EasyUC: using EasyCrypt to mechanize proofs of universally composable security

We present a methodology for using the EasyCrypt proof assistant (originally designed for mechanizing the generation of proofs of game-based security of cryptographic schemes and protocols) to mechanize proofs of security of cryptographic protocols within the universally composable (UC) security framework. This allows, for the first time, the mechanization and formal verification of the entire sequence of steps needed for proving simulation-based security in a modular way: Specifying a protocol and the desired ideal functionality; Constructing a simulator and demonstrating its validity, via reduction to hard computational problems; Invoking the universal composition operation and demonstrating that it indeed preserves security. We demonstrate our methodology on a simple example: stating and proving the security of secure message communication via a one-time pad, where the key comes from a Diffie-Hellman key-exchange, assuming ideally authenticated communication. We first put together EasyCrypt-verified proofs that: (a) the Diffie-Hellman protocol UC-realizes an ideal key-exchange functionality, assuming hardness of the Decisional Diffie-Hellman problem, and (b) one-time-pad encryption, with a key obtained using ideal key-exchange, UC-realizes an ideal secure-communication functionality. We then mechanically combine the two proofs into an EasyCrypt-verified proof that the composed protocol realizes the same ideal secure-communication functionality. Although formulating a methodology that is both sound and workable has proven to be a complex task, we are hopeful that it will prove to be the basis for mechanized UC security analyses for significantly more complex protocols and tasks.Accepted manuscrip

A Framework for Efficient Adaptively Secure Composable Oblivious Transfer in the ROM

Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct a round-optimal (2 rounds) universally composable (UC) protocol for oblivious transfer secure against active adaptive adversaries from any OW-CPA secure public-key encryption scheme with certain properties in the random oracle model (ROM). In terms of computation, our protocol only requires the generation of a public/secret-key pair, two encryption operations and one decryption operation, apart from a few calls to the random oracle. In~terms of communication, our protocol only requires the transfer of one public-key, two ciphertexts, and three binary strings of roughly the same size as the message. Next, we show how to instantiate our construction under the low noise LPN, McEliece, QC-MDPC, LWE, and CDH assumptions. Our instantiations based on the low noise LPN, McEliece, and QC-MDPC assumptions are the first UC-secure OT protocols based on coding assumptions to achieve: 1) adaptive security, 2) optimal round complexity, 3) low communication and computational complexities. Previous results in this setting only achieved static security and used costly cut-and-choose techniques.Our instantiation based on CDH achieves adaptive security at the small cost of communicating only two more group elements as compared to the gap-DH based Simplest OT protocol of Chou and Orlandi (Latincrypt 15), which only achieves static security in the ROM

Structure-Preserving Smooth Projective Hashing

International audienceSmooth projective hashing has proven to be an extremely useful primitive, in particular when used in conjunction with commitments to provide implicit decommitment. This has lead to applications proven secure in the UC framework, even in presence of an adversary which can do adaptive corruptions, like for example Password Authenticated Key Exchange (PAKE), and 1-out-of-m Oblivious Transfer (OT). However such solutions still lack in efficiency, since they heavily scale on the underlying message length. Structure-preserving cryptography aims at providing elegant and efficient schemes based on classical assumptions and standard group operations on group elements. Recent trend focuses on constructions of structure- preserving signatures, which require message, signature and verification keys to lie in the base group, while the verification equations only consist of pairing-product equations. Classical constructions of Smooth Projective Hash Function suffer from the same limitation as classical signatures: at least one part of the computation (messages for signature, witnesses for SPHF) is a scalar. In this work, we introduce and instantiate the concept of Structure- Preserving Smooth Projective Hash Function, and give as applications more efficient instantiations for one-round PAKE and three-round OT, and information retrieval thanks to Anonymous Credentials, all UC- secure against adaptive adversaries

Universally composable end-to-end secure messaging

CNS-1718135 - National Science Foundation; CNS-1801564 - National Science Foundation; CNS-1931714 - National Science Foundation; CNS-1915763 - National Science Foundation; HR00112020021 - Department of Defense/DARPA; 000000000000000000000000000000000000000000000000000000037211 - SRI Internationalhttps://eprint.iacr.org/2022/376.pdfAccepted manuscrip

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