Deterministic Public-Key Encryption under Continual Leakage

Deterministic public-key encryption, introduced by Bellare, Boldyreva, and O’Neill (CRYPTO 2007), is an important technique for searchable encryption; it allows quick, logarithmic-time, search over encrypted data items. The technique is most effective in scenarios where frequent search queries are performed over a huge database of unpredictable data items. We initiate the study of deterministic public-key encryption (D-PKE) in the presence of leakage. We formulate appropriate security notions for leakage-resilient D-PKE, and present constructions that achieve them in the standard model. We work in the continual leakage model, where the secret-key is updated at regular intervals and an attacker can learn arbitrary but bounded leakage on the secret key during each time interval. We, however, do not consider leakage during the updates. Our main construction is based on the (standard) linear assumption in bilinear groups, tolerat- ing up to 0.5 - o(1) fraction of arbitrary leakage. The leakage rate can be improved to 1 - o(1) by relying on the SXDH assumption. At a technical level, we propose and construct a “continual leakage resilient” version of the all-but-one lossy trapdoor functions, introduced by Peikert and Waters (STOC 2008). Our formulation and construction of leakage-resilient lossy-TDFs is of independent general interest for leakage-resilient cryptography

Leakage-Resilient Cryptography from Puncturable Primitives and Obfuscation

In this work, we develop a framework for building leakage-resilient cryptosystems in the bounded leakage model from puncturable primitives and indistinguishability obfuscation ($i\mathcal{O}$). The major insight of our work is that various types of puncturable pseudorandom functions (PRFs) can achieve leakage resilience on an obfuscated street. First, we build leakage-resilient weak PRFs from weak puncturable PRFs and $i\mathcal{O}$, which readily imply leakage-resilient secret-key encryption. Second, we build leakage-resilient publicly evaluable PRFs (PEPRFs) from puncturable PEPRFs and $i\mathcal{O}$, which readily imply leakage-resilient key encapsulation mechanism and thus public-key encryption. As a building block of independent interest, we realize puncturable PEPRFs from either newly introduced puncturable objects such as puncturable trapdoor functions and puncturable extractable hash proof systems or existing puncturable PRFs with $i\mathcal{O}$. Finally, we construct the first leakage-resilient public-coin signature from selective puncturable PRFs, leakage-resilient one-way functions and $i\mathcal{O}$. This settles the open problem posed by Boyle, Segev and Wichs (Eurocrypt 2011). By further assuming the existence of lossy functions, all the above constructions achieve optimal leakage rate of $1 - o(1)$. Such a leakage rate is not known to be achievable for weak PRFs, PEPRFs and public-coin signatures before

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

Regular Lossy Functions and Their Applications in Leakage-Resilient Cryptography

In STOC 2008, Peikert and Waters introduced a powerful primitive called lossy trapdoor functions (LTFs). In a nutshell, LTFs are functions that behave in one of two modes. In the normal mode, functions are injective and invertible with a trapdoor. In the lossy mode, functions statistically lose information about their inputs. Moreover, the two modes are computationally indistinguishable. In this work, we put forward a relaxation of LTFs, namely, regular lossy functions (RLFs). Compared to LTFs, the functions in the normal mode are not required to be efficiently invertible or even unnecessary to be injective. Instead, they could also be lossy, but in a regular manner. We also put forward richer abstractions of RLFs, namely all-but-one regular lossy functions (ABO-RLFs) and one-time regular lossy filters (OT-RLFs). We show that (ABO)-RLFs admit efficient constructions from both a variety of number- theoretic assumptions and hash proof system (HPS) for subset membership problems satisfying natural algebraic properties. Thanks to the relaxations on functionality, the constructions enjoy much compact key size and better computational efficiency than that of (ABO)-LTFs. We demonstrate the utility of RLFs and their extensions in the leakage-resilient cryptography. As a special case of RLFs, lossy functions imply leakage-resilient injective one-way functions with optimal leakage rate $1 - o(1)$. ABO-RLFs (or OT-RLFs) immediately imply leakage-resilient one-time message authentication code (MAC) with optimal leakage rate $1 - o(1)$. ABO-RLFs together with HPS give rise to leakage-resilient chosen-ciphertext (CCA) secure key encapsulation mechanisms (KEM) (this approach extends naturally to the identity-based setting). Combining the construction of ABO-RLFs from HPS, this gives the first leakage-resilient CCA-secure public-key encryption (PKE) with optimal leakage rate based solely on HPS, and thus goes beyond the barrier posed by Dodis et al. (Asiacrypt 2010). Our construction also applies to the identity-based setting, yielding LR-CCA secure IB-KEM with higher leakage rate than previous works

