Non-interactive Zero Knowledge Proofs in the Random Oracle Model

in Codes, Cryptology and Information Security (2019)

The Fiat-Shamir (FS) transform is a well known and widely used technique to convert any constant-round public-coin honest-verifier zero-knowledge (HVZK) proof or argument system CIPC=(Prov,Ver) in a non ... [more ▼]

The Fiat-Shamir (FS) transform is a well known and widely used technique to convert any constant-round public-coin honest-verifier zero-knowledge (HVZK) proof or argument system CIPC=(Prov,Ver) in a non-interactive zero-knowledge (NIZK) argument system NIZK=(NIZK.Prove, NIZK.Verify). The FS transform is secure in the random oracle (RO) model and is extremely efficient: it adds an evaluation of the RO for every message played by Ver. While a major effort has been done to attack the soundness of the transform when the RO is instantiated with a ``secure'' hash function, here we focus on a different limitation of the FS transform that exists even when there is a secure instantiation of the random oracle: the soundness of NIZK holds against polynomial-time adversarial provers only. Therefore even when CIPC is a proof system, NIZK is only an argument system. In this paper we propose a new transform from 3-round public-coin HVZK proof systems for several practical relations to NIZK proof systems in the RO model. Our transform outperforms the FS transform protecting the honest verifier from unbounded adversarial provers with no restriction on the number of RO queries. The protocols our transform can be applied to are the ones for proving membership to the range of a one-way group homomorphism as defined by [Maurer - Design, Codes and Cryptography 2015] except that we additionally require the function to be endowed with a trapdoor and other natural properties. For instance, we obtain new efficient instantiations of NIZK proofs for relations related to quadratic residuosity and the RSA function. As a byproduct, with our transform we obtain essentially for free the first efficient non-interactive zap (i.e., 1-round non-interactive witness indistinguishable proof system for several practical languages in the non-programmable RO model and in an ideal-PUF model. Our approach to NIZK proofs can be seen as an abstraction of the celebrated work of [Feige, Lapidot and Shamir - FOCS 1990]. [less ▲]

Tightly-Secure PAK(E)

in Cryptology and Network Security (2017, December 02)

We present a security reduction for the PAK protocol instantiated over Gap Diffie-Hellman Groups that is tighter than previously known reductions. We discuss the implications of our results for concrete ... [more ▼]

We present a security reduction for the PAK protocol instantiated over Gap Diffie-Hellman Groups that is tighter than previously known reductions. We discuss the implications of our results for concrete security. Our proof is the first to show that the PAK protocol can provide meaningful security guarantees for values of the parameters typical in today’s world. [less ▲]

On the Relation Between SIM and IND-RoR Security Models for PAKEs

Presentation (2017, March 09)

Security models for PAKE protocols aim to capture the desired security properties that such protocols must satisfy when executed in the presence of an active adversary. They are usually classified into i ... [more ▼]

Security models for PAKE protocols aim to capture the desired security properties that such protocols must satisfy when executed in the presence of an active adversary. They are usually classified into i) indistinguishability-based (IND-based) or ii) simulation-based (SIM-based). The relation between these two security notions is unclear and mentioned as a gap in the literature. In this work, we prove that the SIM-based model of Boyko, Mackenzie and Patel [EUROCRYPT00] and the IND-based model of Abdalla, Fouque and Pointcheval are equivalent, in the sense that a protocol proven secure in one model is also secure in the other model. [less ▲]

Privacy-Preserving Verifiability: A Case for an Electronic Exam Protocol

in Giustolisi, Rosario; Iovino, Vincenzo; Lenzini, Gabriele (Eds.) Privacy-Preserving Verifiability: A Case for an Electronic Exam Protocol (2017)

We introduce the notion of privacy-preserving verifiability for security protocols. It holds when a protocol admits a verifiability test that does not reveal, to the verifier that runs it, more pieces of ... [more ▼]

We introduce the notion of privacy-preserving verifiability for security protocols. It holds when a protocol admits a verifiability test that does not reveal, to the verifier that runs it, more pieces of information about the protocol’s execution than those required to run the test. Our definition of privacy-preserving verifiability is general and applies to cryptographic protocols as well as to human security protocols. In this paper we exemplify it in the domain of e-exams. We prove that the notion is meaningful by studying an existing exam protocol that is verifiable but whose verifiability tests are not privacy-preserving. We prove that the notion is applicable: we review the protocol using functional encryption so that it admits a verifiability test that preserves privacy to our definition. We analyse, in ProVerif, that the verifiability holds despite malicious parties and that the new protocol maintains all the security properties of the original protocol, so proving that our privacy-preserving verifiability can be achieved starting from existing security. [less ▲]

