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Lecture notes in computer science

Hedged Public-Key Encryption: How to Protect against Bad Randomness

Mihir Bellare Y, Zvika Brakerski, Moni Naor, Thomas Ristenpart, Gil Segev, Hovav Shacham, Scott Yilek

Published Jan 1, 2009• 133 citations
Publisher
DOI
10.1007/978-3-642-10366-7_14

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Abstract Hedged public-key encryption (HPKE), introduced by Bellare et al. (ASIACRYPT 2009), provides useful security when the per-message randomness fails to be uniform due to faulty implementations or adversarial actions. The HPKE scheme achieves IND-CPA (chosen plaintext attack) security when the randomness they used is of high quality, but, when the randomness is poor quality, rather than breaking completely, it achieves a weaker but a useful notion of security called IND-CDA (chosen distribution attack) as long as the message and randomness together have sufficient min-entropy. However, little research on HPKE in the presence of key leakage was done. In this paper, we study HPKE featuring key leakage-resilience and formulate appropriate security notion for key leakage-resilient HPKE. We work in the continual key leakage model where the secret key is refreshed periodically and an adversary can learn arbitrary but bounded leakage on the secret key between the updates. We present two generic constructions of continual leakage-resilient HPKE in the standard model by using a continual leakage-resilient all-but-one lossy trapdoor function. Finally, we give an instantiation of leakage-resilient HPKE under the linear assumption in bilinear groups.
Most of the existing cryptographic schemes, e.g., key agreement protocol, call for good randomness. Otherwise, the security of these cryptographic schemes cannot be fully guaranteed. Nonce-based cryptosystem is recently introduced to improve the security of public key encryption and digital signature schemes by ensuring security when randomness fails. In this paper, we first investigate the security of key agreement protocols when randomness fails. Then we define the security model for nonce-based key agreement protocols and propose a nonce-based key agreement protocol that protects against bad randomness. The new protocol is proven to be secure in our proposed security model.