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.

Forward-secure hierarchical predicate encryption

Secrecy of decryption keys is an important pre-requisite for security of any encryption scheme and compromised private keys must be immediately replaced. \emph{Forward Security (FS)}, introduced to Public Key Encryption (PKE) by Canetti, Halevi, and Katz (Eurocrypt 2003), reduces damage from compromised keys by guaranteeing confidentiality of messages that were encrypted prior to the compromise event. The FS property was also shown to be achievable in (Hierarchical) Identity-Based Encryption (HIBE) by Yao, Fazio, Dodis, and Lysyanskaya (ACM CCS 2004). Yet, for emerging encryption techniques, offering flexible access control to encrypted data, by means of functional relationships between ciphertexts and decryption keys, FS protection was not known to exist.\smallskip In this paper we introduce FS to the powerful setting of \emph{Hierarchical Predicate Encryption (HPE)}, proposed by Okamoto and Takashima (Asiacrypt 2009). Anticipated applications of FS-HPE schemes can be found in searchable encryption and in fully private communication. Considering the dependencies amongst the concepts, our FS-HPE scheme implies forward-secure flavors of Predicate Encryption and (Hierarchical) Attribute-Based Encryption.\smallskip Our FS-HPE scheme guarantees forward security for plaintexts and for attributes that are hidden in HPE ciphertexts. It further allows delegation of decrypting abilities at any point in time, independent of FS time evolution. It realizes zero-inner-product predicates and is proven adaptively secure under standard assumptions. As the ``cross-product" approach taken in FS-HIBE is not directly applicable to the HPE setting, our construction resorts to techniques that are specific to existing HPE schemes and extends them with what can be seen as a reminiscent of binary tree encryption from FS-PKE.

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.

Establishing initial trust in autonomous delay tolerant networks without centralised PKI

A Delay Tolerant Network (DTN) is one where nodes can be highly mobile, with long message delay times forming dynamic and fragmented networks. Traditional centralised network security is difficult to implement in such a network, therefore distributed security solutions are more desirable in DTN implementations. Establishing effective trust in distributed systems with no centralised Public Key Infrastructure (PKI) such as the Pretty Good Privacy (PGP) scheme usually requires human intervention. Our aim is to build and compare different de- centralised trust systems for implementation in autonomous DTN systems. In this paper, we utilise a key distribution model based on the Web of Trust principle, and employ a simple leverage of common friends trust system to establish initial trust in autonomous DTN’s. We compare this system with two other methods of autonomously establishing initial trust by introducing a malicious node and measuring the distribution of malicious and fake keys. Our results show that the new trust system not only mitigates the distribution of fake malicious keys by 40% at the end of the simulation, but it also improved key distribution between nodes. This paper contributes a comparison of three de-centralised trust systems that can be employed in autonomous DTN systems.

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.

Fast formulas for computing cryptographic pairings

The most powerful known primitive in public-key cryptography is undoubtedly elliptic curve pairings. Upon their introduction just over ten years ago the computation of pairings was far too slow for them to be considered a practical option. This resulted in a vast amount of research from many mathematicians and computer scientists around the globe aiming to improve this computation speed. From the use of modern results in algebraic and arithmetic geometry to the application of foundational number theory that dates back to the days of Gauss and Euler, cryptographic pairings have since experienced a great deal of improvement. As a result, what was an extremely expensive computation that took several minutes is now a high-speed operation that takes less than a millisecond. This thesis presents a range of optimisations to the state-of-the-art in cryptographic pairing computation. Both through extending prior techniques, and introducing several novel ideas of our own, our work has contributed to recordbreaking pairing implementations.

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.

Functional encryption for threshold functions (or fuzzy IBE) from lattices

Cryptosystems based on the hardness of lattice problems have recently acquired much importance due to their average-case to worst-case equivalence, their conjectured resistance to quantum cryptanalysis, their ease of implementation and increasing practicality, and, lately, their promising potential as a platform for constructing advanced functionalities. In this work, we construct “Fuzzy” Identity Based Encryption from the hardness of the Learning With Errors (LWE) problem. We note that for our parameters, the underlying lattice problems (such as gapSVP or SIVP) are assumed to be hard to approximate within supexponential factors for adversaries running in subexponential time. We give CPA and CCA secure variants of our construction, for small and large universes of attributes. All our constructions are secure against selective-identity attacks in the standard model. Our construction is made possible by observing certain special properties that secret sharing schemes need to satisfy in order to be useful for Fuzzy IBE. We also discuss some obstacles towards realizing lattice-based attribute-based encryption (ABE).

Shrinking the keys of discrete-log-type lossy trapdoor functions

To this day, realizations in the standard-model of (lossy) trapdoor functions from discrete-log-type assumptions require large public key sizes, e.g., about Θ(λ 2) group elements for a reduction from the decisional Diffie-Hellman assumption (where λ is a security parameter). We propose two realizations of lossy trapdoor functions that achieve public key size of only Θ(λ) group elements in bilinear groups, with a reduction from the decisional Bilinear Diffie-Hellman assumption. Our first construction achieves this result at the expense of a long common reference string of Θ(λ 2) elements, albeit reusable in multiple LTDF instantiations. Our second scheme also achieves public keys of size Θ(λ), entirely in the standard model and in particular without any reference string, at the cost of a slightly more involved construction. The main technical novelty, developed for the second scheme, is a compact encoding technique for generating compressed representations of certain sequences of group elements for the public parameters.

Strong cryptography from weak secrets

Distributed-password public-key cryptography (DPwPKC) allows the members of a group of people, each one holding a small secret password only, to help a leader to perform the private operation, associated to a public-key cryptosystem. Abdalla et al. recently defined this tool [1], with a practical construction. Unfortunately, the latter applied to the ElGamal decryption only, and relied on the DDH assumption, excluding any recent pairing-based cryptosystems. In this paper, we extend their techniques to support, and exploit, pairing-based properties: we take advantage of pairing-friendly groups to obtain efficient (simulation-sound) zero-knowledge proofs, whose security relies on the Decisional Linear assumption. As a consequence, we provide efficient protocols, secure in the standard model, for ElGamal decryption as in [1], but also for Linear decryption, as well as extraction of several identity-based cryptosystems [6,4]. Furthermore, we strenghten their security model by suppressing the useless testPwd queries in the functionality.

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.

Identity-based signcryption

The notion of identity-based IB cryptography was proposed by Shamir [177] as a specialization of public key PK cryptography which dispensed with the need for cumbersome directories, certificates, and revocation lists.

Expressive cryptography : lattice perspectives

The invention of asymmetric encryption back in the seventies was a conceptual leap that vastly increased the expressive power of encryption of the times. For the first time, it allowed the sender of a message to designate the intended recipient in an cryptographic way, expressed as a “public key” that was related to but distinct from the “private key” that, alone, embodied the ability to decrypt. This made large-scale encryption a practical and scalable endeavour, and more than anything else—save the internet itself—led to the advent of electronic commerce as we know and practice it today.

Lattice-based completely non-malleable PKE in the standard model

This paper presents ongoing work toward constructing efficient completely non-malleable public-key encryption scheme based on lattices in the standard (common reference string) model. An encryption scheme is completely non-malleable if it requires attackers to have negligible advantage, even if they are allowed to transform the public key under which the related message is encrypted. Ventre and Visconti proposed two inefficient constructions of completely non-malleable schemes, one in the common reference string model using non-interactive zero-knowledge proofs, and another using interactive encryption schemes. Recently, two efficient public-key encryption schemes have been proposed, both of them are based on pairing identity-based encryption.