The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Approximating shortest lattice vectors is not harder than approximating closet lattice vectors
Information Processing Letters
Normal subgroup reconstruction and quantum computation using group representations
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Regular Article: On Quantum Algorithms for Noncommutative Hidden Subgroups
Advances in Applied Mathematics
Quantum mechanical algorithms for the nonabelian hidden subgroup problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Improved cryptographic hash functions with worst-case/average-case connection
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Complexity of Lattice Problems
Complexity of Lattice Problems
Lattices and Codes: A Course Partially Based on Lectures by F. Hirzebruch
Lattices and Codes: A Course Partially Based on Lectures by F. Hirzebruch
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Quantum Computation and Lattice Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Eliminating Decryption Errors in the Ajtai-Dwork Cryptosystem
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Hidden translation and orbit coset in quantum computing
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Applications of a New Transference Theorem to Ajtai's Connection Factor
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
An Improved Worst-Case to Average-Case Connection for Lattice Problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Worst-Case to Average-Case Reductions Based on Gaussian Measures
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Lattice problems and norm embeddings
Proceedings of the thirty-eighth 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
If NP Languages are Hard on the Worst-Case, Then it is Easy to Find Their Hard Instances
Computational Complexity
Generalized Compact Knapsacks, Cyclic Lattices, and Efficient One-Way Functions
Computational Complexity
Special Issue On Worst-case Versus Average-case Complexity Editors' Foreword
Computational Complexity
Efficient reductions among lattice problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Lossy trapdoor functions and their applications
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Limits on the Hardness of Lattice Problems in lp Norms
Computational Complexity
Noninteractive Statistical Zero-Knowledge Proofs for Lattice Problems
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
A Framework for Efficient and Composable Oblivious Transfer
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Cryptographic hardness for learning intersections of halfspaces
Journal of Computer and System Sciences
Making Cryptographic Primitives Harder
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Quantum resistant public key cryptography: a survey
Proceedings of the 8th Symposium on Identity and Trust on the Internet
Public-key cryptosystems from the worst-case shortest vector problem: extended abstract
Proceedings of the forty-first annual ACM symposium on Theory of computing
On lattices, learning with errors, random linear codes, and cryptography
Journal of the ACM (JACM)
Brief announcement: global consistency can be easier than point-to-point communication
Proceedings of the 28th ACM symposium on Principles of distributed computing
Fiat-Shamir with Aborts: Applications to Lattice and Factoring-Based Signatures
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Public-key cryptography from different assumptions
Proceedings of the forty-second ACM symposium on Theory of computing
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
Faster exponential time algorithms for the shortest vector problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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
Better key sizes (and attacks) for LWE-based encryption
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
Efficient quantum algorithms for the hidden subgroup problem over semi-direct product groups
Quantum Information & Computation
Authenticated Byzantine generals in dual failure model
ICDCN'10 Proceedings of the 11th international conference on Distributed computing and networking
Using the inhomogeneous simultaneous approximation problem for cryptographic design
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
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
Fully homomorphic encryption over the integers
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices
TCC'06 Proceedings of the Third conference on Theory of Cryptography
A general NTRU-Like framework for constructing lattice-based public-key cryptosystems
WISA'11 Proceedings of the 12th international conference on Information Security Applications
A new lattice-based public-key cryptosystem mixed with a knapsack
CANS'11 Proceedings of the 10th international conference on Cryptology and Network Security
Lossy Trapdoor Functions and Their Applications
SIAM Journal on Computing
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
Attribute-Based functional encryption on lattices
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
Classical hardness of learning with errors
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Lattice-based FHE as secure as PKE
Proceedings of the 5th conference on Innovations in theoretical computer science
Public-key searchable encryption from lattices
International Journal of High Performance Systems Architecture
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We introduce the use of Fourier analysis on lattices as an integral part of a lattice-based construction. The tools we develop provide an elegant description of certain Gaussian distributions around lattice points. Our results include two cryptographic constructions that are based on the worst-case hardness of the unique shortest vector problem. The main result is a new public key cryptosystem whose security guarantee is considerably stronger than previous results (O(n1.5) instead of O(n7)). This provides the first alternative to Ajtai and Dwork's original 1996 cryptosystem. Our second result is a family of collision resistant hash functions with an improved security guarantee in terms of the unique shortest vector problem. Surprisingly, both results are derived from one theorem that presents two indistinguishable distributions on the segment [0, 1). It seems that this theorem can have further applications; as an example, we use it to solve an open problem in quantum computation related to the dihedral hidden subgroup problem.