Dodis, Yevgeniy ; Pietrzak, Krzysztof ZIST Austria ; Przydatek, Bartosz
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.
Supported in part by NSF career award CCR-0133806 and NSF grant CCR-0311095. Supported by the Swiss National Science Foundation, project No. 200020-103847/1.
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TCC: Theory of Cryptography Conference
Dodis Y, Pietrzak KZ, Przydatek B. Separating sources for encryption and secret sharing. In: Vol 3876. Springer; 2006:601-616. doi:10.1007/11681878_31
Dodis, Y., Pietrzak, K. Z., & Przydatek, B. (2006). Separating sources for encryption and secret sharing (Vol. 3876, pp. 601–616). Presented at the TCC: Theory of Cryptography Conference, Springer. https://doi.org/10.1007/11681878_31
Dodis, Yevgeniy, Krzysztof Z Pietrzak, and Bartosz Przydatek. “Separating Sources for Encryption and Secret Sharing,” 3876:601–16. Springer, 2006. https://doi.org/10.1007/11681878_31.
Y. Dodis, K. Z. Pietrzak, and B. Przydatek, “Separating sources for encryption and secret sharing,” presented at the TCC: Theory of Cryptography Conference, 2006, vol. 3876, pp. 601–616.
Dodis Y, Pietrzak KZ, Przydatek B. 2006. Separating sources for encryption and secret sharing. TCC: Theory of Cryptography Conference, LNCS, vol. 3876. 601–616.
Dodis, Yevgeniy, et al. Separating Sources for Encryption and Secret Sharing. Vol. 3876, Springer, 2006, pp. 601–16, doi:10.1007/11681878_31.