formality of symbolic methods. We are in the process of making an automated tool for checking FIR between two terms. First, we extend the work by Ene et al. further, by covering ordered sorts and simplifying the way to cope with random oracles. Second, we investigate the possibility of combining algebras together, since it makes the tool scalable and able to cover a wide class of cryptographic schemes. Specially, we show that the combined algebra is still computationally sound, as long as each algebra is sound. Third, we design some proving strategies and implement the tool. Basically, the strategies allow us to find a sequence of intermediate terms, which are formally indistinguishable, between two given terms. FIR between the two given terms is then guaranteed by the transitivity of FIR. Finally, we show applications of the work, e.g. on key exchanges and encryption schemes. In the future, the tool should be extended easily to cover many schemes. This work continues previous research of ours on use of compilers to aid in automated proofs for key exchange.

Automated proofs of computational indistinguishability

We present a tool for automatic analysis of computational indistinguishability between two strings of information. This is designed as a generic tool for proving cryptographic security based on a formalism that provides computational soundness preservation. The tool has been implemented and tested successfully with several cryptographic schemes.

EFFICIENT QUANTUM RANDOM NUMBER GENERATION USING QUANTUM INDISTINGUISHABILITY

In this paper, we propose a quantum method for generation of random numbers based on bosonic stimulation. Randomness arises through the path-dependent indeterministic amplification of two competing bosonic modes. We show that the process provides an efficient method for macroscopic extraction of microscopic randomness.

Security analysis and enhancement of one-way hash based low-cost authentication protocol (OHLCAP)

Choi et al. recently proposed an efficient RFID authentication protocol for a ubiquitous computing environment, OHLCAP(One-Way Hash based Low-Cost Authentication Protocol). However, this paper reveals that the protocol has several security weaknesses : 1) traceability based on the leakage of counter information, 2) vulnerability to an impersonation attack by maliciously updating a random number, and 3) traceability based on a physically-attacked tag. Finally, a security enhanced group-based authentication protocol is presented.

Publicly verifiable ciphertexts

In many applications, where encrypted traffic flows from an open (public) domain to a protected (private) domain, there exists a gateway that bridges the two domains and faithfully forwards the incoming traffic to the receiver. We observe that indistringuishability against (adaptive) chosen-ciphertext attacks (IND-CCA), which is a mandatory goal in face of active attacks in a public domain, can be essentially relaxed to indistinguishability against chosen-plaintext attacks (IND-CPA) for ciphertexts once they pass the gateway that acts as an IND-CCA/CPA filter by first checking the validity of an incoming IND-CCA ciphertext, then transforming it (if valid) into an IND-CPA ciphertext, and forwarding the latter to the receipient in the private domain. "Non-trivial filtering" can result in reduced decryption costs on the receivers' side. We identify a class of encryption schemes with publicaly verifiable ciphertexts that admit generic constructions of (non-trivial) IND-CCA/CPA filters. These schemes are characterized by existence of public algorithms that can distinguish between valid and invalid ciphertexts. To this end, we formally define (non-trivial) public verifiability of ciphertexts for general encryption schemes, key encapsulation mechanisms, and hybrid encryption schemes, encompassing public-key, identity-based, and tag-based encryption flavours. We further analyze the security impact of public verifiability and discuss generic transformations and concrete constructions that enjoy this property.

Computationally sound automated proofs of cryptographic schemes

Proving security of cryptographic schemes, which normally are short algorithms, has been known to be time-consuming and easy to get wrong. Using computers to analyse their security can help to solve the problem. This thesis focuses on methods of using computers to verify security of such schemes in cryptographic models. The contributions of this thesis to automated security proofs of cryptographic schemes can be divided into two groups: indirect and direct techniques. Regarding indirect ones, we propose a technique to verify the security of public-key-based key exchange protocols. Security of such protocols has been able to be proved automatically using an existing tool, but in a noncryptographic model. We show that under some conditions, security in that non-cryptographic model implies security in a common cryptographic one, the Bellare-Rogaway model [11]. The implication enables one to use that existing tool, which was designed to work with a different type of model, in order to achieve security proofs of public-key-based key exchange protocols in a cryptographic model. For direct techniques, we have two contributions. The first is a tool to verify Diffie-Hellmanbased key exchange protocols. In that work, we design a simple programming language for specifying Diffie-Hellman-based key exchange algorithms. The language has a semantics based on a cryptographic model, the Bellare-Rogaway model [11]. From the semantics, we build a Hoare-style logic which allows us to reason about the security of a key exchange algorithm, specified as a pair of initiator and responder programs. The other contribution to the direct technique line is on automated proofs for computational indistinguishability. Unlike the two other contributions, this one does not treat a fixed class of protocols. We construct a generic formalism which allows one to model the security problem of a variety of classes of cryptographic schemes as the indistinguishability between two pieces of information. We also design and implement an algorithm for solving indistinguishability problems. Compared to the two other works, this one covers significantly more types of schemes, but consequently, it can verify only weaker forms of security.

A state-aware RFID privacy model with reader corruption

A number of security models have been proposed for RFID systems. Recent studies show that current models tend to be limited in the number of properties they capture. Consequently, models are commonly unable to distinguish between protocols with regard to finer privacy properties. This paper proposes a privacy model that introduces previously unavailable expressions of privacy. Based on the well-studied notion of indistinguishability, the model also strives to be simpler, easier to use, and more intuitive compared to previous models.

