Cryptographic primitives based on hard learning problems
CRYPTO '93 Proceedings of the 13th 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
Probabilistic encryption & how to play mental poker keeping secret all partial information
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
On lattices, learning with errors, random linear codes, and cryptography
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
Worst-Case to Average-Case Reductions Based on Gaussian Measures
SIAM Journal on 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
A robust and verifiable cryptographically secure election scheme
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
SWIFFT: A Modest Proposal for FFT Hashing
Fast Software Encryption
Circular-Secure Encryption from Decision Diffie-Hellman
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Fully homomorphic encryption using ideal lattices
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)
Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on 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
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Computationally private information retrieval with polylogarithmic communication
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Asymptotically efficient lattice-based digital signatures
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Circular and leakage resilient public-key encryption under subgroup indistinguishability
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Toward basing fully homomorphic encryption on worst-case hardness
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Black-box circular-secure encryption beyond affine functions
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Homomorphic encryption: from private-key to public-key
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Implementing Gentry's fully-homomorphic encryption scheme
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Efficient circuit-size independent public key encryption with KDM security
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Key-dependent message security: generic amplification and completeness
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Generalized compact knapsacks are collision resistant
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Single-database private information retrieval with constant communication rate
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Evaluating 2-DNF formulas on ciphertexts
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Fully homomorphic encryption with relatively small key and ciphertext sizes
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices
TCC'06 Proceedings of the Third conference on Theory of Cryptography
The geometry of lattice cryptography
Foundations of security analysis and design VI
Can homomorphic encryption be practical?
Proceedings of the 3rd ACM workshop on Cloud computing security workshop
(Leveled) fully homomorphic encryption without bootstrapping
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Functional encryption for inner product predicates from learning with errors
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Improved key generation for gentry's fully homomorphic encryption scheme
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Breaking fully-homomorphic-encryption challenges
CANS'11 Proceedings of the 10th international conference on Cryptology and Network Security
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
Secure two-party computation with low communication
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
On the CCA-1 security of somewhat homomorphic encryption over the integers
ISPEC'12 Proceedings of the 8th international conference on Information Security Practice and Experience
Malleable proof systems and applications
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Public key compression and modulus switching for fully homomorphic encryption over the integers
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Fully homomorphic encryption with polylog overhead
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Multiparty computation with low communication, computation and interaction via threshold FHE
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
Securing cloud-based computations against malicious providers
ACM SIGOPS Operating Systems Review
Better bootstrapping in fully homomorphic encryption
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key 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
Circular and KDM security for identity-based encryption
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Shift-type homomorphic encryption and its application to fully homomorphic encryption
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
Securing cloud-based computations against malicious providers
Proceedings of the 1st European Workshop on Dependable Cloud Computing
Towards an interpreter for efficient encrypted computation
Proceedings of the 2012 ACM Workshop on Cloud computing security workshop
Query encrypted databases practically
Proceedings of the 2012 ACM conference on Computer and communications security
Collaboration-Preserving authenticated encryption for operational transformation systems
ISC'12 Proceedings of the 15th international conference on Information Security
Selective document retrieval from encrypted database
ISC'12 Proceedings of the 15th international conference on Information Security
Ring switching in BGV-Style homomorphic encryption
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
Protecting data confidentiality in cloud systems
Proceedings of the Fourth Asia-Pacific Symposium on Internetware
Solving BDD by enumeration: an update
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
Encrypted messages from the heights of cryptomania
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
Attribute-Based functional encryption on lattices
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
When homomorphism becomes a liability
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
Anonymous lattice-based broadcast encryption
ICT-EurAsia'13 Proceedings of the 2013 international conference on Information and Communication Technology
ML confidential: machine learning on encrypted data
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
Reusable garbled circuits and succinct functional encryption
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Secure pattern matching using somewhat homomorphic encryption
Proceedings of the 2013 ACM workshop on Cloud computing security workshop
Fully homomorphic SIMD operations
Designs, Codes and Cryptography
Field switching in BGV-style homomorphic encryption
Journal of Computer Security - Advances in Security for Communication Networks
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We present a somewhat homomorphic encryption scheme that is both very simple to describe and analyze, and whose security (quantumly) reduces to the worst-case hardness of problems on ideal lattices. We then transform it into a fully homomorphic encryption scheme using standard "squashing" and "bootstrapping" techniques introduced by Gentry (STOC 2009). One of the obstacles in going from "somewhat" to full homomorphism is the requirement that the somewhat homomorphic scheme be circular secure, namely, the scheme can be used to securely encrypt its own secret key. For all known somewhat homomorphic encryption schemes, this requirement was not known to be achievable under any cryptographic assumption, and had to be explicitly assumed. We take a step forward towards removing this additional assumption by proving that our scheme is in fact secure when encrypting polynomial functions of the secret key. Our scheme is based on the ring learning with errors (RLWE) assumption that was recently introduced by Lyubashevsky, Peikert and Regev (Eurocrypt 2010). The RLWE assumption is reducible to worstcase problems on ideal lattices, and allows us to completely abstract out the lattice interpretation, resulting in an extremely simple scheme. For example, our secret key is s, and our public key is (a, b = as+2e), where s, a, e are all degree (n - 1) integer polynomials whose coefficients are independently drawn from easy to sample distributions.