A public key cryptosystem based on the word problem
Proceedings of CRYPTO 84 on Advances in cryptology
Identity-based cryptosystems and signature schemes
Proceedings of CRYPTO 84 on Advances in cryptology
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
On groups in which every element has finite order
American Mathematical Monthly
Matrix Transformation is Complete for the Average Case
SIAM Journal on Computing
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Efficient noise-tolerant learning from statistical queries
Journal of the ACM (JACM)
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Machine Learning
Reaction Attacks against several Public-Key Cryptosystems
ICICS '99 Proceedings of the Second International Conference on Information and Communication Security
An Identity Based Encryption Scheme Based on Quadratic Residues
Proceedings of the 8th IMA International Conference on Cryptography and Coding
Noise-tolerant learning, the parity problem, and the statistical query model
Journal of the ACM (JACM)
Non-abelian key agreement protocols
Discrete Applied Mathematics - Special issue on the 2000 com2MaC workshop on cryptography
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
A Reaction Attack on a Public Key Cryptosystem Based on the Word Problem
Applicable Algebra in Engineering, Communication and Computing
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A Framework for Efficient and Composable Oblivious Transfer
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
Public-key cryptosystems from the worst-case shortest vector problem: extended abstract
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
Toward basing fully homomorphic encryption on worst-case hardness
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
i-hop homomorphic encryption and rerandomizable Yao circuits
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
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
Fully homomorphic encryption over the integers
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
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We propose a generalization of the learning parity with noise (LPN) and learning with errors (LWE) problems to an abstract class of group-theoretic learning problems that we term learning homomorphisms with noise (LHN). This class of problems contains LPN and LWE as special cases, but is much more general. It allows, for example, instantiations based on non-abelian groups, resulting in a new avenue for the application of combinatorial group theory to the development of cryptographic primitives. We then study a particular instantiation using relatively free groups and construct a symmetric cryptosystem based upon it.