Generating quasi-random sequences from semi-random sources
Journal of Computer and System Sciences
Privacy amplification by public discussion
SIAM Journal on Computing - Special issue on cryptography
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
Weak Random Sources, Hitting Sets, and BPP Simulations
SIAM Journal on Computing
On the (non)Universality of the One-Time Pad
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On the Impossibility of Private Key Cryptography with Weakly Random Keys
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Privacy Amplification Secure Against Active Adversaries
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
On Perfect and Adaptive Security in Exposure-Resilient Cryptography
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Extracting randomness from samplable distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Deterministic Extractors for Bit-Fixing Sources and Exposure-Resilient Cryptography
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
On the (Im)possibility of Cryptography with Imperfect Randomness
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Random polynomial time is equal to slightly-random polynomial time
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Exposure-resilient functions and all-or-nothing transforms
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Does privacy require true randomness?
TCC'07 Proceedings of the 4th conference on Theory of cryptography
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Most cryptographic primitives such as encryption, authentication or secret sharing require randomness. Usually one assumes that perfect randomness is available, but those primitives might also be realized under weaker assumptions. In this work we continue the study of building secure cryptographic primitives from imperfect random sources initiated by Dodis and Spencer (FOCS'02). Their main result shows that there exists a (high-entropy) source of randomness allowing for perfect encryption of a bit, and yet from which one cannot extract even a single weakly random bit, separating encryption from extraction. Our main result separates encryption from 2-out-2 secret sharing (both in the information-theoretic and in the computational settings): any source which can be used to achieve one-bit encryption also can be used for 2-out-2 secret sharing of one bit, but the converse is false, even for high-entropy sources. Therefore, possibility of extraction strictly implies encryption, which in turn strictly implies 2-out-2 secret sharing.