Smooth NIZK Arguments with Applications to Asymmetric UC-PAKE and Threshold-IBE

We introduce a novel notion of smooth (-verifier) non-interactive zero-knowledge proofs (NIZK) which parallels the familiar notion of smooth projective hash functions (SPHF). We also show that the recent single group element quasi-adaptive NIZK (QA-NIZK) of Jutla and Roy (CRYPTO 2014) for linear subspaces can be easily extended to be computationally smooth. One important distinction of the new notion from SPHFs is that in a smooth NIZK the public evaluation of the hash on a language member using the projection key does not require the witness of the language member, but instead just requires its NIZK proof. This has the remarkable consequence that in the Gennaro-Lindell paradigm of designing universally-composable password-authenticated key-exchange (UC-PAKE) protocols, if one replaces the traditionally employed SPHFs with the novel smooth QA-NIZK, one gets highly efficient UC-PAKE protocols that are secure even under dynamic corruption. This simpler and modular design methodology allows us to give the first single-round asymmetric UC-PAKE protocol, which is also secure under dynamic corruption in the erasure model. We also define a related concept of smooth signatures, which we show is black-box equivalent to identity-based encryption (IBE). The novel abstraction allows us to give the first threshold (private-key generation) fully-secure IBE in the standard model

Updatable Trapdoor SPHFs: Modular Construction of Updatable Zero-Knowledge Arguments and More

Recently, motivated by its increased use in real-world applications, there has been a growing interest on the reduction of trust in the generation of the common reference string (CRS) for zero-knowledge (ZK) proofs. This line of research was initiated by the introduction of subversion non-interactive ZK (NIZK) proofs by Bellare et al. (ASIACRYPT\u2716). Here, the zero-knowledge property needs to hold even in case of a malicious generation of the CRS. Groth et al. (CRYPTO\u2718) then introduced the notion of updatable zk-SNARKS, later adopted by Lipmaa (SCN\u2720) to updatable quasi-adaptive NIZK (QA-NIZK) proofs. In contrast to the subversion setting, in the updatable setting one can achieve stronger soundness guarantees at the cost of reintroducing some trust, resulting in a model in between the fully trusted CRS generation and the subversion setting. It is a promising concept, but all previous updatable constructions are ad-hoc and tailored to particular instances of proof systems. Consequently, it is an interesting question whether it is possible to construct updatable ZK primitives in a more modular way from simpler building blocks. In this work we revisit the notion of trapdoor smooth projective hash functions (TSPHFs) in the light of an updatable CRS. TSPHFs have been introduced by Benhamouda et al. (CRYPTO\u2713) and can be seen as a special type of a 2-round ZK proof system. In doing so, we first present a framework called lighter TSPHFs (L-TSPHFs). Building upon it, we introduce updatable L-TSPHFs as well as instantiations in bilinear groups. We then show how one can generically construct updatable quasi-adaptive zero-knowledge arguments from updatable L-TSPHFs. Our instantiations are generic and more efficient than existing ones. Finally, we discuss applications of (updatable) L-TSPHFs to efficient (updatable) 2-round ZK arguments as well as updatable password-authenticated key-exchange (uPAKE)

