Input-shrinking functions: theory and application

In this thesis, we contribute to the emerging field of the Leakage-Resilient Cryptography by studying the problem of secure data storage on hardware that may leak information, introducing a new primitive, a leakage-resilient storage, and showing two different constructions of such storage scheme provably secure against a class of leakage functions that can depend only on some restricted part of the memory and against a class of computationally weak leakage functions, e.g. functions computable by small circuits, respectively. Our results come with instantiations and analysis of concrete parameters. Furthermore, as second contribution, we present our implementation in C programming language, using the cryptographic library of the OpenSSL project, of a two-party Authenticated Key Exchange (AKE) protocol, which allows a client and a server, who share a huge secret file, to securely compute a shared key, providing client-to-server authentication, also in the presence of active attackers. Following the work of Cash et al. (TCC 2007), we based our construction on a Weak Key Exchange (WKE) protocol, developed in the BRM, and a Password-based Authenticated Key Exchange (PAKE) protocol secure in the Universally Composable (UC) framework. The WKE protocol showed by Cash et al. uses an explicit construction of averaging sampler, which uses less random bits than the random choice but does not seem to be efficiently implementable in practice. In this thesis, we propose a WKE protocol similar but simpler than that one of Cash et al.: our protocol uses more randomness than the Cash et al.'s one, as it simply uses random choice instead of averaging sampler, but we are able to show an efficient implementation of it. Moreover, we formally adapt the security analysis of the WKE protocol of Cash et al. to our WKE protocol. To complete our AKE protocol, we implement the PAKE protocol showed secure in the UC framework by Abdalla et al. (CT-RSA 2008), which is more efficient than the Canetti et al.'s UC-PAKE protocol (EuroCrypt 2005) used in Cash et al.'s work. In our implementation of the WKE protocol, to achieve small constant communication complexity and amount of randomness, we rely on the Random Oracle (RO) model. However, we would like to note that in our implementation of the AKE protocol we need also a UC-PAKE protocol which already relies on RO, as it is impossible to achieve UC-PAKE in the standard model. In our work we focus not only on the theoretical aspects of the area, providing formal models and proofs, but also on the practical ones, analyzing instantiations, concrete parameters and implementation of the proposed solutions, to contribute to bridge the gap between theory and practice in this field

Universally Composable Two-Server PAKE

Two-Server Password Authenticated Key Exchange (2PAKE) protocols apply secret shar-ing techniques to achieve protection against server-compromise attacks. 2PAKE protocols eliminate the need for password hashing and remain secure as long as one of the servers remains honest. This concept has also been explored in connection with two-server password authenticated secret sharing (2PASS) protocols for which game-based and universally composable versions have been proposed. In contrast, universally composable PAKE protocols exist currently only in the single-server scenario and all proposed 2PAKE protocols use game-based security definitions. In this paper we propose the first construction of an universally composable 2PAKE protocol, alongside with its ideal functionality. The protocol is proven UC-secure in the standard model, assuming a common reference string which is a common assumption to many UC-secure PAKE and PASS protocols. The proposed protocol remains secure for arbitrary password distributions. As one of the building blocks we define and construct a new cryptographic primitive, called Trapdoor Distributed Smooth Projective Hash Function (TD-SPHF), which could be of independent interest

Auditable Asymmetric Password Authenticated Public Key Establishment

Non-repudiation of messages generated by users is a desirable feature in a number of applications ranging from online banking to IoT scenarios. However, it requires certified public keys and usually results in poor usability as a user must carry around his certificate (e.g., in a smart-card) or must install it in all of his devices. A user-friendly alternative, adopted by several companies and national administrations, is to have a ``cloud-based\u27\u27 PKI. In a nutshell, each user has a PKI certificate stored at a server in the cloud; users authenticate to the server---via passwords or one-time codes---and ask it to sign messages on their behalf. As such, there is no way for the server to prove to a third party that a signature on a given message was authorized by a user. As the server holds the user\u27s certified key, it might as well have signed arbitrary messages in an attempt to impersonate that user. In other words, a user could deny having signed a message, by claiming that the signature was produced by the server without his consent. The same holds in case the secret key is derived deterministically from the user\u27s password, for the server, by knowing the password, may still frame the user. In this paper we provide a password-only solution to non-repudiation of user messages by introducing Auditable Asymmetric Password Authenticated Public Key Establishment (A2PAKE). This is a PAKE-like protocol that generates an asymmetric key-pair where the public key is output to every participant, but the secret key is private output to just one of the parties (e.g., the user). Further, the protocol can be audited, i.e., given the public key output by a protocol run with a user, the server can prove to a third party that the corresponding secret key is held by that specific user. Thus, if the user signs messages with that secret key, then signatures are non-repudiable. We provide a universally composable definition of A2PAKE and an instantiation based on a distributed oblivious pseudo-random function. We also develop a prototype implementation of our instantiation and use it to evaluate its performance in realistic settings

Two-Server Password-Authenticated Secret Sharing UC-Secure Against Transient Corruptions

