Pseudo-random generation from one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Cryptographic primitives based on hard learning problems
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Linear cryptanalysis method for DES cipher
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Secure Human Identification Protocols
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Noise-tolerant learning, the parity problem, and the statistical query model
Journal of the ACM (JACM)
How to Encrypt with the LPN Problem
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
On cryptography with auxiliary input
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
On Agnostic Learning of Parities, Monomials, and Halfspaces
SIAM Journal on Computing
Public-key cryptography from different assumptions
Proceedings of the forty-second ACM symposium on Theory of computing
The Learning with Errors Problem (Invited Survey)
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
On noise-tolerant learning of sparse parities and related problems
ALT'11 Proceedings of the 22nd international conference on Algorithmic learning theory
Authenticating pervasive devices with human protocols
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
SCN'06 Proceedings of the 5th international conference on Security and Cryptography for Networks
Cryptography from learning parity with noise
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Finding Correlations in Subquadratic Time, with Applications to Learning Parities and Juntas
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
Commitments and efficient zero-knowledge proofs from learning parity with noise
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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The classical cryptographic primitives are constructed on the assumptions that the private key is securely kept and uniformly distributed. Learning parity with noise is a famous problem used to construct several cryptographic primitives. This research studies the open question about the hardness of the learning parity with noise assumption when the secret vector is not uniform and has sufficient min-entropy. The proofs show that the standard learning parity with noise implies that it is secure even if the secret vector is sampled from an arbitrary distribution with sufficient entropy. Furthermore, this paper shows that the symmetric encryption scheme from learning parity with noise is secure even if the secret key has min-entropy at least k.