A state-aware RFID privacy model with reader corruption

A number of security models have been proposed for RFID systems. Recent studies show that current models tend to be limited in the number of properties they capture. Consequently, models are commonly unable to distinguish between protocols with regard to finer privacy properties. This paper proposes a privacy model that introduces previously unavailable expressions of privacy. Based on the well-studied notion of indistinguishability, the model also strives to be simpler, easier to use, and more intuitive compared to previous models.

Multipurpose identity-based signcryption : a Swiss army knife for identity-based cryptography

Identity-Based (IB) cryptography is a rapidly emerging approach to public-key cryptography that does not require principals to pre-compute key pairs and obtain certificates for their public keys— instead, public keys can be arbitrary identifiers such as email addresses, while private keys are derived at any time by a trusted private key generator upon request by the designated principals. Despite the flurry of recent results on IB encryption and signature, some questions regarding the security and efficiency of practicing IB encryption (IBE) and signature (IBS) as a joint IB signature/encryption (IBSE) scheme with a common set of parameters and keys, remain unanswered. We first propose a stringent security model for IBSE schemes. We require the usual strong security properties of: (for confidentiality) indistinguishability against adaptive chosen-ciphertext attacks, and (for nonrepudiation) existential unforgeability against chosen-message insider attacks. In addition, to ensure as strong as possible ciphertext armoring, we also ask (for anonymity) that authorship not be transmitted in the clear, and (for unlinkability) that it remain unverifiable by anyone except (for authentication) by the legitimate recipient alone. We then present an efficient IBSE construction, based on bilinear pairings, that satisfies all these security requirements, and yet is as compact as pairing-based IBE and IBS in isolation. Our scheme is secure, compact, fast and practical, offers detachable signatures, and supports multirecipient encryption with signature sharing for maximum scalability.

Cryptographic techniques for managing computational effort

Availability has become a primary goal of information security and is as significant as other goals, in particular, confidentiality and integrity. Maintaining availability of essential services on the public Internet is an increasingly difficult task in the presence of sophisticated attackers. Attackers may abuse limited computational resources of a service provider and thus managing computational costs is a key strategy for achieving the goal of availability. In this thesis we focus on cryptographic approaches for managing computational costs, in particular computational effort. We focus on two cryptographic techniques: computational puzzles in cryptographic protocols and secure outsourcing of cryptographic computations. This thesis contributes to the area of cryptographic protocols in the following ways. First we propose the most efficient puzzle scheme based on modular exponentiations which, unlike previous schemes of the same type, involves only a few modular multiplications for solution verification; our scheme is provably secure. We then introduce a new efficient gradual authentication protocol by integrating a puzzle into a specific signature scheme. Our software implementation results for the new authentication protocol show that our approach is more efficient and effective than the traditional RSA signature-based one and improves the DoSresilience of Secure Socket Layer (SSL) protocol, the most widely used security protocol on the Internet. Our next contributions are related to capturing a specific property that enables secure outsourcing of cryptographic tasks in partial-decryption. We formally define the property of (non-trivial) public verifiability for general encryption schemes, key encapsulation mechanisms (KEMs), and hybrid encryption schemes, encompassing public-key, identity-based, and tag-based encryption avors. We show that some generic transformations and concrete constructions enjoy this property and then present a new public-key encryption (PKE) scheme having this property and proof of security under the standard assumptions. Finally, we combine puzzles with PKE schemes for enabling delayed decryption in applications such as e-auctions and e-voting. For this we first introduce the notion of effort-release PKE (ER-PKE), encompassing the well-known timedrelease encryption and encapsulated key escrow techniques. We then present a security model for ER-PKE and a generic construction of ER-PKE complying with our security notion.

A framework for security analysis of key derivation functions

This paper presents a comprehensive formal security framework for key derivation functions (KDF). The major security goal for a KDF is to produce cryptographic keys from a private seed value where the derived cryptographic keys are indistinguishable from random binary strings. We form a framework of five security models for KDFs. This consists of four security models that we propose: Known Public Inputs Attack (KPM, KPS), Adaptive Chosen Context Information Attack (CCM) and Adaptive Chosen Public Inputs Attack(CPM); and another security model, previously defined by Krawczyk [6], which we refer to as Adaptive Chosen Context Information Attack(CCS). These security models are simulated using an indistinguisibility game. In addition we prove the relationships between these five security models and analyse KDFs using the framework (in the random oracle model).

Publicly verifiable ciphertexts

In many applications, where encrypted traffic flows from an open (public) domain to a protected (private) domain, there exists a gateway that bridges the two domains and faithfully forwards the incoming traffic to the receiver. We observe that indistinguishability against (adaptive) chosen-ciphertext attacks (IND-CCA), which is a mandatory goal in face of active attacks in a public domain, can be essentially relaxed to indistinguishability against chosen-plaintext attacks (IND-CPA) for ciphertexts once they pass the gateway that acts as an IND-CCA/CPA filter by first checking the validity of an incoming IND-CCA ciphertext, then transforming it (if valid) into an IND-CPA ciphertext, and forwarding the latter to the recipient in the private domain. “Non-trivial filtering'' can result in reduced decryption costs on the receivers' side. We identify a class of encryption schemes with publicly verifiable ciphertexts that admit generic constructions of (non-trivial) IND-CCA/CPA filters. These schemes are characterized by existence of public algorithms that can distinguish between valid and invalid ciphertexts. To this end, we formally define (non-trivial) public verifiability of ciphertexts for general encryption schemes, key encapsulation mechanisms, and hybrid encryption schemes, encompassing public-key, identity-based, and tag-based encryption flavours. We further analyze the security impact of public verifiability and discuss generic transformations and concrete constructions that enjoy this property.