Mitte-interaktiivsed nullteadmusprotokollid nõrgemate usalduseeldustega

Väitekirja elektrooniline versioon ei sisalda publikatsiooneTäieliku koosluskindlusega (TK) kinnitusskeemid ja nullteadmustõestused on ühed põhilisemad krüptograafilised primitiivid, millel on hulgaliselt päriselulisi rakendusi. (TK) Kinnitusskeem võimaldab osapoolel arvutada salajasest sõnumist kinnituse ja hiljem see verifitseeritaval viisil avada. Täieliku koosluskindlusega protokolle saab vabalt kombineerida teiste täieliku koosluskindlusega protokollidega ilma, et see mõjutaks nende turvalisust. Nullteadmustõestus on protokoll tõestaja ja verifitseerija vahel, mis võimaldab tõestajal veenda verifitseerijat mingi väite paikapidavuses ilma rohkema informatsiooni lekitamiseta. Nullteadmustõestused pakuvad suurt huvi ka praktilistes rakendustes, siinkohal on olulisemateks näideteks krüptorahad ja hajusandmebaasid üldisemalt. Siin on eriti asjakohased just lühidad mitteinteraktiivsed nullteadmustõestused (SNARKid) ning kvaasiadaptiivsed mitteinteraktiivsed nullteadmustõestused (QA-NIZKid). Mitteinteraktiivsetel nullteadmustõestustel juures on kaks suuremat praktilist nõrkust. Esiteks on tarvis usaldatud seadistusfaasi osapoolte ühisstringi genereerimiseks ja teiseks on tarvis täielikku koosluskindlust. Käesolevas doktoritöös me uurime neid probleeme ja pakume välja konkreetseid konstruktsioone nende leevendamiseks. Esmalt uurime me õõnestuskindlaid SNARKe juhu jaoks, kus seadistusfaasi ühisstring on õõnestatud. Me konstrueerime õõnestuskindla versiooni seni kõige tõhusamast SNARKist. Samuti uurime me QA-NIZKide õõnestuskindlust ja konstrueerime kõige efektiivsemate QA-NIZKide õõnestuskindla versiooni. Mis puutub teise uurimissuunda, nimelt täielikku koosluskindlusesse, siis sel suunal kasutame me pidevaid projektiivseid räsifunktsioone. Me pakume välja uue primitiivi, kus eelmainitud räsifunktsioonid on avalikult verifitseeritavad. Nende abil me konstrueerime seni kõige tõhusama mitteinteraktiivse koosluskindla kinnitusskeemi. Lõpetuseks me töötame välja uue võtte koosluskindlate kinnitusskeemide jaoks, mis võimaldab ühisarvutuse abil luua nullteadmustõestuste ühisstringe.Quite central primitives in cryptographic protocols are (Universally composable (UC)) commitment schemes and zero-knowledge proofs that getting frequently employed in real-world applications. A (UC) commitment scheme enables a committer to compute a commitment to a secret message, and later open it in a verifiable manner (UC protocols can seamlessly be combined with other UC protocols and primitives while the entire protocol remains secure). A zero-knowledge proof is a protocol usually between a prover and a verifier that allows the prover to convince the verifier of the legality of a statement without disclosing any more information. Zero-knowledge proofs and in particular Succinct non-interactive zero-knowledge proofs (SNARKs) and quasi adaptive NIZK (QA-NIZK) are of particular interest in the real-world applications, with cryptocurrencies or more generally distributed ledger technologies being the prime examples. The two serious issues and the main drawbacks of the practical usage of NIZKs are (i) the demand for a trusted setup for generating the common reference string (CRS) and (ii) providing the UC security. In this thesis, we essentially investigate the aforementioned issues and propose concrete constructions for them. We first investigate subversion SNARKs (Sub zk-SNARKs) when the CRS is subverted. In particular, we build a subversion of the most efficient SNARKs. Then we initiate the study of subversion QA-NIZK (Sub-QA-NIZK) and construct subversion of the most efficient QA-NIZKs. For the second issue, providing UC-security, we first using hash proof systems or smooth projective hash functions (SPHFs), we introduce a new cryptographic primitive called publicly computable SPHFs (PC-SPHFs) and construct the currently most efficient non-interactive UC-secure commitment. Finally, we develop a new technique for constructing UC-secure commitments schemes that enables one to generate CRS of NIZKs by using MPC in a UC-secure mannerhttps://www.ester.ee/record=b535926

LATKE: An identity-binding PAKE from lattice assumptions

In a recent work, Cremers, Naor, Paz, and Ronen (CRYPTO \u2722) point out the problem of catastrophic impersonation in balanced password authenticated key exchange protocols (PAKEs). Namely, in a balanced PAKE, when a single party is compromised, the attacker learns the password and can subsequently impersonate anyone to anyone using the same password. The authors of the work present two solutions to this issue: CHIP, an identity-binding PAKE (iPAKE), and CRISP, a strong identity-binding PAKE (siPAKE). These constructions prevent the impersonation attack by generating a secret key on setup that is inextricably tied to the party\u27s identity, and then deleting the password. Thus, upon compromise, all an attacker can immediately do is impersonate the victim. The strong variant goes further, preventing attackers from performing any precomputation before the compromise occurs. In this work we present LATKE, an iPAKE from lattice assumptions in the random oracle model. In order to achieve security and correctness, we must make changes to CHIP\u27s primitives, security models, and protocol structure

