[Resource Topic] 2017/146: Toward Fine-Grained Blackbox Separations Between Semantic and Circular-Security Notions

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Toward Fine-Grained Blackbox Separations Between Semantic and Circular-Security Notions

Authors: Mohammad Hajiabadi, Bruce M. Kapron


We address the problems of whether t-circular-secure encryption can be based on (t-1)-circular-secure encryption or on semantic (CPA) security, if t = 1. While for t = 1 a folklore construction, based on CPA-secure encryption, can be used to build a 1-circular-secure encryption with the same secret-key and message space, no such constructions are known for the bit-encryption case, which is of particular importance in fully-homomorphic encryption. Also, for t \geq 2, all constructions of t-circular-secure encryption (bitwise or otherwise) are based on specific assumptions. We make progress toward these problems by ruling out all fully-blackbox constructions of – 1-seed circular-secure public-key bit encryption from CPA-secure public-key encryption; – t-seed circular-secure public-key encryption from (t-1)-seed circular-secure public-key encryption, for any t \geq 2. Informally, seed-circular security is a variant of the circular security notion in which the seed of the key-generation algorithm, instead of the secret key, is encrypted. We also show how to extend our first result to rule out a large and non-trivial class of constructions of 1-circular-secure bit encryption, which we dub key-isolating constructions. Our separation model follows that of Gertner, Malkin and Reingold (FOCS’01), which is a weaker separation model than that of Impagliazzo and Rudich.

ePrint: https://eprint.iacr.org/2017/146

Talk: https://www.youtube.com/watch?v=E4UPfzBJIR4

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