172 research outputs found
Delegating Quantum Computation in the Quantum Random Oracle Model
A delegation scheme allows a computationally weak client to use a server's
resources to help it evaluate a complex circuit without leaking any information
about the input (other than its length) to the server. In this paper, we
consider delegation schemes for quantum circuits, where we try to minimize the
quantum operations needed by the client. We construct a new scheme for
delegating a large circuit family, which we call "C+P circuits". "C+P" circuits
are the circuits composed of Toffoli gates and diagonal gates. Our scheme is
non-interactive, requires very little quantum computation from the client
(proportional to input length but independent of the circuit size), and can be
proved secure in the quantum random oracle model, without relying on additional
assumptions, such as the existence of fully homomorphic encryption. In practice
the random oracle can be replaced by an appropriate hash function or block
cipher, for example, SHA-3, AES.
This protocol allows a client to delegate the most expensive part of some
quantum algorithms, for example, Shor's algorithm. The previous protocols that
are powerful enough to delegate Shor's algorithm require either many rounds of
interactions or the existence of FHE. The protocol requires asymptotically
fewer quantum gates on the client side compared to running Shor's algorithm
locally.
To hide the inputs, our scheme uses an encoding that maps one input qubit to
multiple qubits. We then provide a novel generalization of classical garbled
circuits ("reversible garbled circuits") to allow the computation of Toffoli
circuits on this encoding. We also give a technique that can support the
computation of phase gates on this encoding.
To prove the security of this protocol, we study key dependent message(KDM)
security in the quantum random oracle model. KDM security was not previously
studied in quantum settings.Comment: 41 pages, 1 figures. Update to be consistent with the proceeding
versio
Hiding secrets in public random functions
Constructing advanced cryptographic applications often requires the ability of privately embedding messages or functions in the code of a program. As an example, consider the task of building a searchable encryption scheme, which allows the users to search over the encrypted data and learn nothing other than the search result. Such a task is achievable if it is possible to embed the secret key of an encryption scheme into the code of a program that performs the "decrypt-then-search" functionality, and guarantee that the code hides everything except its functionality.
This thesis studies two cryptographic primitives that facilitate the capability of hiding secrets in the program of random functions.
1. We first study the notion of a private constrained pseudorandom function (PCPRF). A PCPRF allows the PRF master secret key holder to derive a public constrained key that changes the functionality of the original key without revealing the constraint description. Such a notion closely captures the goal of privately embedding functions in the code of a random function.
Our main contribution is in constructing single-key secure PCPRFs for NC^1 circuit constraints based on the learning with errors assumption. Single-key secure PCPRFs were known to support a wide range of cryptographic applications, such as private-key deniable encryption and watermarking. In addition, we build reusable garbled circuits from PCPRFs.
2. We then study how to construct cryptographic hash functions that satisfy strong random oracle-like properties. In particular, we focus on the notion of correlation intractability, which requires that given the description of a function, it should be hard to find an input-output pair that satisfies any sparse relations.
Correlation intractability captures the security properties required for, e.g., the soundness of the Fiat-Shamir heuristic, where the Fiat-Shamir transformation is a practical method of building signature schemes from interactive proof protocols. However, correlation intractability was shown to be impossible to achieve for certain length parameters, and was widely considered to be unobtainable.
Our contribution is in building correlation intractable functions from various cryptographic assumptions. The security analyses of the constructions use the techniques of secretly embedding constraints in the code of random functions
Randomness Recoverable Secret Sharing Schemes
It is well-known that randomness is essential for secure cryptography. The randomness used in cryptographic primitives is not necessarily recoverable even by the party who can, e.g., decrypt or recover the underlying secret/message. Several cryptographic primitives that support randomness recovery have turned out useful in various applications. In this paper, we study randomness recoverable secret sharing schemes (RR-SSS), in both information-theoretic and computational settings and provide two results. First, we show that while every access structure admits a perfect RR-SSS, there are very simple access structures (e.g., in monotone AC?) that do not admit efficient perfect (or even statistical) RR-SSS. Second, we show that the existence of efficient computational RR-SSS for certain access structures in monotone AC? implies the existence of one-way functions. This stands in sharp contrast to (non-RR) SSS schemes for which no such results are known.