Studies in authentication

This thesis presents advances in several areas of authentication. First, we consider cryptographic accumulators, which are compact digital objects representing arbitrarily large sets. They support efficient proofs of membership (or, alternatively, of non-membership). We give the first definition of cryptographic accumulators in the UC framework, and construct two new accumulators: one uniquely suited for use in a revokable anonymous credential scheme, and one uniquely suited for use in a distributed system such as a blockchain-based PKI. Next, we consider multi-designated verifier signatures (MDVS). An MDVS is a special kind of signature that can only be verified by parties explicitly specified by the signer; more than that, even if those designated verifiers wanted to prove to an external party (e.g. an adversary) that a certain message was signed by the signer, they should be unable to do so. This is crucial in contexts where off-the-record communication is desirable; the sender may not want to be provably linked to a possibly sensitive message, but still want the intended recipients to be able to verify the authenticity of the message. Existing literature defines and builds limited notions of MDVS, where the off-the-record property only holds when it is conceivable that all verifiers collude. We strengthen this property to support any subset of colluding verifiers, and give two constructions of our stronger notion of MDVS: one from functional encryption, and one from standard primitives (but with a slightly larger signature size). Finally, we consider fuzzy password authenticated key exchange (Fuzzy PAKE). PAKEs are protocols which enable two parties holding the same password (that is, the same potentially low-entropy, non-uniform string) to agree on a (high-entropy, uniform) secret key in a way that resists man-in-the-middle attacks and offline dictionary attacks on the password. We define Fuzzy PAKE, a special kind of PAKE where the passwords used for authentication may contain some errors. We provide the first efficient and general solutions to this problem that enable, for example, key agreement based on commonly used biometrics such as iris scans

Strong Asymmetric PAKE based on Trapdoor CKEM

Password-Authenticated Key Exchange (PAKE) protocols allow two parties that share a password to establish a shared key in a way that is immune to oine attacks. Asymmetric PAKE (aPAKE) [21] adapts this notion to the common client-server setting, where the server stores a one-way hash of the password instead of the password itself, and server compromise allows the adversary to recover the password only via the (inevitable) offline dictionary attack. Most aPAKE protocols, however, allow an attacker to pre-compute a dictionary of hashed passwords, thus instantly learning the password on server compromise. Recently, Jarecki, Krawczyk, and Xu formalized a Universally Composable strong aPAKE (saPAKE) [24], which requires the password hash to be salted so that the dictionary attack can only start after the server compromise leaks the salt and the salted hash. The UC saPAKE protocol shown in [24], called OPAQUE, uses 3 protocol ows, 3-4 exponentiations per party, and relies on the One-More Diffie-Hellman assumption in ROM. We propose an alternative UC saPAKE construction based on a novel use of the encryption+SPHF paradigm for UC PAKE design [27, 20]. Compared to OPAQUE, our protocol uses only 2 flows, has comparable costs, avoids hashing onto a group, and relies on different assumptions, namely Decisional Diffie-Hellman (DDH), Strong Diffie-Hellman (SDH), and an assumption that the Boneh-Boyen function is a Salted Tight One-Way Function (STOWF). We formalize a UC model for STOWF and analyze the Boneh-Boyen function as UC STOWF in the generic group model and ROM. Our saPAKE protocol employs a new form of Conditional Key Encapsulation Mechanism (CKEM), a generalization of SPHF, which we call an implicit-statement CKEM. This strengthening of SPHF allows for a UC (sa)PAKE design where only the client commits to its password, and only the server performs an SPHF, compared to the standard UC PAKE design paradigm where the encrypt+SPHF subroutine is used symmetrically by both parties

Improved (Almost) Tightly-Secure Simulation-Sound QA-NIZK with Applications

We construct the first (almost) tightly-secure unbounded-simulation-sound quasi-adaptive non-interactive zero-knowledge arguments (USS-QA-NIZK) for linear-subspace languages with compact (number of group elements independent of the security parameter) common reference string (CRS) and compact proofs under standard assumptions in bilinear-pairings groups. Specifically, our construction has $O(\log Q)$ reduction to the SXDH, DLIN and matrix-DDH assumptions, where $Q$ is the number of simulated proofs given out. The USS-QA-NIZK primitive has many applications, including structure-preserving signatures (SPS), CCA2-secure publicly-verifiable public-key encryption (PKE), which in turn have applications to CCA-anonymous group signatures, blind signatures and unbounded simulation-sound Groth-Sahai NIZK proofs. We show that the almost tight security of our USS-QA-NIZK translates into constructions of all of the above applications with (almost) tight-security to standard assumptions such as SXDH and, more generally, \D_k-MDDH. Thus, we get the first publicly-verifiable (almost) tightly-secure multi-user/multi-challenge CCA2-secure PKE with practical efficiency under standard bilinear assumptions. Our (almost) tight SPS construction is also improved in the signature size over previously known constructions

