Reverse Firewalls for Oblivious Transfer Extension and Applications to Zero-Knowledge

In the setting of subversion, an adversary tampers with the machines of the honest parties thus leaking the honest parties\u27 secrets through the protocol transcript. The work of Mironov and Stephens-Davidowitz (EUROCRYPT’15) introduced the idea of reverse firewalls (RF) to protect against tampering of honest parties\u27 machines. All known constructions in the RF framework rely on the malleability of the underlying operations in order for the RF to rerandomize/sanitize the transcript. RFs are thus limited to protocols that offer some structure, and hence based on public-key operations. In this work, we initiate the study of $efficient$ Multiparty Computation (MPC) protocols in the presence of tampering. In this regard, - We construct the $first$ Oblivious Transfer (OT) extension protocol in the RF setting. We obtain $poly(\kappa)$ maliciously-secure OTs using $O(\kappa)$ public key operations and $O(1)$ inexpensive symmetric key operations, where $\kappa$ is the security parameter. - We construct the $first$ Zero-knowledge protocol in the RF setting where each multiplication gate can be proven using $O(1)$ symmetric key operations. We achieve this using our OT extension protocol and by extending the ZK protocol of Quicksilver (Yang, Sarkar, Weng and Wang, CCS\u2721) to the RF setting. - Along the way, we introduce new ideas for malleable interactive proofs that could be of independent interest. We define a notion of $full$ $malleability$ for Sigma protocols that unlike prior notions allow modifying the instance as well, in addition to the transcript. We construct new protocols that satisfy this notion, construct RFs for such protocols and use them in constructing our OT extension. The key idea of our work is to demonstrate that correlated randomness may be obtained in an RF-friendly way $without$ having to rerandomize the entire transcript. This enables us to avoid expensive public-key operations that grow with the circuit-size

A Map of Witness Maps: New Definitions and Connections

A \emph{witness map} deterministically maps a witness $w$ of some NP statement $x$ into computationally sound proof that $x$ is true, with respect to a public common reference string (CRS). In other words, it is a deterministic, non-interactive, computationally sound proof system in the CRS model. A \emph{unique witness map} (UWM) ensures that for any fixed statement $x$, the witness map should output the same \emph{unique} proof for $x$, no matter what witness $w$ it is applied to. More generally a \emph{compact witness map} (CWM) can only output one of at most $2^\alpha$ proofs for any given statement $x$, where $\alpha$ is some compactness parameter. Such compact/unique witness maps were proposed recently by Chakraborty, Prabhakaran and Wichs (PKC \u2720) as a tool for building tamper-resilient signatures, who showed how to construct UWMs from indistinguishability obfuscation (iO). In this work, we study CWMs and UWMs as primitives of independent interest and present a number of interesting connections to various notions in cryptography. \begin{itemize} \item First, we show that UWMs lie somewhere between witness PRFs (Zhandry; TCC \u2716) and iO -- they imply the former and are implied by the latter. In particular, we show that a relaxation of UWMs to the ``designated verifier (dv-UWM)\u27\u27 setting is \emph{equivalent} to witness PRFs. Moreover, we consider two flavors of such dv-UWMs, which correspond to two flavors of witness PRFs previously considered in the literature, and show that they are all in fact equivalent to each other in terms of feasibility. \item Next, we consider CWMs that are extremely compact, with $\alpha = O(\log \kappa)$, where $\kappa$ is the security parameter. We show that such CWMs imply \emph{pseudo-UWMs} where the witness map is allowed to be \emph{pseudo-deterministic} -- i.e., for every true statement $x$, there is a unique proof such that, on any witness $w$, the witness map outputs this proof with $1-1/p(\lambda)$ probability, for a polynomial $p$ that we can set arbitrarily large. \item Lastly, we consider CWMs that are mildly compact, with $\alpha = p(\lambda)$ for some a-priori fixed polynomial $p$, independent of the length of the statement $x$ or witness $w$. Such CWMs are implied by succinct non-interactive arguments (SNARGs). We show that such CWMs imply NIZKs, and therefore lie somewhere between NIZKs and SNARGs. \end{itemize