On the Relation Between SIM and IND-RoR Security Models for PAKEs

in Proceedings of the International Conference on Security and Cryptography (2017)

Password-based Authenticated Key-Exchange (PAKE) protocols allow users, who need only to share a password, to compute a high-entropy shared session key despite passwords being taken from a dictionary ... [more ▼]

Password-based Authenticated Key-Exchange (PAKE) protocols allow users, who need only to share a password, to compute a high-entropy shared session key despite passwords being taken from a dictionary. Security models for PAKE protocols aim to capture the desired security properties that such protocols must satisfy when executed in the presence of an active adversary. They are usually classified into i) indistinguishability-based (IND-based) or ii) simulation-based (SIM-based). The relation between these two security notions is unclear and mentioned as a gap in the literature. In this work, we prove that SIM-BMP security from Boyko et al.~(EUROCRYPT 2000) implies IND-RoR security from Abdalla et al.~(PKC 2005) and that IND-RoR security implies a slightly modified version of SIM-BMP security. We also investigate whether IND-RoR security implies (unmodified) SIM-BMP security. [less ▲]

Updatable Functional Encryption

in Paradigms in Cryptology - Mycrypt 2016. Malicious and Exploratory Cryptology, Second International Conference, Mycrypt 2016, Kuala Lumpur, Malaysia, December 1-2, 2016, Revised Selected Papers (2016, December)

Functional encryption (FE) allows an authority to issue tokens associated with various functions, allowing the holder of some token for function f to learn only f(D) from a ciphertext that encrypts D. The ... [more ▼]

Functional encryption (FE) allows an authority to issue tokens associated with various functions, allowing the holder of some token for function f to learn only f(D) from a ciphertext that encrypts D. The standard approach is to model f as a circuit, which yields inefficient evaluations over large inputs. Here, we propose a new primitive that we call updatable functional encryption (UFE), where instead of circuits we deal with RAM programs, which are closer to how programs are expressed in von Neumann architecture. We impose strict efficiency constrains in that the run-time of a token P' on ciphertext CT is proportional to the run-time of its clear-form counterpart (program P on memory D) up to a polylogarithmic factor in the size of D, and we envision tokens that are capable to update the ciphertext, over which other tokens can be subsequently executed. We define a security notion for our primitive and propose a candidate construction from obfuscation, which serves as a starting point towards the realization of other schemes and contributes to the study on how to compute RAM programs over public-key encrypted data. [less ▲]

On the power of Public-key Function-Private Functional Encryption

in 15th International Conference on Cryptology and Network Security (2016)

In the public-key setting, known constructions of function-private functional encryption (FPFE) were limited to very restricted classes of functionalities like inner-product [Agrawal et al. - PKC 2015 ... [more ▼]

In the public-key setting, known constructions of function-private functional encryption (FPFE) were limited to very restricted classes of functionalities like inner-product [Agrawal et al. - PKC 2015]. Moreover, its power has not been well investigated. In this paper, we construct FPFE for general functions and explore its powerful applications, both for general and specific functionalities. As warmup, we construct from FPFE a natural generalization of a signature scheme endowed with functional properties, that we call functional anonymous signature (FAS) scheme. In a FAS, Alice can sign a circuit C chosen from some distribution D to get a signature s and can publish a verification key that allows anybody holding a message m to verify that (1) s is a valid signature of Alice for some (possibly unknown to him) circuit C and (2) C(m)=1. Beyond unforgeability the security of FAS guarantees that the signature s hide as much information as possible about C except what can be inferred from knowledge of D. Then, we show that FPFE can be used to construct in a black-box way functional encryption schemes for randomized functionalities (RFE). %Previous constructions of (public-key) RFE relied on iO [Goyal et al. - TCC 2015]. As further application, we show that specific instantiations of FPFE can be used to achieve adaptively-secure CNF/DNF encryption for bounded degree formulae (BoolEnc). Though it was known how to implement BoolEnc from inner-product encryption (IPE) [Katz et al. - EUROCRYPT 2008], as already observed by Katz et al. this reduction only works for selective security and completely breaks down for adaptive security; however, we show that the reduction works if the IPE scheme is function-private. Finally, we present a general picture of the relations among all these related primitives. One key observation is that Attribute-based Encryption with function privacy implies FE, a notable fact that sheds light on the importance of the function privacy property for FE. [less ▲]

