Concrete Chosen-Ciphertext Secure Encryption from Subgroup Membership Problems

@inproceedings{Brown2006ConcreteCS,
  title={Concrete Chosen-Ciphertext Secure Encryption from Subgroup Membership Problems},
  author={Jaimee Brown and Juan Manuel Gonz{\'a}lez Nieto and Colin Boyd},
  booktitle={CANS},
  year={2006}
}
Using three previously studied subgroup membership problems, we obtain new concrete encryption schemes secure against adaptive chosen-ciphertext attack in the standard model, from the Cramer-Shoup and Kurosawa-Desmedt constructions. The schemes obtained are quite efficient. In fact, the Cramer-Shoup derived schemes are more efficient than the previous schemes from this construction, including the Cramer-Shoup cryptosystem, when long messages are considered. The hybrid variants are even more… 
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References

SHOWING 1-10 OF 11 REFERENCES
Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption
TLDR
A general framework that allows one to construct secure encryption schemes in a generic fashion from language membership problems that satisfy certain technical requirements is introduced, as does the Cramer-Shoup scheme based on the Decision Diffie-Hellman assumption.
Symmetric Subgroup Membership Problems
  • K. Gjøsteen
  • Computer Science, Mathematics
    Public Key Cryptography
  • 2005
TLDR
The Cramer-Shoup framework is modified, so that it can derive a chosen ciphertext secure cryptosystem in the standard model from symmetric subgroup membership problems, giving a very efficient Cryptosystem whose security relies solely on the symmetricSubgroup membership problem.
A Note on An Encryption Scheme of Kurosawa and Desmedt
TLDR
A proof of security is presented which shows that the KurosawaDesmedt scheme can be instantiated with any computationally secure key derivation and message authentication functions, thus extending the applicability of their paradigm, and improving its eciency.
Public-Key Cryptosystems Based on Composite Degree Residuosity Classes
TLDR
A new trapdoor mechanism is proposed and three encryption schemes are derived : a trapdoor permutation and two homomorphic probabilistic encryption schemes computationally comparable to RSA, which are provably secure under appropriate assumptions in the standard model.
A New Paradigm of Hybrid Encryption Scheme
TLDR
It is shown that a key encapsulation mechanism (KEM) does not have to be IND-CCA secure in the construction of hybrid encryption schemes, as was previously believed, and this result is further generalized to universal2 projective hash families.
A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack
A new public key cryptosystem is proposed and analyzed. The scheme is quite practical, and is provably secure against adaptive chosen ciphertext attack under standard intractability assumptions.
A New Public-Key Cryptosystem as Secure as Factoring
TLDR
This paper proposes a novel public-key cryptosystem, which is practical, provably secure and has some other interesting properties as follows: It can be proven to be as secure as the intractability of factoring n = p2q (in the sense of the security of the whole plaintext) against passive adversaries.
General Public Key Residue Cryptosystems and Mental Poker Protocols
TLDR
A general method to construct public key cryptosystems based on the r-th residue problem is presented, and the first mental poker protocol which can shuffle any set of cards is presented.
Private Information Retrieval Based on the Subgroup Membership Problem
TLDR
The subgroup membership problem is applied to private information retrieval schemes following the method by Kushilevitz and Ostrovsky and the resulting scheme has the same communication complexity as the original scheme.
A Public Key Cryptosystem Based On A Subgroup Membership Problem
We present a novel public key encryption scheme semantically secure in the standard model under the intractability assumption of a subgroup membership problem related to the factorization problem.
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