Protecting user data entails providing authenticated users access to their data. The most prevalent and probably also the most feasible approach to the latter is by username and password. With password breaches through server compromise now reaching billions of affected passwords, distributing the password files and user data over multiple servers is not just a good idea, it is a dearly needed solution to a topical problem. Threshold password-authenticated secret sharing (TPASS) protocols enable users to share secret data among a set of servers so that they can later recover that data using a single password. No coalition of servers up to a certain threshold can learn anything about the data or perform an offline dictionary attack on the password. Several TPASS protocols have appeared in the literature and one is even available commercially. Although designed to tolerate corrupted servers, unfortunately none of these protocols provide details let alone security proofs about the steps that need to be taken when a compromise actually occurs and how to proceed. Indeed, they consider static corruptions only which for instance does not model real world attacks by hackers. We provide the first TPASS protocol that is provably secure against adaptive server corruptions. Moreover, our protocol contains an efficient recovery procedure allowing one to re-initialize servers to recover from corruption. We prove our protocol secure in the universal composability model where servers can be corrupted adaptively at any time; the users\u27 passwords and secrets remain safe as long as both servers are not corrupted at the same time. Our protocol does not require random oracles but does assume that servers have certified public keys

TOPPSS: Cost-minimal Password-Protected Secret Sharing based on Threshold OPRF

We present TOPPSS, the most efficient Password-Protected Secret Sharing (PPSS) scheme to date. A (t; n)-threshold PPSS, introduced by Bagherzandi et al, allows a user to share a secret among n servers so that the secret can later be reconstructed by the user from any subset of t+1 servers with the sole knowledge of a password. It is guaranteed that any coalition of up to t corrupt servers learns nothing about the secret (or the password). In addition to providing strong protection to secrets stored online, PPSS schemes give rise to efficient Threshold PAKE (T-PAKE) protocols that armor single-server password authentication against the inherent vulnerability to offline dictionary attacks in case of server compromise. TOPPSS is password-only, i.e. it does not rely on public keys in reconstruction, and enjoys remarkable efficiency: A single communication round, a single exponentiation per server and just two exponentiations per client regardless of the number of servers. TOPPSS satises threshold security under the (Gap) One-More Diffie-Hellman (OMDH) assumption in the random-oracle model as in several prior efficient realizations of PPSS/TPAKE. Moreover, we show that TOPPSS realizes the Universally Composable PPSS notion of Jarecki et al under a generalization of OMDH, the Threshold One-More Diffie-Hellman (T-OMDH) assumption. We show that the T-OMDH and OMDH assumptions are both hard in the generic group model. The key technical tool we introduce is a universally composable Threshold Oblivious PRF which is of independent interest and applicability

Highly-Efficient and Composable Password-Protected Secret Sharing (Or: How to Protect Your Bitcoin Wallet Online)

PPSS is a central primitive introduced by Bagherzandi et al [BJSL10] which allows a user to store a secret among n servers such that the user can later reconstruct the secret with the sole possession of a single password by contacting t+1 servers for t<n. At the same time, an attacker breaking into t of these servers - and controlling all communication channels - learns nothing about the secret (or the password). Thus, PPSS schemes are ideal for on-line storing of valuable secrets when retrieval solely relies on a memorizable password. We show the most efficient Password-Protected Secret Sharing (PPSS) to date (and its implied Threshold-PAKE scheme), which is optimal in round communication as in Jarecki et al [JKK14] but which improves computation and communication complexity over that scheme requiring a single per-server exponentiation for the client and a single exponentiation for the server. As with the schemes from [JKK14] and Camenisch et al [CLLN14], we do not require secure channels or PKI other than in the initialization stage. We prove the security of our PPSS scheme in the Universally Composable (UC) model. For this we present a UC definition of PPSS that relaxes the UC formalism of [CLLN14] in a way that enables more efficient PPSS schemes (by dispensing with the need to extract the user\u27s password in the simulation) and present a UC-based definition of Oblivious PRF (OPRF) that is more general than the (Verifiable) OPRF definition from [JKK14] and is also crucial for enabling our performance optimization

SoK: Oblivious Pseudorandom Functions

In recent years, oblivious pseudorandom functions (OPRFs) have become a ubiquitous primitive used in cryptographic protocols and privacy-preserving technologies. The growing interest in OPRFs, both theoretical and applied, has produced a vast number of different constructions and functionality variations. In this paper, we provide a systematic overview of how to build and use OPRFs. We first categorize existing OPRFs into essentially four families based on their underlying PRF (Naor-Reingold, Dodis-Yampolskiy, Hashed Diffie-Hellman, and generic constructions). This categorization allows us to give a unified presentation of all oblivious evaluation methods in the literature, and to understand which properties OPRFs can (or cannot) have. We further demonstrate the theoretical and practical power of OPRFs by visualizing them in the landscape of cryptographic primitives, and by providing a comprehensive overview of how OPRFs are leveraged for improving the privacy of internet users. Our work systematizes 15 years of research on OPRFs and provides inspiration for new OPRF constructions and applications thereof