Practical Witness Encryption for Algebraic Languages Or How to Encrypt Under Groth-Sahai Proofs

Witness encryption (WE) is a recent powerful encryption paradigm, which allows to encrypt a message using the description of a hard problem (a word in an NP-language) and someone who knows a solution to this problem (a witness) is able to efficiently decrypt the ciphertext. Recent work thereby focuses on constructing WE for NP complete languages (and thus NP). While this rich expressiveness allows flexibility w.r.t. applications, it makes existing instantiations impractical. Thus, it is interesting to study practical variants of WE schemes for subsets of NP that are still expressive enough for many cryptographic applications. We show that such WE schemes can be generically constructed from smooth projective hash functions (SPHFs). In terms of concrete instantiations of SPHFs (and thus WE), we target languages of statements proven in the popular Groth-Sahai (GS) non-interactive witness-indistinguishable/zero-knowledge proof framework. This allows us to provide a novel way to encrypt. In particular, encryption is with respect to a GS proof and efficient decryption can only be done by the respective prover. The so obtained constructions are entirely practical. To illustrate our techniques, we apply them in context of privacy-preserving exchange of information

Separating Symmetric and Asymmetric Password-Authenticated Key Exchange

Password-Authenticated Key Exchange (PAKE) is a method to establish cryptographic keys between two users sharing a low-entropy password. In its asymmetric version, one of the users acts as a server and only stores some function of the password, e.g., a hash. Upon server compromise, the adversary learns H(pw). Depending on the strength of the password, the attacker now has to invest more or less work to reconstruct pw from H(pw). Intuitively, asymmetric PAKE seems more challenging than symmetric PAKE since the latter is not supposed to protect the password upon compromise. In this paper, we provide three contributions: - Separating symmetric and asymmetric PAKE. We prove that a strong assumption like a programmable random oracle is necessary to achieve security of asymmetric PAKE in the Universal Composability (UC) framework. For symmetric PAKE, programmability is not required. Our results also rule out the existence of UC-secure asymmetric PAKE in the CRS model. - Revising the security definition. We identify and close some gaps in the UC security definition of 2-party asymmetric PAKE given by Gentry, MacKenzie and Ramzan (Crypto 2006). For this, we specify a natural corruption model for server compromise attacks. We further remove an undesirable weakness that lets parties wrongly believe in security of compromised session keys. We demonstrate usefulness by proving that the Omega-method proposed by Gentry et al. satisfies our new security notion for asymmetric PAKE. To our knowledge, this is the first formal security proof of the Omega-method in the literature. - Composable multi-party asymmetric PAKE. We showcase how our revisited security notion for 2-party asymmetric PAKE can be used to obtain asymmetric PAKE protocols in the multi-user setting and discuss important aspects for implementing such a protocol

Randomized Half-Ideal Cipher on Groups with applications to UC (a)PAKE

An Ideal Cipher (IC) is a cipher where each key defines a random permutation on the domain. Ideal Cipher on a group has many attractive applications, e.g., the Encrypted Key Exchange (EKE) protocol for Password Authenticated Key Exchange (PAKE) [10], or asymmetric PAKE (aPAKE) [40, 36]. However, known constructions for IC on a group domain all have drawbacks, including key leakage from timing information [15], requiring 4 hash-onto-group operations if IC is an 8-round Feistel [27], and limiting the domain to half the group [12] or using variable-time encoding [56, 48] if IC is implemented via (quasi-) bijections from groups to bitstrings [40]. We propose an IC relaxation called a (Randomized) Half-Ideal Cipher (HIC), and we show that HIC on a group can be realized by a modified 2-round Feistel (m2F), at a cost of 1 hash-onto-group operation, which beats existing IC constructions in versatility and computational cost. HIC weakens IC properties by letting part of the ciphertext be non-random, but we exemplify that it can be used as a drop-in replacement for IC by showing that EKE [10] and aPAKE of [40] realize respectively UC PAKE and UC aPAKE even if they use HIC instead of IC. The m2F construction can also serve as IC domain extension, because m2F constructs HIC on domain D from an RO-indiferrentiable hash onto D and an IC on 2κ-bit strings, for κ a security parameter. One application of such extender is a modular lattice-based UC PAKE using EKE instantiated with HIC and anonymous lattice-based KEM