A Provably-Secure Unidirectional Proxy Re-Encryption Scheme Without Pairing in the Random Oracle Model

Proxy re-encryption (PRE) enables delegation of decryption rights by entrusting a proxy server with special information, that allows it to transform a ciphertext under one public key into a ciphertext of the same message under a different public key. It is important to note that, the proxy which performs the re-encryption learns nothing about the message encrypted under either public keys. Due to its transformation property, proxy re-encryption schemes have practical applications in distributed storage, encrypted email forwarding, Digital Rights Management (DRM) and cloud storage. From its introduction, several proxy re-encryption schemes have been proposed in the literature, and a majority of them have been realized using bilinear pairing. In Africacrypt 2010, the first PKI-based collusion resistant CCA secure PRE scheme without pairing was proposed in the random oracle model. In this paper, we point out an important weakness in the scheme. We also present the first collusion-resistant pairing-free unidirectional proxy re-encryption scheme which meets CCA security under a variant of the computational Diffie-Hellman hardness assumption in the random oracle model

The Theory and Applications of Homomorphic Cryptography

Homomorphic cryptography provides a third party with the ability to perform simple computations on encrypted data without revealing any information about the data itself. Typically, a third party can calculate one of the encrypted sum or the encrypted product of two encrypted messages. This is possible due to the fact that the encryption function is a group homomorphism, and thus preserves group operations. This makes homomorphic cryptosystems useful in a wide variety of privacy preserving protocols. A comprehensive survey of known homomorphic cryptosystems is provided, including formal definitions, security assumptions, and outlines of security proofs for each cryptosystem presented. Threshold variants of several homomorphic cryptosystems are also considered, with the first construction of a threshold Boneh-Goh-Nissim cryptosystem given, along with a complete proof of security under the threshold semantic security game of Fouque, Poupard, and Stern. This approach is based on Shoup's approach to threshold RSA signatures, which has been previously applied to the Paillier and Damg\aa rd-Jurik cryptosystems. The question of whether or not this approach is suitable for other homomorphic cryptosystems is investigated, with results suggesting that a different approach is required when decryption requires a reduction modulo a secret value. The wide variety of protocols utilizing homomorphic cryptography makes it difficult to provide a comprehensive survey, and while an overview of applications is given, it is limited in scope and intended to provide an introduction to the various ways in which homomorphic cryptography is used beyond simple addition or multiplication of encrypted messages. In the case of strong conditional oblivious tranfser, a new protocol implementing the greater than predicate is presented, utilizing some special properties of the Boneh-Goh-Nissim cryptosystem to achieve security against a malicious receiver