Witness Maps and Applications

We introduce the notion of Witness Maps as a cryptographic notion of a proof system. A Unique Witness Map (UWM) deterministically maps all witnesses for an $\mathbf{NP}$ statement to a single representative witness, resulting in a computationally sound, deterministic-prover, non-interactive witness independent proof system. A relaxation of UWM, called Compact Witness Map (CWM), maps all the witnesses to a small number of witnesses, resulting in a ``lossy\u27\u27 deterministic-prover, non-interactive proof-system. We also define a Dual Mode Witness Map (DMWM) which adds an ``extractable\u27\u27 mode to a CWM. \medskip Our main construction is a DMWM for all $\mathbf{NP}$ relations, assuming sub-exponentially secure indistinguishability obfuscation ($i\mathcal{O}$), along with standard cryptographic assumptions. The DMWM construction relies on a CWM and a new primitive called Cumulative All-Lossy-But-One Trapdoor Functions (C-ALBO-TDF), both of which are in turn instantiated based on $i\mathcal{O}$ and other primitives. Our instantiation of a CWM is in fact a UWM; in turn, we show that a UWM implies Witness Encryption. Along the way to constructing UWM and C-ALBO-TDF, we also construct, from standard assumptions, Puncturable Digital Signatures and a new primitive called Cumulative Lossy Trapdoor Functions (C-LTDF). The former improves up on a construction of Bellare et al. (Eurocrypt 2016), who relied on sub-exponentially secure $i\mathcal{O}$ and sub-exponentially secure OWF. \medskip As an application of our constructions, we show how to use a DMWM to construct the first leakage and tamper-resilient signatures with a deterministic signer, thereby solving a decade old open problem posed by Katz and Vaikunthanathan (Asiacrypt 2009), by Boyle, Segev and Wichs (Eurocrypt 2011), as well as by Faonio and Venturi (Asiacrypt 2016). Our construction achieves the optimal leakage rate of $1 - o(1)$

Efficient Compilers for After-the-Fact Leakage: from CPA to CCA-2 secure PKE to AKE

The goal of leakage-resilient cryptography is to construct cryptographic algorithms that are secure even if the adversary obtains side-channel information from the real world implementation of these algorithms. Most of the prior works on leakage-resilient cryptography consider leakage models where the adversary has access to the leakage oracle before the challenge-ciphertext is generated (before-the-fact leakage). In this model, there are generic compilers that transform any leakage-resilient CPA-secure public key encryption (PKE) scheme to its CCA-2 variant using Naor-Yung type of transformations. In this work, we give an efficient generic compiler for transforming a leakage-resilient CPA-secure PKE to leakage-resilient CCA-2 secure PKE in presence of after-the-fact split-state (bounded) memory leakage model, where the adversary has access to the leakage oracle even after the challenge phase. The salient feature of our transformation is that the leakage rate (defined as the ratio of the amount of leakage to the size of secret key) of the transformed after-the-fact CCA-2 secure PKE is same as the leakage rate of the underlying after-the-fact CPA-secure PKE, which is $1-o(1)$. We then present another generic compiler for transforming an after-the-fact leakage-resilient CCA-2 secure PKE to a leakage-resilient authenticated key exchange (AKE) protocol in the bounded after-the-fact leakage-resilient eCK (BAFL-eCK) model proposed by Alawatugoda et al. (ASIACCS\u2714). To the best of our knowledge, this gives the first compiler that transform any leakage-resilient CCA-2 secure PKE to an AKE protocol in the leakage variant of the eCK model

New Approach to Practical Leakage-Resilient Public-Key Cryptography

We present a new approach to construct several leakage-resilient cryptographic primitives, including leakage-resilient public-key encryption (PKE) schemes, authenticated key exchange (AKE) protocols and low-latency key exchange (LLKE) protocols. To this end, we introduce a new primitive called leakage-resilient non-interactive key exchange (LR-NIKE) protocol. We introduce a generic security model for LR-NIKE protocols, which can be instantiated in both the bounded and continuous-memory leakage ((B/C)-ML) settings. We then show a secure construction of LR-NIKE protocol in the bounded- memory leakage (BML) setting, that achieves an optimal leakage rate, i.e., 1-o(1). Finally, we show how to construct the aforementioned leakage-resilient primitives from such a LR-NIKE protocol as summarized below. All the primitives also achieve the same (optimal) leakage rate as the underlying LR-NIKE protocol. We show how to construct a leakage-resilient IND-CCA-2-secure PKE scheme in the BML model generically from a LR-NIKE protocol. Our construction differs from the state-of-the-art constructions of leakage-resilient IND-CCA-2-secure PKE schemes, which use hash proof techniques to achieve leakage-resilience. Moreover, our transformation preserves the leakage-rate of the underlying LR- NIKE and admits more efficient construction than previous such PKE constructions. We introduce a new leakage model for AKE protocols, in the BML setting. We show how to construct a leakage-resilient AKE protocol starting from LR-NIKE protocol. We introduce the first-ever leakage model for LLKE protocols in the BML setting, and the first construction of such a leakage-resilient LLKE from LR-NIKE protocol