RR-SSS plays a key role in making advanced attributed-based encryption schemes randomness recoverable, which in turn have applications in the context of designated-verifier non-interactive zero knowledge
Bounded KDM Security from iO and OWF
To date, all constructions in the standard model (i.e., without random oracles) of Bounded Key-Dependent Message (KDM) secure (or even just circularly-secure) encryption schemes rely on specific assumptions (LWE, DDH, QR or DCR); all of these assumptions are known to imply the existence of collision-resistant hash functions. In this work, we demonstrate the existence of bounded KDM secure encryption assuming indistinguishability obfsucation for and just one-way functions. Relying on the recent result of Asharov and Segev (STOC\u2715), this yields the first construction of a Bounded KDM secure (or even circularly secure) encryption scheme from an assumption that provably does not imply collision-resistant hash functions w.r.t. black-box constructions. Combining this with prior constructions, we show how to augment this Bounded KDM scheme into a Bounded CCA2-KDM scheme
A Survey on Homomorphic Encryption Schemes: Theory and Implementation
Legacy encryption systems depend on sharing a key (public or private) among
the peers involved in exchanging an encrypted message. However, this approach
poses privacy concerns. Especially with popular cloud services, the control
over the privacy of the sensitive data is lost. Even when the keys are not
shared, the encrypted material is shared with a third party that does not
necessarily need to access the content. Moreover, untrusted servers, providers,
and cloud operators can keep identifying elements of users long after users end
the relationship with the services. Indeed, Homomorphic Encryption (HE), a
special kind of encryption scheme, can address these concerns as it allows any
third party to operate on the encrypted data without decrypting it in advance.
Although this extremely useful feature of the HE scheme has been known for over
30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE)
scheme, which allows any computable function to perform on the encrypted data,
was introduced by Craig Gentry in 2009. Even though this was a major
achievement, different implementations so far demonstrated that FHE still needs
to be improved significantly to be practical on every platform. First, we
present the basics of HE and the details of the well-known Partially
Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which
are important pillars of achieving FHE. Then, the main FHE families, which have
become the base for the other follow-up FHE schemes are presented. Furthermore,
the implementations and recent improvements in Gentry-type FHE schemes are also
surveyed. Finally, further research directions are discussed. This survey is
intended to give a clear knowledge and foundation to researchers and
practitioners interested in knowing, applying, as well as extending the state
of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the
survey that is being submitted to ACM CSUR and has been uploaded to arXiv for
feedback from stakeholder
On Improving Communication Complexity in Cryptography
Cryptography grew to be much more than "the study of secret writing". Modern cryptography is concerned with establishing properties such as privacy, integrity and authenticity in protocols for secure communication and computation. This comes at a price: Cryptographic tools usually introduce an overhead, both in terms of communication complexity (that is, number and size of messages transmitted) and computational efficiency (that is, time and memory required). As in many settings communication between the parties involved is the bottleneck, this thesis is concerned with improving communication complexity in cryptographic protocols.
One direction towards this goal is scalable cryptography: In many cryptographic schemes currently deployed, the security degrades linearly with the number of instances (e.g. encrypted messages) in the system. As this number can be huge in contexts like cloud computing, the parameters of the scheme have to be chosen considerably larger - and in particular depending on the expected number of instances in the system - to maintain security guarantees. We advance the state-of-the-art regarding scalable cryptography by constructing schemes where the security guarantees are independent of the number of instances. This allows to choose smaller parameters, even when the expected number of instances is immense.
- We construct the first scalable encryption scheme with security against active adversaries which has both compact public keys and ciphertexts. In particular, we significantly reduce the size of the public key to only about 3% of the key-size of the previously most efficient scalable encryption scheme. (Gay,Hofheinz, and Kohl, CRYPTO, 2017)
- We present a scalable structure-preserving signature scheme which improves both in terms of public-key and signature size compared to the previously best construction to about 40% and 56% of the sizes, respectively. (Gay, Hofheinz, Kohl, and Pan, EUROCRYPT, 2018)
Another important area of cryptography is secure multi-party computation, where the goal is to jointly evaluate some function while keeping each party’s input private. In traditional approaches towards secure multi-party computation either the communication complexity scales linearly in the size of the function, or the computational efficiency is poor. To overcome this issue, Boyle, Gilboa, and Ishai (CRYPTO, 2016) introduced the notion of homomorphic secret sharing. Here, inputs are shared between parties such that each party does not learn anything about the input, and such that the parties can locally evaluate functions on the shares. Homomorphic secret sharing implies secure computation where the communication complexity only depends on the size of the inputs, which is typically much smaller than the size of the function. A different approach towards efficient secure computation is to split the protocol into an input-independent preprocessing phase, where long correlated strings are generated, and a very efficient online phase. One example for a useful correlation are authenticated Beaver triples, which allow to perform efficient multiplications in the online phase such that privacy of the inputs is preserved and parties deviating the protocol can be detected. The currently most efficient protocols implementing the preprocessing phase require communication linear in the number of triples to be generated. This results typically in high communication costs, as the online phase requires at least one authenticated Beaver triple per multiplication.
