Fiat-Shamir for highly sound protocols is instantiable

The Fiat–Shamir (FS) transformation (Fiat and Shamir, Crypto '86) is a popular paradigm for constructing very efficient non-interactive zero-knowledge (NIZK) arguments and signature schemes from a hash function and any three-move interactive protocol satisfying certain properties. Despite its wide-spread applicability both in theory and in practice, the known positive results for proving security of the FS paradigm are in the random oracle model only, i.e., they assume that the hash function is modeled as an external random function accessible to all parties. On the other hand, a sequence of negative results shows that for certain classes of interactive protocols, the FS transform cannot be instantiated in the standard model. We initiate the study of complementary positive results, namely, studying classes of interactive protocols where the FS transform does have standard-model instantiations. In particular, we show that for a class of “highly sound” protocols that we define, instantiating the FS transform via a q-wise independent hash function yields NIZK arguments and secure signature schemes. In the case of NIZK, we obtain a weaker “q-bounded” zero-knowledge flavor where the simulator works for all adversaries asking an a-priori bounded number of queries q; in the case of signatures, we obtain the weaker notion of random-message unforgeability against q-bounded random message attacks. Our main idea is that when the protocol is highly sound, then instead of using random-oracle programming, one can use complexity leveraging. The question is whether such highly sound protocols exist and if so, which protocols lie in this class. We answer this question in the affirmative in the common reference string (CRS) model and under strong assumptions. Namely, assuming indistinguishability obfuscation and puncturable pseudorandom functions we construct a compiler that transforms any 3-move interactive protocol with instance-independent commitments and simulators (a property satisfied by the Lapidot–Shamir protocol, Crypto '90) into a compiled protocol in the CRS model that is highly sound. We also present a second compiler, in order to be able to start from a larger class of protocols, which only requires instance-independent commitments (a property for example satisfied by the classical protocol for quadratic residuosity due to Blum, Crypto '81). For the second compiler we require dual-mode commitments. We hope that our work inspires more research on classes of (efficient) 3-move protocols where Fiat–Shamir is (efficiently) instantiable

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 of 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

Standard Security Does Imply Security Against Selective Opening for Markov Distributions

About three decades ago it was realized that implementing private channels between parties which can be adaptively corrupted requires an encryption scheme that is secure against selective opening attacks. Whether standard (IND-CPA) security implies security against selective opening attacks has been a major open question since. The only known reduction from selective opening to IND-CPA security loses an exponential factor. A polynomial reduction is only known for the very special case where the distribution considered in the selective opening security experiment is a product distribution, i.e., the messages are samples independent from each other. In this paper we give a reduction whose loss is quantified via the dependence graph (where message dependencies correspond to edges) of the underlying message distribution. In particular, for some concrete distributions including Markov distributions, our reduction is polynomial

Selective Opening Security from Simulatable Data Encapsulation

The confidentiality notion of security against selective opening attacks considers adver- saries that obtain challenge ciphertexts and are allowed to adaptively open them, thereby revealing the encrypted message and the randomness used to encrypt. The SO notion is stronger than that of CCA security and is often required when formally arguing towards the security of multi-user applications. While different ways of achieving correspondingly secure schemes are known, as they generally employ expensive asymmetric building blocks like lossy trapdoor functions or lossy en- cryption, such constructions are routinely left aside by practitioners and standardization bodies. So far, formal arguments towards the SO security of schemes used in practice (e.g., for email encryption) are not known. In this work we shift the focus from the asymmetric to the symmetric building blocks of PKE and prove the following statement: If a PKE scheme is composed of a key encapsulation mechanism (KEM) and a blockcipher-based data encapsulation mechanism (DEM), and the DEM meets spe- cific combinatorial properties, then the PKE scheme offers SO security, in the ideal cipher model. Fortunately, as we show, the required properties hold for popular modes of operation like CTR, CBC, CCM, and GCM. This paper not only establishes the corresponding theoretical framework of analysis, but also contributes very concretely to practical cryptography by concluding that selective opening security is given for many real-world schemes

Collusion Resistant Broadcast and Trace from Positional Witness Encryption

An emerging trend is for researchers to identify cryptography primitives for which feasibility was first established under obfuscation and then move the realization to a different setting. In this work we explore a new such avenue — to move obfuscation-based cryptography to the assumption of (positional) witness encryption. Our goal is to develop techniques and tools, which we will dub “witness encryption friendly” primitives and use these to develop a methodology for building advanced cryptography from positional witness encryption. We take a bottom up approach and pursue our general agenda by attacking the specific problem of building collusion-resistant broadcast systems with tracing from positional witness encryption. We achieve a system where the size of ciphertexts, public key and private key are polynomial in the security parameter $\lambda$ and independent of the number of users N in the broadcast system. Currently, systems with such parameters are only known from indistinguishability obfuscation

KDM Security for Identity-Based Encryption: Constructions and Separations

For encryption schemes, key dependent message (KDM) security requires that ciphertexts preserve secrecy even when the messages to be encrypted depend on the secret keys. While KDM security has been extensively studied for public-key encryption (PKE), it receives much less attention in the setting of identity-based encryption (IBE). In this work, we focus on the KDM security for IBE. Our results are threefold. We first propose a generic approach to transfer the KDM security results (both positive and negative) from PKE to IBE. At the heart of our approach is a neat structure-mirroring PKE-to-IBE transformation based on indistinguishability obfuscation and puncturable PRFs, which establishes a connection between PKE and IBE in general. However, the obtained results are restricted to selective-identity sense. We then concentrate on results in adaptive-identity sense. On the positive side, we present two constructions that achieve KDM security in the adaptive-identity sense for the first time. One is built from identity-based hash proof system (IB-HPS) with homomorphic property, which indicates that the IBE schemes of Gentry (Eurocrypt 2006), Coron (DCC 2009), Chow et al. (CCS 2010) are actually KDM-secure in the single-key setting. The other is built from indistinguishability obfuscation and a new notion named puncturable unique signature, which is bounded KDM-secure in the single-key setting. On the negative side, we separate CPA/CCA security from $n$-circular security (which is a prototypical case of KDM security) for IBE by giving a counterexample based on differing-inputs obfuscation and a new notion named puncturable IBE. We further propose a general framework for generating $n$-circular security counterexamples in identity-based setting, which might be of independent interest