Deniable Functional Encryption

in Public-key Cryptography - PKC 2016, 19th IACR International Conference on Practice and Theory in Public-Key Cryptography, Taipei, Taiwan, March 6-9, 2016, Proceedings, Part I (2016)

Deniable encryption, first introduced by Canetti et al. (CRYPTO 1997), allows a sender and/or receiver of encrypted communication to produce fake but authentic-looking coins and/or secret keys that “open” ... [more ▼]

Deniable encryption, first introduced by Canetti et al. (CRYPTO 1997), allows a sender and/or receiver of encrypted communication to produce fake but authentic-looking coins and/or secret keys that “open” the communication to a different message. Here we initiate its study for the more general case of functional encryption (FE), as introduced by Boneh et al. (TCC 2011), wherein a receiver in possession of a key k can compute from any encryption of a message x the value F (k, x) according to the scheme’s functionality F . Our results are summarized as follows: We put forth and motivate the concept of deniable FE, for which we consider two models. In the first model, as previously considered by O’Neill et al. (CRYPTO 2011) in the case of identity-based encryption, a receiver gets assistance from the master authority to generate a fake secret key. In the second model, there are “normal” and “deniable” secret keys, and a receiver in possession of a deniable secret key can produce a fake but authentic-looking normal key on its own. This parallels the “multi-distributional” model of deniability previously considered for public-key encryption. In the first model, we show that any FE scheme for the general circuit functionality (as several recent candidate construction achieve) can be converted into an FE scheme having receiver deniability, without introducing any additional assumptions. In addition we show an efficient receiver deniable FE for Boolean Formulae from bilinear maps. In the second (multi-distributional) model, we show a specific FE scheme for the general circuit functionality having receiver deniability. This result additionally assumes differing-inputs obfuscation and relies on a new technique we call delayed trapdoor circuits. To our knowledge, a scheme in the multi-distributional model was not previously known even in the simpler case of identity-based encryption. Finally, we show that receiver deniability for FE implies some form of simulation security, further motivating study of the latter and implying optimality of our results. [less ▲]

Mergeable Functional Encryption

Scientific Conference (2015, September 11)

Simulation-Based Secure Functional Encryption in the Random Oracle Model

in Progress in Cryptology -- LATINCRYPT 2015 (2015)

One of the main lines of research in functional encryption (FE) has consisted in studying the security notions for FE and their achievability. This study was initiated by [Boneh et al. – TCC’11, O’Neill – ... [more ▼]

One of the main lines of research in functional encryption (FE) has consisted in studying the security notions for FE and their achievability. This study was initiated by [Boneh et al. – TCC’11, O’Neill – ePrint’10] where it was first shown that for FE the indistinguishability-based (IND) security notion is not sufficient in the sense that there are FE schemes that are provably IND-Secure but concretely insecure. For this reason, researchers investigated the achievability of Simulation-based (SIM) security, a stronger notion of security. Unfortunately, the above-mentioned works and others [e.g., Agrawal et al. – CRYPTO’13] have shown strong impossibility results for SIM-Security. One way to overcome these impossibility results was first suggested in the work of Boneh et al. where it was shown how to construct, in the Random Oracle (RO) model, SIM-Secure FE for restricted functionalities and was asked the generalization to more complex functionalities as a challenging problem in the area. Subsequently, [De Caro et al. – CRYPTO’13] proposed a candidate construction of SIM-Secure FE for all circuits in the RO model assuming the existence of an IND-Secure FE scheme for circuits with RO gates. To our knowledge there are no proposed candidate IND-Secure FE schemes for circuits with RO gates and they seem unlikely to exist. We propose the first constructions of SIM-Secure FE schemes in the RO model that overcome the current impossibility results in different settings. We can do that because we resort to the two following models: In the public-key setting we assume a bound on the number of queries but this bound only affects the running-times of our encryption and decryption procedures. We stress that our FE schemes in this model are SIM-Secure and have ciphertexts and tokens of constant-size, whereas in the standard model, the current SIM-Secure FE schemes for general functionalities [De Caro et al., Gorbunov et al. – CRYPTO’12] have ciphertexts and tokens of size growing as the number of queries. In the symmetric-key setting we assume a timestamp on both ciphertexts and tokens. In this model, we provide FE schemes with short ciphertexts and tokens that are SIM-Secure against adversaries asking an unbounded number of queries. Both results also assume the RO model, but not functionalities with RO gates and rely on extractability obfuscation [Boyle et al. – TCC’14] (and other standard primitives) secure only in the standard model. [less ▲]