Efficient Public Key Encryption Based on Ideal Lattices
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Provably Secure Code-Based Threshold Ring Signatures
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Toward basing fully homomorphic encryption on worst-case hardness
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Additively homomorphic encryption with d-operand multiplications
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Algorithms for the shortest and closest lattice vector problems
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
The geometry of lattice cryptography
Foundations of security analysis and design VI
Pseudorandom knapsacks and the sample complexity of LWE search-to-decision reductions
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Approximating the closest vector problem using an approximate shortest vector oracle
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Public-key cryptographic primitives provably as secure as subset sum
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
The leakage-resilience limit of a computational problem is equal to its unpredictability entropy
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Identity-Based (lossy) trapdoor functions and applications
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Classical hardness of learning with errors
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
A note on BDD problems with λ2 -gap
Information Processing Letters
Hi-index | 0.00 |
We prove the equivalence, up to a small polynomial approximation factor $\sqrt{n/\log n}$, of the lattice problems uSVP (unique Shortest Vector Problem), BDD (Bounded Distance Decoding) and GapSVP (the decision version of the Shortest Vector Problem). This resolves a long-standing open problem about the relationship between uSVP and the more standard GapSVP, as well the BDD problem commonly used in coding theory. The main cryptographic application of our work is the proof that the Ajtai-Dwork ([2]) and the Regev ([33]) cryptosystems, which were previously only known to be based on the hardness of uSVP, can be equivalently based on the hardness of worst-case GapSVP${_{O({n^{2.5}})}}$ and GapSVP${_{O(n^{2})}}$, respectively. Also, in the case of uSVP and BDD, our connection is very tight, establishing the equivalence (within a small constant approximation factor) between the two most central problems used in lattice based public key cryptography and coding theory.