Cryptology ePrint Archive: Report 2010/154

Efficient Public-Key Cryptography in the Presence of Key Leakage

Yevgeniy Dodis and Kristiyan Haralambiev and Adriana Lopez-Alt and Daniel Wichs

Abstract: We study the design of cryptographic primitives resistant to a large class of side-channel attacks, called "memory attacks", where an attacker can repeatedly and adaptively learn information about the secret key, subject *only* to the constraint that the *overall amount* of such information is bounded by some parameter $\ell$. Although the study of such primitives was initiated only recently by Akavia et al. [AGV09], subsequent work already produced many such "leakage-resilient" primitives [NS09,ADW09,KV09], including signature, encryption, identification (ID) and authenticated key agreement (AKA) schemes. Unfortunately, every existing scheme, --- for any of the four fundamental primitives above, --- fails to satisfy at least one of the following desirable properties:

- Efficiency. While the construction may be generic, it should have some *efficient* instantiations, based on standard cryptographic assumptions, and without relying on random oracles.

- Strong Security. The construction should satisfy the strongest possible definition of security (even in the presence of leakage). For example, encryption schemes should be secure against chosen *ciphertext* attack (CCA), while signatures should be *existentially* unforgeable.

- Leakage Flexibility. It should be possible to set the parameters of the schemes so that the leakage bound $\ell$ can come arbitrarily close to the size of the secret key $sk$.

In this work we design the first signature, encryption, ID and AKA schemes which overcome these limitations, and satisfy all the properties above. Moreover, all our constructions are generic, in several cases elegantly simplifying and generalizing the prior constructions (which did not have any efficient instantiations). We also introduce several tools of independent interest, such as the abstraction (and constructions) of *simulation extractable* NIZK arguments, and a new *deniable* DH-based AKA protocol based on any CCA-secure encryption.

Category / Keywords: public-key cryptography / leakage resilience, NIZK simulation extractability

Date: received 22 Mar 2010, last revised 15 Sep 2010

Contact author: kkh at cs nyu edu

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Version: 20100915:181314 (All versions of this report)

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