Reproducible Circularly-Secure Bit Encryption: Applications and Realizations

We give generic constructions of several fundamental cryptographic primitives based on a new encryption primitive that combines circular security for bit encryption with the so-called reproducibility property (Bellare et al. PKC 2003). At the heart of our constructions is a novel technique which gives a way of de-randomizing reproducible public-key bit-encryption schemes and also a way of reducing one-wayness conditions of a constructed trapdoor-function family (TDF) to circular security of the base scheme. The main primitives that we build from our encryption primitive include k-wise one- way TDFs (Rosen and Segev TCC 2009), CCA2-secure encryption and deterministic encryption. Our results demonstrate a new set of applications of circularly-secure encryption beyond fully-homomorphic encryption and symbolic soundness. Finally, we show the plausibility of our assumptions by showing that the DDH-based circularly-secure scheme of Boneh et al. (Crypto 2008) and the subgroup indistinguishability based scheme of Brakerski and Goldwasser (Crypto 2010) are both reproducible

On Generic Constructions of Circularly-Secure, Leakage-Resilient Public-Key Encryption Schemes

Abstract. We propose generic constructions of public-key encryption schemes, satisfying key- dependent message (KDM) security for projections and different forms of key-leakage resilience, from CPA-secure private key encryption schemes with two main abstract properties: (1) additive homomorphism with respect to both messages and randomness, and (2) reproducibility, providing a means for reusing encryption randomness across independent secret keys. More precisely, our construction transforms a private-key scheme with the stated properties (and one more mild condition) into a public-key one, providing: - n-KDM-projection security, an extension of circular security, where the adversary may also ask for encryptions of negated secret key bits; – a (1-o(1)) resilience rate in the bounded-memory leakage model of Akavia et al. (TCC 2009); and – Auxiliary-input security against subexponentially-hard functions. We introduce homomorphic weak pseudorandom functions, a homomorphic version of the weak PRFs proposed by Naor and Reingold (FOCS ’95) and use them to realize our base encryption scheme. We obtain homomorphic weak PRFs under assumptions including subgroup indistinguishability (implied, in particular, by QR and DCR) and homomorphic hash-proof systems (HHPS). As corollaries of our results, we obtain (1) a projection-secure encryption scheme (as well as a scheme with a (1-o(1)) resilience rate) based solely on the HHPS assumption, and (2) a unifying approach explaining the results of Boneh et al (CRYPTO ’08) and Brakerski and Goldwasser (CRYPTO ’10). Finally, by observing that Applebaum’s KDM amplification method (EUROCRYPT ’11) preserves both types of leakage resilience, we obtain schemes providing at the same time high leakage resilience and KDM security against any fixed polynomial-sized circuit family

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

CPA-to-CCA Transformation for KDM Security

We show that chosen plaintext attacks (CPA) security is equivalent to chosen ciphertext attacks (CCA) security for key-dependent message (KDM) security. Concretely, we show how to construct a public-key encryption (PKE) scheme that is KDM-CCA secure with respect to all functions computable by circuits of a-priori bounded size, based only on a PKE scheme that is KDM-CPA secure with respect to projection functions. Our construction works for KDM security in the single user setting. Our main result is achieved by combining the following two steps. First, we observe that by combining the results and techniques from the recent works by Lombardi et al. (CRYPTO 2019), and by Kitagawa et al. (CRYPTO 2019), we can construct a reusable designated-verifier non-interactive zero-knowledge (DV-NIZK) argument system based on an IND-CPA secure PKE scheme and a secret-key encryption (SKE) scheme satisfying one-time KDM security with respect to projection functions. This observation leads to the first reusable DV-NIZK argument system under the learning-parity-with-noise (LPN) assumption. Then, as the second and main technical step, we show a generic construction of a KDM-CCA secure PKE scheme using an IND-CPA secure PKE scheme, a reusable DV-NIZK argument system, and an SKE scheme satisfying one-time KDM security with respect to projection functions. Since the classical Naor-Yung paradigm (STOC 1990) with a DV-NIZK argument system does not work for proving KDM security, we propose a new construction methodology to achieve this generic construction. Moreover, we show how to extend our generic construction and achieve KDM-CCA security in the multi-user setting, by additionally requiring the underlying SKE scheme in our generic construction to satisfy a weak form of KDM security against related-key attacks (RKA-KDM security) instead of one-time KDM security. From this extension, we obtain the first KDM-CCA secure PKE schemes in the multi-user setting under the CDH or LPN assumption

Trading Plaintext-Awareness for Simulatability to Achieve Chosen Ciphertext Security

