A new cramer-shoup like methodology for group based provably secure encryption schemes

Proceedings of: TCC 2005: Theory of Cryptography Conference, 10-12 February 2005, Cambridge, MA, USA.A theoretical framework for the design of - in the sense of IND-CCA - provably secure public key cryptosystems taking non-abelian groups as a base is given. Our construction is inspired by Cramer and Shoup's general framework for developing secure encryption schemes from certain language membership problems; thus all our proofs are in the standard model, without any idealization assumptions. The skeleton we present is conceived as a guiding tool towards the construction of secure concrete schemes from finite non-abelian groups (although it is possible to use it also in conjunction with finite abelian groups)

Security of signed ELGamal encryption

Assuming a cryptographically strong cyclic group G of prime order q and a random hash function H, we show that ElGamal encryption with an added Schnorr signature is secure against the adaptive chosen ciphertext attack, in which an attacker can freely use a decryption oracle except for the target ciphertext. We also prove security against the novel one-more-decyption attack. Our security proofs are in a new model, corresponding to a combination of two previously introduced models, the Random Oracle model and the Generic model. The security extends to the distributed threshold version of the scheme. Moreover, we propose a very practical scheme for private information retrieval that is based on blind decryption of ElGamal ciphertexts

Security of discrete log cryptosystems in the random oracle and the generic model

We introduce novel security proofs that use combinatorial counting arguments rather than reductions to the discrete logarithm or to the Diffie-Hellman problem. Our security results are sharp and clean with no polynomial reduction times involved. We consider a combination of the random oracle model and the generic model. This corresponds to assuming an ideal hash function H given by an oracle and an ideal group of prime order q, where the binary encoding of the group elements is useless for cryptographic attacks In this model, we first show that Schnorr signatures are secure against the one-more signature forgery : A generic adversary performing t generic steps including l sequential interactions with the signer cannot produce l+1 signatures with a better probability than (t 2)/q. We also characterize the different power of sequential and of parallel attacks. Secondly, we prove signed ElGamal encryption is secure against the adaptive chosen ciphertext attack, in which an attacker can arbitrarily use a decryption oracle except for the challenge ciphertext. Moreover, signed ElGamal encryption is secure against the one-more decryption attack: A generic adversary performing t generic steps including l interactions with the decryption oracle cannot distinguish the plaintexts of l + 1 ciphertexts from random strings with a probability exceeding (t 2)/q

An instantiation of the Cramer-Shoup encryption paradigm using bilinear map groups

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In search of mathematical primitives for deriving universal projective hash families

We provide some guidelines for deriving new projective hash families of cryptographic interest. Our main building blocks are so called group action systems; we explore what properties of this mathematical primitives may lead to the construction of cryptographically useful projective hash families. We point out different directions towards new constructions, deviating from known proposals arising from Cramer and Shoup's seminal work

A Brief History of Provably-Secure Public-Key Encryption

Public-key encryption schemes are a useful and interesting field of cryptographic study. The ultimate goal for the cryptographer in the field of public-key encryption would be the production of a very efficient encryption scheme with a proof of security in a strong security model using a weak and reasonable computational assumption. This ultimate goal has yet to be reached. In this invited paper, we survey the major results that have been achieved in the quest to find such a scheme

Structure-Preserving Smooth Projective Hashing

International audienceSmooth projective hashing has proven to be an extremely useful primitive, in particular when used in conjunction with commitments to provide implicit decommitment. This has lead to applications proven secure in the UC framework, even in presence of an adversary which can do adaptive corruptions, like for example Password Authenticated Key Exchange (PAKE), and 1-out-of-m Oblivious Transfer (OT). However such solutions still lack in efficiency, since they heavily scale on the underlying message length. Structure-preserving cryptography aims at providing elegant and efficient schemes based on classical assumptions and standard group operations on group elements. Recent trend focuses on constructions of structure- preserving signatures, which require message, signature and verification keys to lie in the base group, while the verification equations only consist of pairing-product equations. Classical constructions of Smooth Projective Hash Function suffer from the same limitation as classical signatures: at least one part of the computation (messages for signature, witnesses for SPHF) is a scalar. In this work, we introduce and instantiate the concept of Structure- Preserving Smooth Projective Hash Function, and give as applications more efficient instantiations for one-round PAKE and three-round OT, and information retrieval thanks to Anonymous Credentials, all UC- secure against adaptive adversaries