NDLI: Paillier's Trapdoor Function Hides up to O(n) Bits

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Paillier's Trapdoor Function Hides up to O(n) Bits

Content Provider	Springer Nature Link
Author	Catala, Dario Gennaro, Rosario Howgrave Graham, Nick
Copyright Year	2002
Abstract	At EuroCrypt '99 Paillier proposed a new encryption scheme based on higher residuosity classes. The new scheme was proven to be one-way under the assumption that computing N -residuosity classes in Z N2 * is hard. Similarly the scheme can be proven to be semantically secure under a much stronger decisional assumption: given w ∈ Z N2 * it is impossible to decide if w is an N -residue or not. In this paper we examine the bit security of Paillier's scheme. We prove that if computing residuosity classes is hard, then given a random w it is impossible to predict the least significant bit of its class significantly better than at random. This immediately yields a way to obtain semantic security without relying on the decisional assumption (at the cost of several invocations of Paillier's original function). In order to improve efficiency we then turn to the problem of simultaneous security of many bits. We prove that Paillier's scheme hides n-b (up to O(n) ) bits if one assumes that computing the class c of a random w remains hard even when we are told that c<2 b . We thoroughly examine the security of this stronger version of the intractability of the class problem. An important theoretical implication of our result is the construction of the first trapdoor function that hides super-logarithmically (up to O(n) ) many bits. We generalize our techniques to provide sufficient conditions for a trapdoor function to have this property.
Starting Page	251
Ending Page	269
Page Count	19
File Format	PDF
ISSN	09332790
Journal	Journal of Cryptology
Volume Number	15
Issue Number	4
e-ISSN	14321378
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-07-23
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Coding and Information Theory Computational Mathematics and Numerical Analysis Combinatorics Probability Theory and Stochastic Processes Communications Engineering, Networks
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications Software

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