Obfuscation for Cryptographic Purposes

An obfuscation of a function F should satisfy two requirements: firstly, using it should be possible to evaluate F; secondly, should not reveal anything about F that cannot be learnt from oracle access to F. Several definitions for obfuscation exist. However, most of them are either too weak for or incompatible with cryptographic applications, or have been shown impossible to achieve, or both. We give a new definition of obfuscation and argue for its reasonability and usefulness. In particular, we show that it is strong enough for cryptographic applications, yet we show that it has the potential for interesting positive results. We illustrat

CCA-secure Predicate Encryption from Pair Encoding in Prime Order Groups: Generic and Efficient

Attrapadung (Eurocrypt 2014) proposed a generic framework called pair encoding to simplify the design and proof of security of CPA-secure predicate encryption (PE) in composite order groups. Later Attrapadung (Asiacrypt 2016) extended this idea in prime order groups. Yamada et al. (PKC 2011, PKC 2012) and Nandi et al. (ePrint Archive: 2015/457, AAECC 2017) proposed generic conversion frameworks to achieve CCA-secure PE from CPA-secure PE provided the encryption schemes have properties like delegation or verifiability. The delegation property is harder to achieve and verifiability based conversion degrades the decryption performance due to a large number of additional pairing evaluations. Blömer et al. (CT-RSA 2016) proposed a direct fully CCA-secure predicate encryption in composite order groups but it was less efficient as it needed a large number of pairing evaluations to check ciphertext consistency. As an alternative, Nandi et al. (ePrint Archive: 2015/955) proposed a direct conversion technique in composite order groups. We extend the direct conversion technique of Nandi et al. in the prime order groups on the CPA-secure PE construction by Attrapadung (Asiacrypt 2016) and prove our scheme to be CCA-secure in a quite different manner. Our first direct CCA-secure predicate encryption scheme requires exactly one additional ciphertext component and three additional units of pairing evaluation during decryption. The second construction requires exactly three additional ciphertext components but needs only one additional unit pairing evaluation during decryption. This is a significant improvement over conventional approach for CPA-to-CCA conversion in prime order groups

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

A Study of Separations in Cryptography: New Results and New Models

For more than 20 years, black-box impossibility results have been used to argue the infeasibility of constructing certain cryptographic primitives (e.g., key agreement) from others (e.g., one-way functions). In this dissertation we further extend the frontier of this field by demonstrating several new impossibility results as well as a new framework for studying a more general class of constructions. Our first two results demonstrate impossibility of black-box constructions of two commonly used cryptographic primitives. In our first result we study the feasibility of black-box constructions of predicate encryption schemes from standard assumptions and demonstrate strong limitations on the types of schemes that can be constructed. In our second result we study black-box constructions of constant-round zero-knowledge proofs from one-way permutations and show that, under commonly believed complexity assumptions, no such constructions exist. A widely recognized limitation of black-box impossibility results, however, is that they say nothing about the usefulness of (known) non-black-box techniques. This state of affairs is unsatisfying as we would at least like to rule out constructions using the set of techniques we have at our disposal. With this motivation in mind, in the final result of this dissertation we propose a new framework for black-box constructions with a non-black-box flavor, specifically, those that rely on zero-knowledge proofs relative to some oracle. Our framework is powerful enough to capture a large class of known constructions, however we show that the original black-box separation of key agreement from one-way functions still holds even in this non-black-box setting that allows for zero-knowledge proofs

Delegatable homomorphic encryption with applications to secure outsourcing of computation

In this work we propose a new cryptographic primitive called Delegatable Homomorphic Encryption (DHE). This allows a Trusted Authority to control/delegate the capability to evaluate circuits over encrypted data to untrusted workers/evaluators by issuing tokens. This primitive can be both seen as a public-key counterpart to Verifiable Computation, where input generation and output verification are performed by different entities, or as a generalisation of Fully Homomorphic Encryption enabling control over computations on encrypted data. Our primitive comes with a series of extra features as follows: 1) there is a one-time setup procedure for all circuits; 2) senders do not need to be aware of the functions which will be evaluated on the encrypted data, nor do they need to register keys; 3) tokens are independent of senders and receiver; and 4) receivers are able to verify the correctness of computation given short auxiliary information on the input data and the function, independently of the complexity of the computed circuit. We give a modular construction of such a DHE scheme from three components: Fully Homomorphic Encryption (FHE), Functional Encryption (FE), and a (customised) MAC. As a stepping stone, we first define Verifiable Functional Encryption (VFE), and then show how one can build a secure DHE scheme from a VFE and an FHE scheme. We also show how to build the required VFE from a standard FE together with a MAC scheme. All our results hold in the standard model.Finally, we show how one can build a verifiable computation (VC) scheme generically from a DHE. As a corollary, we get the first VC scheme which remains verifiable even if the attacker can observe verification result