A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Cryptographic primitives based on hard learning problems
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Complexity of Lattice Problems
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SIAM Journal on Computing
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On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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Journal of the ACM (JACM)
Introduction to Modern Cryptography (Chapman & Hall/Crc Cryptography and Network Security Series)
Introduction to Modern Cryptography (Chapman & Hall/Crc Cryptography and Network Security Series)
Worst-Case to Average-Case Reductions Based on Gaussian Measures
SIAM Journal on Computing
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
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Cryptographic hardness for learning intersections of halfspaces
Journal of Computer and System Sciences
Public-key cryptosystems from the worst-case shortest vector problem: extended abstract
Proceedings of the forty-first annual ACM symposium on Theory of computing
Multi-bit cryptosystems based on lattice problems
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
On bounded distance decoding for general lattices
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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
An efficient and parallel Gaussian sampler for lattices
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE
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
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
Key dependent message security: recent results and applications
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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
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
New algorithms for learning in presence of errors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
The geometry of lattice cryptography
Foundations of security analysis and design VI
Classical cryptographic protocols in a quantum world
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Pseudorandom knapsacks and the sample complexity of LWE search-to-decision reductions
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Fully homomorphic encryption from ring-LWE and security for key dependent messages
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Bi-deniable public-key encryption
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On noise-tolerant learning of sparse parities and related problems
ALT'11 Proceedings of the 22nd international conference on Algorithmic learning theory
SIAM Journal on Computing
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
A simple BGN-Type cryptosystem from LWE
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
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On CCA-Secure somewhat homomorphic encryption
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
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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
Pseudorandom functions and lattices
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Lattice signatures without trapdoors
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Lossy Trapdoor Functions and Their Applications
SIAM Journal on Computing
Public-Key cryptography from new multivariate quadratic assumptions
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Circular and KDM security for identity-based encryption
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
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
Full lattice basis reduction on graphics cards
WEWoRC'11 Proceedings of the 4th Western European conference on Research in Cryptology
Lapin: an efficient authentication protocol based on Ring-LPN
FSE'12 Proceedings of the 19th international conference on Fast Software Encryption
Fully anonymous attribute tokens from lattices
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
A fully homomorphic cryptosystem with approximate perfect secrecy
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
Attribute-based encryption for circuits
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Classical hardness of learning with errors
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Solving the learning parity with noise's open question
Information Processing Letters
Privacy-preserving matrix factorization
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
How to share a lattice trapdoor: threshold protocols for signatures and (H)IBE
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
On Ideal Lattices and Learning with Errors over Rings
Journal of the ACM (JACM)
Lattice-based FHE as secure as PKE
Proceedings of the 5th conference on Innovations in theoretical computer science
Linear-time encodable codes meeting the gilbert-varshamov bound and their cryptographic applications
Proceedings of the 5th conference on Innovations in theoretical computer science
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Our main result is a reduction from worst-case lattice problems such as GapSVP and SIVP to a certain learning problem. This learning problem is a natural extension of the “learning from parity with error” problem to higher moduli. It can also be viewed as the problem of decoding from a random linear code. This, we believe, gives a strong indication that these problems are hard. Our reduction, however, is quantum. Hence, an efficient solution to the learning problem implies a quantum algorithm for GapSVP and SIVP. A main open question is whether this reduction can be made classical (i.e., nonquantum). We also present a (classical) public-key cryptosystem whose security is based on the hardness of the learning problem. By the main result, its security is also based on the worst-case quantum hardness of GapSVP and SIVP. The new cryptosystem is much more efficient than previous lattice-based cryptosystems: the public key is of size Õ(n2) and encrypting a message increases its size by a factor of Õ(n) (in previous cryptosystems these values are Õ(n4) and Õ(n2), respectively). In fact, under the assumption that all parties share a random bit string of length Õ(n2), the size of the public key can be reduced to Õ(n).