Efficient public-key cryptography with bounded leakage and tamper resilience

We revisit the question of constructing public-key encryption and signature schemes with security in the presence of bounded leakage and tampering memory attacks. For signatures we obtain the first construction in the standard model; for public-key encryption we obtain the first construction free of pairing (avoiding non-interactive zero-knowledge proofs). Our constructions are based on generic building blocks, and, as we show, also admit efficient instantiations under fairly standard number-theoretic assumptions. The model of bounded tamper resistance was recently put forward by Damgård et al. (Asiacrypt 2013) as an attractive path to achieve security against arbitrary memory tampering attacks without making hardware assumptions (such as the existence of a protected self-destruct or key-update mechanism), the only restriction being on the number of allowed tampering attempts (which is a parameter of the scheme). This allows to circumvent known impossibility results for unrestricted tampering (Gennaro et al., TCC 2010), while still being able to capture realistic tampering attack

Chosen-ciphertext security from subset sum

We construct a public-key encryption (PKE) scheme whose security is polynomial-time equivalent to the hardness of the Subset Sum problem. Our scheme achieves the standard notion of indistinguishability against chosen-ciphertext attacks (IND-CCA) and can be used to encrypt messages of arbitrary polynomial length, improving upon a previous construction by Lyubashevsky, Palacio, and Segev (TCC 2010) which achieved only the weaker notion of semantic security (IND-CPA) and whose concrete security decreases with the length of the message being encrypted. At the core of our construction is a trapdoor technique which originates in the work of Micciancio and Peikert (Eurocrypt 2012

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 $1 - o(1)$

Correlated Product Security from Any One-Way Function

It is well-known that the k-wise product of one-way functions remains one-way, but may no longer be when the k inputs are correlated. At TCC 2009, Rosen and Segev introduced a new notion known as Correlated Product secure functions. These functions have the property that a k-wise product of them remains one-way even under correlated inputs. Rosen and Segev gave a construction of injective trapdoor functions which were correlated product secure from the existence of Lossy Trapdoor Functions (introduced by Peikert and Waters in STOC 2008). The first main result of this work shows the surprising fact that a family of correlated prod-uct secure functions can be constructed from any one-way function. Because correlated product secure functions are trivially one-way, this shows an equivalence between the existence of these two cryptographic primitives. In the second main result of this work, we consider a natural decisional variant of correlated product security. Roughly, a family of functions are Decisional Correlated Product (DCP) secure if f1(x1),..., fk(x1) is indistinguishable from f1(x1),..., fk(xk) when x1,..., xk are chosen uniformly at random

08491 Abstracts Collection -- Theoretical Foundations of Practical Information Security

From 30.11. to 05.12.2008, the Dagstuhl Seminar 08491 ``Theoretical Foundations of Practical Information Security \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Circular and leakage resilient public-key encryption under subgroup indistinguishability (or: Quadratic residuosity strikes back)

30th Annual Cryptology Conference, Santa Barbara, CA, USA, August 15-19, 2010. ProceedingsThe main results of this work are new public-key encryption schemes that, under the quadratic residuosity (QR) assumption (or Paillier’s decisional composite residuosity (DCR) assumption), achieve key-dependent message security as well as high resilience to secret key leakage and high resilience to the presence of auxiliary input information. In particular, under what we call the subgroup indistinguishability assumption, of which the QR and DCR are special cases, we can construct a scheme that has: • Key-dependent message (circular) security. Achieves security even when encrypting affine functions of its own secret key (in fact, w.r.t. affine “key-cycles” of predefined length). Our scheme also meets the requirements for extending key-dependent message security to broader classes of functions beyond affine functions using previous techniques of Brakerski et al. or Barak et al. • Leakage resiliency. Remains secure even if any adversarial low-entropy (efficiently computable) function of the secret key is given to the adversary. A proper selection of parameters allows for a “leakage rate” of (1 − o(1)) of the length of the secret key. • Auxiliary-input security. Remains secure even if any sufficiently hard to invert (efficiently computable) function of the secret key is given to the adversary. Our scheme is the first to achieve key-dependent security and auxiliary-input security based on the DCR and QR assumptions. Previous schemes that achieved these properties relied either on the DDH or LWE assumptions. The proposed scheme is also the first to achieve leakage resiliency for leakage rate (1 − o(1)) of the secret key length, under the QR assumption. We note that leakage resilient schemes under the DCR and the QR assumptions, for the restricted case of composite modulus product of safe primes, were implied by the work of Naor and Segev, using hash proof systems. However, under the QR assumption, known constructions of hash proof systems only yield a leakage rate of o(1) of the secret key length.Microsoft Researc