General Impossibility of Group Homomorphic Encryption in the Quantum World

@article{Armknecht2014GeneralIO,
  title={General Impossibility of Group Homomorphic Encryption in the Quantum World},
  author={Frederik Armknecht and Tommaso Gagliardoni and Stefan Katzenbeisser and Andreas Peter},
  journal={IACR Cryptol. ePrint Arch.},
  year={2014},
  volume={2014},
  pages={29}
}
Group homomorphic encryption represents one of the most important building blocks in modern cryptography. It forms the basis of widely-used, more sophisticated primitives, such as CCA2-secure encryption or secure multiparty computation. Unfortunately, recent advances in quantum computation show that many of the existing schemes completely break down once quantum computers reach maturity mainly due to Shor's algorithm. This leads to the challenge of constructing quantum-resistant group… 

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References

SHOWING 1-10 OF 37 REFERENCES

Multiparty Computation from Threshold Homomorphic Encryption

It is shown that given keys for any sufficiently efficient system of this type, general MPC protocols for n parties can be devised which are secure against an active adversary that corrupts any minority of the parties.

Group homomorphic encryption: characterizations, impossibility results, and applications

A new cryptosystem is designed which provides features that are unique up to now: Its IND-CPA security is based on the k-linear problem introduced by Shacham, and Hofheinz and Kiltz, while its IND-CCA1 security isbased on a new k-problem that is proved to have the same progressive property.

On Homomorphic Encryption and Chosen-Ciphertext Security

The main results give natural and efficient constructions of IND-CCA secure cryptosystems from any homomorphic encryption scheme that satisfies weak cyclic properties, either in the plaintext, ciphertext or randomness space.

(Leveled) fully homomorphic encryption without bootstrapping

A novel approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions, using some new techniques recently introduced by Brakerski and Vaikuntanathan (FOCS 2011).

Shift-Type Homomorphic Encryption and Its Application to Fully Homomorphic Encryption

It is proved that the IND-CPA security of FHE schemes that offer a certain type of circuit privacy and are based on Gentry’s bootstrapping technique is equivalent to the circular security of the underlying bootstrappable scheme.

Homomorphic encryption and secure comparison

It is shown how the proposed protocol for secure comparison of integers based on homomorphic encryption can be used to improve security of online auctions, and that it is efficient enough to be used in practice.

Classical Cryptographic Protocols in a Quantum World

The result shows that the basic two-party feasibility picture from classical cryptography remains unchanged in a quantum world, and shows the existence of classical two- party protocols for the secure evaluation of any polynomial-time function under reasonable computational assumptions.

Additively Homomorphic Encryption with a Double Decryption Mechanism, Revisited

This work proposes the first additively homomorphic DD-PKE scheme which allows the master to detect invalid ciphertexts and has the additional property that the master decryption is independent of the users' public keys.

Fully homomorphic encryption using ideal lattices

This work proposes a fully homomorphic encryption scheme that allows one to evaluate circuits over encrypted data without being able to decrypt, and describes a public key encryption scheme using ideal lattices that is almost bootstrappable.

Algorithms for Black-Box Fields and their Application to Cryptography (Extended Abstract)

The results show that any algebraically homomorphic cryptosystem can be broken in sub-exponential time and it is proved that manipulating black box fields over the rationals is as hard as factoring integers.