A Note on Attribute-Based Group Homomorphic Encryption

Group Homomorphic Encryption (GHE), formally defined by Armknecht, Katzenbeisser and Peter, is a public-key encryption primitive where the decryption algorithm is a group homomorphism. Hence it supports homomorphic evaluation of a single algebraic operation such as modular addition or modular multiplication. Most classical homomorphic encryption schemes such as as Goldwasser-Micali and Paillier are instances of GHE. In this work, we extend GHE to the attribute-based setting. We introduce and formally define the notion of Attribute-Based GHE (ABGHE) and explore its properties. We then examine the algebraic structure on attributes induced by the group operation in an ABGHE. This algebraic stricture is a bounded semilattice. We consider some possible semilattices and how they can be realized by an ABGHE supporting inner product predicates. We then examine existing schemes from the literature and show that they meet our definition of ABGHE for either an additive or multiplicative homomorphism. Some of these schemes are in fact Identity-Based Group Homomorphic Encryption (IBGHE) schemes i.e. instances of ABGHE whose class of access policies are point functions. We then present a possibility result for IBGHE from indistinguishability obfuscation for any group for which a (public-key) GHE scheme exists

On the Composability of Statistically Secure Random Oblivious Transfer

We show that random oblivious transfer protocols that are statistically secure according to a definition based on a list of information-theoretical properties are also statistically universally composable. That is, they are simulatable secure with an unlimited adversary, an unlimited simulator, and an unlimited environment machine. Our result implies that several previous oblivious transfer protocols in the literature that were proven secure under weaker, non-composable definitions of security can actually be used in arbitrary statistically secure applications without lowering the security

Improving Key-Recovery in Linear Attacks: Application to 28-Round PRESENT

International audienceLinear cryptanalysis is one of the most important tools in usefor the security evaluation of symmetric primitives. Many improvementsand refinements have been published since its introduction, and manyapplications on different ciphers have been found. Among these upgrades,Collard et al. proposed in 2007 an acceleration of the key-recovery partof Algorithm 2 for last-round attacks based on the FFT.In this paper we present a generalized, matrix-based version of the pre-vious algorithm which easily allows us to take into consideration an ar-bitrary number of key-recovery rounds. We also provide efficient variantsthat exploit the key-schedule relations and that can be combined withmultiple linear attacks.Using our algorithms we provide some new cryptanalysis on PRESENT,including, to the best of our knowledge, the first attack on 28 rounds

Tightly Secure Chameleon Hash Functions in the Multi-User Setting and Their Applications

We define the security notion of (strong) collision resistance for chameleon hash functions in the multi-user setting ((S-)MU-CR security). We also present three constructions, CHF_dl, CHF_rsa and CHF_fac, and prove their tight S-MU-CR security based on the discrete logarithm, RSA and factoring assumptions, respectively. In applications, our tightly S-MU-CR secure chameleon hash functions help us to lift a signature scheme from (weak) unforgeability to strong unforgeability in the multi-user setting, and the security reduction is tightness preserving. Furthermore, they can also be used to construct tightly secure online/offline signatures, chameleon signatures and proxy signatures, etc., in the multi-user setting

Multi-Identity and Multi-Key Leveled FHE from Learning with Errors

Gentry, Sahai and Waters recently presented the first (leveled) identity-based fully homomorphic (IBFHE) encryption scheme (CRYPTO 2013). Their scheme however only works in the single-identity setting; that is, homomorphic evaluation can only be performed on ciphertexts created with the same identity. In this work, we extend their results to the multi-identity setting and obtain a multi-identity IBFHE scheme that is selectively secure in the random oracle model under the hardness of Learning with Errors (LWE). We also obtain a multi-key fully-homomorphic encryption (FHE) scheme that is secure under LWE in the standard model. This is the first multi-key FHE based on a well-established assumption such as standard LWE. The multi-key FHE of López-Alt, Tromer and Vaikuntanathan (STOC 2012) relied on a non-standard assumption, referred to as the Decisional Small Polynomial Ratio assumption

Cryptography Based on Correlated Data: Foundations and Practice

Correlated data can be very useful in cryptography. For instance, if a uniformly random key is available to Alice and Bob, it can be used as an one-time pad to transmit a message with perfect security. With more elaborate forms of correlated data, the parties can achieve even more complex cryptographic tasks, such as secure multiparty computation. This thesis explores (from both a theoretical and a practical point of view) the topic of cryptography based on correlated data