Randomness Condensers for Efficiently Samplable, Seed-Dependent Sources

We initiate a study of randomness condensers for sources that are efficiently samplable but may depend on the seed of the con- denser. That is, we seek functions Cond : {0, 1}n ×{0, 1}d → {0, 1}m such that if we choose a random seed S ← {0,1}d, and a source X = A(S) is generated by a randomized circuit A of size t such that X has min- entropy at least k given S, then Cond(X;S) should have min-entropy at least some k′ given S. The distinction from the standard notion of ran- domness condensers is that the source X may be correlated with the seed S (but is restricted to be efficiently samplable). Randomness extractors of this type (corresponding to the special case where k′ = m) have been implicitly studied in the past (by Trevisan and Vadhan, FOCS ‘00). We show that: – Unlike extractors, we can have randomness condensers for samplable, seed-dependent sources whose computational complexity is smaller than the size t of the adversarial sampling algorithm A. Indeed, we show that sufficiently strong collision-resistant hash functions are seed-dependent condensers that produce outputs with min-entropy k′ = m − O(log t), i.e. logarithmic entropy deficiency. – Randomness condensers suffice for key derivation in many crypto- graphic applications: when an adversary has negligible success proba- bility (or negligible “squared advantage” [3]) for a uniformly random key, we can use instead a key generated by a condenser whose output has logarithmic entropy deficiency. – Randomness condensers for seed-dependent samplable sources that are robust to side information generated by the sampling algorithm imply soundness of the Fiat-Shamir Heuristic when applied to any constant-round, public-coin interactive proof system.Engineering and Applied Science

An Efficient Transform from Sigma Protocols to NIZK with a CRS and Non-Programmable Random Oracle

In this short paper, we present a Fiat-Shamir type transform that takes any Sigma protocol for a relation $R$ and outputs a non-interactive zero-knowledge proof (not of knowledge) for the associated language $L_R$, in the common reference string model. As in the Fiat-Shamir transform, we use a hash function $H$. However, zero-knowledge is achieved under standard assumptions in the common reference string model (without any random oracle), and soundness is achieved in the \emph{non-programmable} random oracle model. The concrete computational complexity of the transform is only slightly higher than the original Fiat-Shamir transform

On Pseudorandom Encodings

We initiate a study of pseudorandom encodings: efficiently computable and decodable encoding functions that map messages from a given distribution to a random-looking distribution. For instance, every distribution that can be perfectly and efficiently compressed admits such a pseudorandom encoding. Pseudorandom encodings are motivated by a variety of cryptographic applications, including password-authenticated key exchange, “honey encryption” and steganography. The main question we ask is whether every efficiently samplable distribution admits a pseudorandom encoding. Under different cryptographic assumptions, we obtain positive and negative answers for different flavors of pseudorandom encodings, and relate this question to problems in other areas of cryptography. In particular, by establishing a two-way relation between pseudorandom encoding schemes and efficient invertible sampling algorithms, we reveal a connection between adaptively secure multiparty computation for randomized functionalities and questions in the domain of steganography

Standard Security Does Not Imply Indistinguishability Under Selective Opening

In a selective opening attack (SOA) on an encryption scheme, the adversary is given a collection of ciphertexts and selectively chooses to see some subset of them ``opened\u27\u27, meaning that the messages and the encryption randomness are revealed to her. A scheme is SOA secure if the data contained in the unopened ciphertexts remains hidden. A fundamental question is whether every CPA secure scheme is necessarily also SOA secure. The work of Bellare et al. (EUROCRYPT \u2712) gives a partial negative answer by showing that some CPA secure schemes do not satisfy a simulation-based definition of SOA security called SIM-SOA. However, until now, it remained possible that every CPA secure scheme satisfies an indistinguishability-based definition of SOA security called IND-SOA. In this work, we resolve the above question in the negative and construct a highly contrived encryption scheme which is CPA (and even CCA) secure but is not IND-SOA secure. In fact, it is broken in a very obvious sense by a selective opening attack as follows. A random value is secret-shared via Shamir\u27s scheme so that any t out of n shares reveal no information about the shared value. The n shares are individually encrypted under a common public key and the n resulting ciphertexts are given to the adversary who selectively chooses to see t of the ciphertexts opened. Counter-intuitively, this suffices for the adversary to completely recover the shared value. Our contrived scheme relies on strong assumptions: public-coin differing inputs obfuscation and a certain type of correlation intractable hash functions. We also extend our negative result to the setting of SOA attacks with key opening (IND-SOA-K) where the adversary is given a collection of ciphertexts under different public keys and selectively chooses to see some subset of the secret keys

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

Big-Key Symmetric Encryption: Resisting Key Exfiltration

This paper aims to move research in the bounded retrieval model (BRM) from theory to practice by considering symmetric (rather than public-key) encryption, giving efficient schemes, and providing security analyses with sharp, concrete bounds. The threat addressed is malware that aims to exfiltrate a user\u27s key. Our schemes aim to thwart this by using an enormously long key, yet paying for this almost exclusively in storage cost, not speed. Our main result is a general-purpose lemma, the subkey prediction lemma, that gives a very good bound on an adversary\u27s ability to guess a (modest length) subkey of a big-key, the subkey consisting of the bits of the big-key found at random, specified locations, after the adversary has exfiltrated partial information about the big key (e.g., half as many bits as the big-key is long). We then use this to design a new kind of key encapsulation mechanism, and, finally, a symmetric encryption scheme. Both are in the random-oracle model. We also give a less efficient standard-model scheme that is based on universal computational extractors (UCE). Finally, we define and achieve hedged BRM symmetric encryption, which provides authenticity in the absence of leakage

SoK: Security Models for Pseudo-Random Number Generators

Randomness plays an important role in multiple applications in cryptography. It is required in fundamental tasks such as key generation, masking and hiding values, nonces and initialization vectors generation. Pseudo-random number generators have been studied by numerous authors, either to propose clear security notions and associated constructions or to point out potential vulnerabilities. In this systematization of knowledge paper, we present the three notions of generators that have been successively formalized: standard generators, stateful generators and generators with input. For each notion, we present expected security properties, where adversaries have increasing capabilities (including access to partial information on the internal variables) and we propose secure and efficient constructions, all based on the block cipher AES. In our description of generators with input, we revisit the notions of accumulator and extractor and we point out that security crucially relies on the independence between the randomness source and the seeds of the accumulator and the extractor. To illustrate this requirement, we identify a potential vulnerability of the NIST standard CTR_DRBG

Interactive Message-Locked Encryption and Secure Deduplication

This paper considers the problem of secure storage of outsourced data in a way that permits deduplication. We are for the first time able to provide privacy for messages that are both correlated and dependent on the public system parameters. The new ingredient that makes this possible is interaction. We extend the message-locked encryption (MLE) primitive of prior work to interactive message-locked encryption (iMLE) where upload and download are protocols. Our scheme, providing security for messages that are not only correlated but allowed to depend on the public system parameters, is in the standard model. We explain that interaction is not an extra assumption in practice because full, existing deduplication systems are already interactive