Reverse Firewalls for Adaptively Secure MPC without Setup

We study Multi-party computation (MPC) in the setting of subversion, where the adversary tampers with the machines of honest parties. Our goal is to construct actively secure MPC protocols where parties are corrupted adaptively by an adversary (as in the standard adaptive security setting), and in addition, honest parties\u27 machines are compromised. The idea of reverse firewalls (RF) was introduced at EUROCRYPT\u2715 by Mironov and Stephens-Davidowitz as an approach to protecting protocols against corruption of honest parties\u27 devices. Intuitively, an RF for a party $\mathcal{P}$ is an external entity that sits between $\mathcal{P}$ and the outside world and whose scope is to sanitize $\mathcal{P}$’s incoming and outgoing messages in the face of subversion of their computer. Mironov and Stephens-Davidowitz constructed a protocol for passively-secure two-party computation. At CRYPTO\u2720, Chakraborty, Dziembowski and Nielsen constructed a protocol for secure computation with firewalls that improved on this result, both by extending it to multi-party computation protocol, and considering active security in the presence of static corruptions. In this paper, we initiate the study of RF for MPC in the adaptive setting. We put forward a definition for adaptively secure MPC in the reverse firewall setting, explore relationships among the security notions, and then construct reverse firewalls for MPC in this stronger setting of adaptive security. We also resolve the open question of Chakraborty, Dziembowski and Nielsen by removing the need for a trusted setup in constructing RF for MPC. Towards this end, we construct reverse firewalls for adaptively secure augmented coin tossing and adaptively secure zero-knowledge protocols and obtain a constant round adaptively secure MPC protocol in the reverse firewall setting without setup. Along the way, we propose a new multi-party adaptively secure coin tossing protocol in the plain model, that is of independent interest

A Pairing-Free, One Round Identity Based Authenticated Key Exchange Protocol Secure Against Memory-Scrapers

Security of a key exchange protocol is formally established through an abstract game between a challenger and an adversary. In this game the adversary can get various information which are modeled by giving the adversary access to appropriate oracle queries. Empowered with all these information, the adversary will try to break the protocol. This is modeled by a test query which asks the adversary to distinguish between a session key of a fresh session from a random session key; properly guessing which correctly leads the adversary to win the game. In this traditional model of security the adversary sees nothing apart from the input/ output relationship of the algorithms. However, in recent past an adversary could obtain several additional information beyond what he gets to learn in these black box models of computation, thanks to the availability of powerful malwares. This data exfiltration due to the attacks of Memory Scraper/Ram-Scraper-type malwares is an emerging threat. In order to realistically capture these advanced classes of threats posed by such malwares we propose a new security model for identity-based authenticated key exchange (ID-AKE) which we call the Identity based Strong Extended Canetti Krawzyck (ID-seCK) model. Our security model captures leakages of intermediate values by appropriate oracle queries given to the adversary. Following this, we propose a round optimal (i.e., single round) ID-AKE protocol for two-party settings. Our design assumes a hybrid system equipped with a bare minimal Trusted Platform Module (TPM) that can only perform group exponentiations. One of the major advantages of our construction is that it does not involve any pairing operations, works in prime order group and have a tight security reduction to the Gap Diffie Hellman (GDH) problem under our new ID-seCK model. Our scheme also has the capability to handle active adversaries while most of the previous ID-AKE protocols are secure only against passive adversaries. The security of our protocol is proved in the Random Oracle (RO) model

