New lattice based cryptographic constructions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
New lattice-based cryptographic constructions
Journal of the ACM (JACM)
Representing hard lattices with O(n log n) bits
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Lattices that admit logarithmic worst-case to average-case connection factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Generalized Compact Knapsacks, Cyclic Lattices, and Efficient One-Way Functions
Computational Complexity
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Lattice-based identification schemes secure under active attacks
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Toward basing fully homomorphic encryption on worst-case hardness
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Faster and smoother: VSH revisited
ACISP'11 Proceedings of the 16th Australasian conference on Information security and privacy
Generalized compact knapsacks are collision resistant
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Zero-knowledge proof of generalized compact knapsacks (or a novel identification/signature scheme)
ATC'06 Proceedings of the Third international conference on Autonomic and Trusted Computing
Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Functional encryption for threshold functions (or fuzzy IBE) from lattices
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Revocable identity-based encryption from lattices
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
A ciphertext policy attribute-based encryption scheme without pairings
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
A polynomial time algorithm for computing the HNF of a module over the integers of a number field
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Attribute-Based functional encryption on lattices
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
Public-key searchable encryption from lattices
International Journal of High Performance Systems Architecture
| Hi-index | 0.00 |
We study a generalization of the compact knapsack problem for arbitrary rings: given m = O(log n) ring elements a_1 , \ldots ,a_m \varepsilon R and a target value b\varepsilon R, find coefficients x_1 , \ldots ,x_m \varepsilon X (where X is a subset of R of size 2^n) such thatsum {a_i } x_i= b. The computational complexity of this problem depends on the choice of the ring R and set of coefficients X. This problem is known to be solvable in quasi polynomial time when R is the ring of the integers and X is the set of small integers { 0, \ldots ,2^n- 1}. We show that if R is an appropriately chosen ring of modular polynomials and X is the subset of polynomials with small coefficients, then the compact knapsack problem is as hard to solve on the average as the worst case instance of approximating the covering radius (or the length of the shortest vector, or various other well known lattice problems) of any cyclic lattice within a polynomial factor. Our proof adapts, to the cyclic lattice setting, techniques initially developed by Ajtai for the case of general lattices.