In PKC 2014, Dachman-Soled showed a construction of a chosen ciphertext (CCA) secure public key encryption (PKE) scheme based on a PKE scheme which simultaneously satisfies a security property called weak simulatability and (standard model) plaintext awareness (sPA1) in the presence of multiple public keys. It is not well-known if plaintext awareness for the multiple keys setting is equivalent to the more familiar notion of that in the single key setting, and it is typically considered that plaintext awareness is a strong security assumption (because to achieve it we have to rely on a knowledge -type assumption). In Dachman-Soled\u27s construction, the underlying PKE scheme needs to be plaintext aware in the presence of $2k+2$ public keys. The main result in this work is to show that the strength of plaintext awareness required in the Dachman-Soled construction can be somehow traded with the strength of a simulatability property of other building blocks. Furthermore, we also show that we can separate the assumption that a single PKE scheme needs to be both weakly simulatable and plaintext aware in her construction. Specifically, in this paper we show two new constructions of CCA secure key encapsulation mechanisms (KEMs): Our first scheme is based on a KEM which is chosen plaintext (CPA) secure and plaintext aware only under the $2$ keys setting, and a PKE scheme satisfying a slightly stronger simulatability than weak simulatability, called \emph{trapdoor simulatability} (introduced by Choi et al. ASIACRYPT 2009). Our second scheme is based on a KEM which is $1$-bounded CCA secure (Cramer et al. ASIACRYPT 2007) and plaintext aware only in the \emph{single} key setting, and a trapdoor simulatable PKE scheme. Our results add new recipes for constructing CCA secure PKE/KEM from general assumptions (that are incomparable to those used by Dachman-Soled), and in particular show interesting trade-offs among building blocks with those used in Dachman-Soled\u27s construction

Classical secure delegation of quantum computations

The rapid evolution of quantum technologies is likely to cause major shifts in the mainstream computing landscape. In order to fully reach their potential in a wide base accessible to any user, remote access of quantum computers and manipulation of data with strong privacy and integrity guarantees are essential. Consider a setting where a client having a fully classical computer wants to determine the result of some quantum computation, but lacks the necessary resources to perform the computation herself. She has access to a more powerful server which has quantum resources and can solve the problem and send the outcome back to the client. However, the client does not trust the powerful server, so she needs to find a way to hide her data. Therefore, the main question that arises is how can we guarantee the client’s privacy of the input and even the computation itself against the server possessing quantum computational capabilities. In the present thesis, we study this problem, denoted here as classical secure delegation of quantum computations (CSDQC) between a fully classical honest client and a quantum untrusted server. We focus on different models of security, analyzing the limitations and potential of each of the settings. Concretely, we first study the CSDQC problem under information-theoretic security. We analyse two categories of quantum computations, decision and sampling problems and in both cases we provide evidence indicating the impossibility of achieving information-theoretic security. Subsequently, we consider relaxing the security framework and specifically, we will analyze this task in the computational security setting (against quantum polynomial-time adversaries). As a result, in the second part of the thesis we put forward the remote state preparation as a key component that would allow us to achieve classical secure delegation of universal quantum computations. We present two protocols realizing the remote state preparation primitive assuming only a classical channel between client and server. The first candidate is shown to be secure in the honest-but-curious model, while the second candidate is proven secure against the server in the malicious setting. The security of both constructions relies on the hardness of the learning with errors problem. Finally, given the important role the remote state preparation plays not only in CSDQC, but also in other quantum communication protocols, we analyze its composable security to determine the privacy loss as a result of using remote state preparation as a sub-module in different protocols

Advances in Functional Encryption

Functional encryption is a novel paradigm for public-key encryption that enables both fine-grained access control and selective computation on encrypted data, as is necessary to protect big, complex data in the cloud. In this thesis, I provide a brief introduction to functional encryption, and an overview of my contributions to the area

Biometrics & [and] Security:Combining Fingerprints, Smart Cards and Cryptography

Since the beginning of this brand new century, and especially since the 2001 Sept 11 events in the U.S, several biometric technologies are considered mature enough to be a new tool for security. Generally associated to a personal device for privacy protection, biometric references are stored in secured electronic devices such as smart cards, and systems are using cryptographic tools to communicate with the smart card and securely exchange biometric data. After a general introduction about biometrics, smart cards and cryptography, a second part will introduce our work with fake finger attacks on fingerprint sensors and tests done with different materials. The third part will present our approach for a lightweight fingerprint recognition algorithm for smart cards. The fourth part will detail security protocols used in different applications such as Personal Identity Verification cards. We will discuss our implementation such as the one we developed for the NIST to be used in PIV smart cards. Finally, a fifth part will address Cryptography-Biometrics interaction. We will highlight the antagonism between Cryptography – determinism, stable data – and Biometrics – statistical, error-prone –. Then we will present our application of challenge-response protocol to biometric data for easing the fingerprint recognition process