Possibility and Impossibility Results for Receiver Selective Opening Secure PKE in the Multi-Challenge Setting 📺
Public key encryption (PKE) schemes are usually deployed in an open system with numerous users. In practice, it is common that some users are corrupted. A PKE scheme is said to be receiver selective opening (RSO) secure if it can still protect messages transmitted to uncorrupted receivers after the adversary corrupts some receivers and learns their secret keys. This is usually defined by requiring the existence of a simulator that can simulate the view of the adversary given only the opened messages. Existing works construct RSO secure PKE schemes in a single-challenge setting, where the adversary can only obtain one challenge ciphertext for each public key. However, in practice, it is preferable to have a PKE scheme with RSO security in the multi-challenge setting, where public keys can be used to encrypt multiple messages. In this work, we explore the possibility for achieving PKE schemes with receiver selective opening security in the multi-challenge setting. Our contributions are threefold. First, we demonstrate that PKE schemes with RSO security in the single-challenge setting are not necessarily RSO secure in the multi-challenge setting. Then, we show that it is impossible to achieve RSO security for PKE schemes if the number of challenge ciphertexts under each public key is a priori unbounded. In particular, we prove that no PKE scheme can be RSO secure in the $k$-challenge setting (i.e., the adversary can obtain $k$ challenge ciphertexts for each public key) if its secret key contains less than $k$ bits. On the positive side, we give a concrete construction of PKE scheme with RSO security in the $k$-challenge setting, where the ratio of the secret key length to $k$ approaches the lower bound 1.
Hedged Nonce-Based Public-Key Encryption: Adaptive Security Under Randomness Failures
Nowadays it is well known that randomness may fail due to bugs or deliberate randomness subversion. As a result, the security of traditional public-key encryption (PKE) cannot be guaranteed any more. Currently there are mainly three approaches dealing with the problem of randomness failures: deterministic PKE, hedged PKE, and nonce-based PKE. However, these three approaches only apply to different application scenarios respectively. Since the situations in practice are dynamic and very complex, it’s almost impossible to predict the situation in which a scheme is deployed, and determine which approach should be used beforehand.In this paper, we initiate the study of hedged security for nonce-based PKE, which adaptively applies to the situations whenever randomness fails, and achieves the best-possible security. Specifically, we lift the hedged security to the setting of nonce-based PKE, and formalize the notion of chosen-ciphertext security against chosen-distribution attacks (IND-CDA2) for nonce-based PKE. By presenting two counterexamples, we show a separation between our IND-CDA2 security for nonce-based PKE and the original NBP1/NBP2 security defined by Bellare and Tackmann (EUROCRYPT 2016). We show two nonce-based PKE constructions meeting IND-CDA2, NBP1 and NBP2 security simultaneously. The first one is a concrete construction in the random oracle model, and the second one is a generic construction based on a nonce-based PKE scheme and a deterministic PKE scheme.