A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On the limits of nonapproximability of lattice problems
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Complexity of Lattice Problems
Complexity of Lattice Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Design Principle for Hash Functions
CRYPTO '89 Proceedings of the 9th 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
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
Almost Perfect Lattices, the Covering Radius Problem, and Applications to Ajtai's Connection Factor
SIAM Journal on Computing
Journal of the ACM (JACM)
Cryptanalysis of the hash functions MD4 and RIPEMD
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
How to break MD5 and other hash functions
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Collisions of SHA-0 and reduced SHA-1
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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
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
SWIFFT: A Modest Proposal for FFT Hashing
Fast Software Encryption
Hash Functions from Sigma Protocols and Improvements to VSH
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Concurrently Secure Identification Schemes Based on the Worst-Case Hardness of Lattice Problems
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of 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
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
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
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
Asymptotically efficient lattice-based digital signatures
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Toward basing fully homomorphic encryption on worst-case hardness
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
A lattice-based threshold ring signature scheme
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Adaptively secure identity-based identification from lattices without random oracles
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
Improved zero-knowledge identification with lattices
ProvSec'10 Proceedings of the 4th international conference on Provable security
Interpreting hash function security proofs
ProvSec'10 Proceedings of the 4th international conference on Provable security
Making NTRU as secure as worst-case problems over ideal lattices
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Homomorphic signatures for polynomial functions
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
The geometry of lattice cryptography
Foundations of security analysis and design VI
Faster and smoother: VSH revisited
ACISP'11 Proceedings of the 16th Australasian conference on Information security and privacy
Fully homomorphic encryption from ring-LWE and security for key dependent messages
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Can homomorphic encryption be practical?
Proceedings of the 3rd ACM workshop on Cloud computing security workshop
On ideal lattices and learning with errors over rings
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Perfectly secure multiparty computation and the computational overhead of cryptography
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Bonsai trees, or how to delegate a lattice basis
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Efficient lattice (H)IBE in the standard model
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
On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Tightly-Secure signatures from lossy identification schemes
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Trapdoors for lattices: simpler, tighter, faster, smaller
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
NTRUCCA: how to strengthen NTRUEncrypt to chosen-ciphertext security in the standard model
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Strongly secure authenticated key exchange from factoring, codes, and lattices
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
An efficient lattice-based secret sharing construction
WISTP'12 Proceedings of the 6th IFIP WG 11.2 international conference on Information Security Theory and Practice: security, privacy and trust in computing systems and ambient intelligent ecosystems
Towards efficient arithmetic for lattice-based cryptography on reconfigurable hardware
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
Practical lattice-based cryptography: a signature scheme for embedded systems
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
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
Classical hardness of learning with errors
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On Ideal Lattices and Learning with Errors over Rings
Journal of the ACM (JACM)
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In (Micciancio, FOCS 2002), it was proved that solving the generalized compact knapsack problem on the average is as hard as solving certain worst-case problems for cyclic lattices. This result immediately yielded very efficient one-way functions whose security was based on worst-case hardness assumptions. In this work, we show that, while the function proposed by Micciancio is not collision resistant, it can be easily modified to achieve collision resistance under essentially the same complexity assumptions on cyclic lattices. Our modified function is obtained as a special case of a more general result, which yields efficient collision-resistant hash functions based on the worst-case hardness of various new problems. These include new problems from algebraic number theory as well as classic lattice problems (e.g., the shortest vector problem) over ideal lattices, a class of lattices that includes cyclic lattices as a special case