Leakage-Resilient Tweakable Encryption from One-Way Functions

In this paper, we initiate the study of leakage-resilient tweakable encryption schemes in the relative key-leakage model, where the adversary can obtain (arbitrary) partial information about the secret key. We also focus on the minimal and generic assumptions needed to construct such a primitive. Interestingly, we show provably secure constructions of leakage-resilient (LR) tweakable encryption based on the sole assumption that one-way functions (OWF) exist via some interesting intermediate generic connections. A central tool used in our construction of LR-tweakable encryption is the notion of Symmetric-key tweakable weak hash proof system, which we introduce. This can be seen as a generalization of the Symmetric-key weak hash proof framework of Hazay et. al (Eurocrypt\u2713). Along the way, we also introduce a new primitive called tweakable weak pseudo-random functions (t-wPRF) and show how to generically construct it from weak-PRF. We then construct LR-version of t-wPRF and use it to construct LR-tweakable encryption

Deniable Authentication when Signing Keys Leak

Deniable Authentication is a highly desirable property for secure messaging protocols: it allows a sender Alice to authentically transmit messages to a designated receiver Bob in such a way that only Bob gets convinced that Alice indeed sent these messages. In particular, it guarantees that even if Bob tries to convince a (non-designated) party Judy that Alice sent some message, and even if Bob gives Judy his own secret key, Judy will not be convinced: as far as Judy knows, Bob could be making it all up! In this paper we study Deniable Authentication in the setting where Judy can additionally obtain Alice\u27s secret key. Informally, we want that knowledge of Alice\u27s secret key does not help Judy in learning whether Alice sent any messages, even if Bob does not have Alice\u27s secret key and even if Bob cooperates with Judy by giving her his own secret key. This stronger flavor of Deniable Authentication was not considered before and is particularly relevant for Off-The-Record Group Messaging as it gives users stronger deniability guarantees. Our main contribution is a scalable ``MDRS-PKE\u27\u27 (Multi-Designated Receiver Signed Public Key Encryption) scheme---a technical formalization of Deniable Authentication that is particularly useful for secure messaging for its confidentiality guarantees---that provides this stronger deniability guarantee. At its core lie new MDVS (Multi-Designated Verifier Signature) and PKEBC (Public Key Encryption for Broadcast) scheme constructions: our MDVS is not only secure with respect to the new deniability notions, but it is also the first to be tightly secure under standard assumptions; our PKEBC---which is also of independent interest---is the first with ciphertext sizes and encryption and decryption times that grow only linearly in the number of receivers. This is a significant improvement upon the construction given by Maurer et al. (EUROCRYPT \u2722), where ciphertext sizes and encryption and decryption times are quadratic in the number of receivers

A Constant Time, Single Round Attribute-Based Authenticated Key Exchange in Random Oracle Model

In this paper, we present a single round two-party {\em attribute-based authenticated key exchange} (ABAKE) protocol in the framework of ciphertext-policy attribute-based systems. Since pairing is a costly operation and the composite order groups must be very large to ensure security, we focus on pairing free protocols in prime order groups. The proposed protocol is pairing free, working in prime order group and having tight reduction to Strong Diffie Hellman (SDH) problem under the attribute-based Canetti Krawzyck (CK) model which is a natural extension of the CK model (which is for the PKI-based authenticated key exchange) for the attribute-based setting. The security proof is given in the random oracle model. Our ABAKE protocol does not depend on any underlying attribute-based encryption or signature schemes unlike the previous solutions for ABAKE. Ours is the \textit{first} scheme that removes this restriction. Thus, the first major advantage is that smaller key sizes are sufficient to achieve comparable security. Another notable feature of our construction is that it involves only constant number of exponentiations per party unlike the state-of-the-art ABAKE protocols where the number of exponentiations performed by each party depends on the size of the linear secret sharing matrix. We achieve this by doing appropriate precomputation of the secret share generation. Ours is the \textit{first} construction that achieves this property. Our scheme has several other advantages. The major one being the capability to handle active adversaries. Most of the previous ABAKE protocols can offer security only under passive adversaries. Our protocol recognizes the corruption by an active adversary and aborts the process. In addition to this property, our scheme satisfies other security properties that are not covered by CK model such as forward secrecy, key compromise impersonation attacks and ephemeral key compromise impersonation attacks