Fully leakage-resilient signatures revisited: Graceful degradation, noisy leakage, and construction in the bounded-retrieval model

We construct new leakage-resilient signature schemes. Our schemes remain unforgeable against an adversary leaking arbitrary (yet bounded) information on the entire state of the signer (sometimes known as fully leakage resilience), including the random coin tosses of the signing algorithm. The main feature of our constructions is that they offer a graceful degradation of security in situations where standard existential unforgeability is impossible

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

Naor-Yung paradigm with shared randomness and applications

The Naor-Yung paradigm (Naor and Yung, STOC’90) allows to generically boost security under chosen-plaintext attacks (CPA) to security against chosen-ciphertext attacks (CCA) for public-key encryption (PKE) schemes. The main idea is to encrypt the plaintext twice (under independent public keys), and to append a non-interactive zero-knowledge (NIZK) proof that the two ciphertexts indeed encrypt the same message. Later work by Camenisch, Chandran, and Shoup (Eurocrypt’09) and Naor and Segev (Crypto’09 and SIAM J. Comput.’12) established that the very same techniques can also be used in the settings of key-dependent message (KDM) and key-leakage attacks (respectively). In this paper we study the conditions under which the two ciphertexts in the Naor-Yung construction can share the same random coins. We find that this is possible, provided that the underlying PKE scheme meets an additional simple property. The motivation for re-using the same random coins is that this allows to design much more efficient NIZK proofs. We showcase such an improvement in the random oracle model, under standard complexity assumptions including Decisional Diffie-Hellman, Quadratic Residuosity, and Subset Sum. The length of the resulting ciphertexts is reduced by 50%, yielding truly efficient PKE schemes achieving CCA security under KDM and key-leakage attacks. As an additional contribution, we design the first PKE scheme whose CPA security under KDM attacks can be directly reduced to (low-density instances of) the Subset Sum assumption. The scheme supports keydependent messages computed via any affine function of the secret ke

Review on Leakage Resilient Key Exchange Security Model

In leakage resilient cryptography, leakage resilient key exchange protocols are constructed to defend against leakage attacks. Then, the key exchange protocol is proved with leakage resilient security model to determine whether its security proof can provide the security properties it claimed or to find out any unexamined flaw during protocol building. It is an interesting work to review the meaningful security properties provided by these security models. This work review how a leakage resilient security model for a key exchange protocol has been evolved over years according to the increasing security requirement which covers a different range of attacks. The relationship on how an adversary capability in the leakage resilient security model can be related to real-world attack scenarios is studied. The analysis work for each leakage resilient security model here enables a better knowledge on how an adversary query addresses different leakage attacks setting, thereby understand the motive of design for a cryptographic primitive in the security model

A Survey of Leakage-Resilient Cryptography

In the past 15 years, cryptography has made considerable progress in expanding the adversarial attack model to cover side-channel attacks, and has built schemes to provably defend against some of them. This survey covers the main models and results in this so-called leakage-resilient cryptography

Leakage-Resilient Inner-Product Functional Encryption in the Bounded-Retrieval Model

We propose a leakage-resilient inner-product functional encryption scheme (IPFE) in the bounded-retrieval model (BRM). This is the first leakage-resilient functional encryption scheme in the BRM. In our leakage model, an adversary is allowed to obtain at most $l$-bit knowledge from each secret key. And our scheme can flexibly tolerate arbitrarily leakage bound $l$, by only increasing the size of secret keys, while keeping all other parts small and independent of $l$. Technically, we develop a new notion: Inner-product hash proof system (IP-HPS). IP-HPS is a variant of traditional hash proof systems. Its output of decapsulation is an inner-product value, instead of the encapsulated key. We propose an IP-HPS scheme under DDH-assumption. Then we show how to make an IP-HPS scheme to tolerate $l\u27$-bit leakage, and we can achieve arbitrary large $l\u27$ by only increasing the size of secret keys. Finally, we show how to build a leakage-resilient IPFE in the BRM with leakage bound $l=\frac{l\u27}{n}$ from our IP-HPS scheme

Secure data storage and retrieval in cloud computing

Nowadays cloud computing has been widely recognised as one of the most inuential information technologies because of its unprecedented advantages. In spite of its widely recognised social and economic benefits, in cloud computing customers lose the direct control of their data and completely rely on the cloud to manage their data and computation, which raises significant security and privacy concerns and is one of the major barriers to the adoption of public cloud by many organisations and individuals. Therefore, it is desirable to apply practical security approaches to address the security risks for the wide adoption of cloud computing

Adaptive-secure identity-based inner-product functional encryption and its leakage-resilience

There are lots of applications of inner-product functional encryption (IPFE). In this paper, we consider two important extensions of it. One is to enhance IPFE with access control such that only users with a pre-defined identity are allowed to compute the inner product, referred as identity-based inner-product functional encryption (IBIPFE). We formalize the definition of IBIPFE, and propose the first adaptive-secure IBIPFE scheme from Decisional Bilinear Diffie-Hellman (DBDH) assumption. In an IBIPFE scheme, the ciphertext is related to a vector $\vec{x}$ and a new parameter, identity ID. Each secret key is also related to a vector $\vec{y}$ and an identity ID\u27. The decryption algorithm will output the inner-product value $$ only if ID $=$ ID\u27. The other extension is to make IBIPFE leakage resilient. We consider the bounded-retrieval model (BRM) in which an adversary can learn at most $l$ bits information from each secret key. Here, $l$ is the leakage bound determined by some external parameters, and it can be set arbitrarily large. After giving the security definition of leakage-resilient IBIPFE, we extend our IBIPFE scheme into a leakage-resilient IBIPFE scheme in the BRM by hash proof system (HPS)

On the Security of Leakage Resilient Public Key Cryptography

Side channel attacks, where an attacker learns some physical information about the state of a device, are one of the ways in which cryptographic schemes are broken in practice. "Provably secure" schemes are subject to these attacks since the traditional models of security do not account for them. The theoretical community has recently proposed leakage resilient cryptography in an effort to account for side channel attacks in the security model. This thesis provides an in-depth look into what security guarantees public key leakage resilient schemes provide in practice