We advance the state-of-the art regarding efficient protocols for secure computation with low communication complexity as follows.
- We construct the first homomorphic secret sharing scheme for computing arbitrary functions in NC 1 (that is, functions that are computably by circuits with logarithmic depth) which supports message spaces of arbitrary size, has only negligible correctness error, and does not require expensive multiplication on ciphertexts. (Boyle, Kohl, and Scholl, EUROCRYPT, 2019)
- We introduce the notion of a pseudorandom correlation generator for general correlations. Pseudorandom correlation generators allow to locally extend short correlated seeds into long pseudorandom correlated strings. We show that pseudorandom correlation generators can replace the preprocessing phase in many protocols, leading to a preprocessing phase with sublinear communication complexity. We show connections to homomorphic secret sharing schemes and give the first instantiation of pseudorandom correlation generators for authenticated Beaver triples at reasonable computational efficiency. (Boyle, Couteau, Gilboa, Ishai, Kohl, and Scholl, CRYPTO, 2019
Fiat-Shamir From Simpler Assumptions
We present two new protocols:
(1) A succinct publicly verifiable non-interactive argument system for log-space uniform NC computations, under the assumption that any one of a broad class of fully homomorphic encryption (FHE) schemes has almost optimal security against polynomial-time adversaries. The class includes all FHE schemes in the literature that are based on the learning with errors (LWE) problem.
(2) A non-interactive zero-knowledge argument system for NP in the common random string model, assuming almost optimal hardness of search-LWE against polynomial-time adversaries.
Both results are obtained by applying the Fiat-Shamir transform with explicit, efficiently computable functions (specifically, correlation intractable functions) to certain classes of interactive proofs. We improve over prior work by reducing the security of these protocols to qualitatively weaker computational hardness assumptions. Along the way, we also show that the Fiat-Shamir transform can be soundly applied (in the plain model) to a richer class of protocols than was previously known
KDM Security for Identity-Based Encryption: Constructions and Separations
For encryption schemes, key dependent message (KDM) security requires that ciphertexts preserve secrecy even when the messages to be encrypted depend on the secret keys.
While KDM security has been extensively studied for public-key encryption (PKE), it receives much less attention in the setting of identity-based encryption (IBE). In this work, we focus on the KDM security for IBE. Our results are threefold.
We first propose a generic approach to transfer the KDM security results (both positive and negative) from PKE to IBE. At the heart of our approach is a neat structure-mirroring PKE-to-IBE transformation based on indistinguishability obfuscation and puncturable PRFs, which establishes a connection between PKE and IBE in general. However, the obtained results are restricted to selective-identity sense. We then concentrate on results in adaptive-identity sense.
On the positive side, we present two constructions that achieve KDM security in the adaptive-identity sense for the first time. One is built from identity-based hash proof system (IB-HPS) with homomorphic property, which indicates that the IBE schemes of Gentry (Eurocrypt 2006), Coron (DCC 2009), Chow et al. (CCS 2010) are actually KDM-secure in the single-key setting. The other is built from indistinguishability obfuscation and a new notion named puncturable unique signature, which is bounded KDM-secure in the single-key setting.
On the negative side, we separate CPA/CCA security from -circular security (which is a prototypical case of KDM security) for IBE by giving a counterexample based on differing-inputs obfuscation and a new notion named puncturable IBE. We further propose a general framework for generating -circular security counterexamples in identity-based setting,
which might be of independent interest
On Symmetric Encryption and Point Obfuscation
We show tight connections between several cryptographic primitives, namely encryption with weakly random keys, encryption with key-dependent messages (KDM), and obfuscation of point functions with multi-bit output(which we call multi-bit point functions, or MBPFs, for short). These primitives, which have been studied mostly separately in recent works, bear some apparent similarities, both in the flavor of their security requirements and in the flavor of their constructions and assumptions. Still, rigorous connections have not been drawn.
Our results can be interpreted as indicating that MBPF obfuscators imply a very strong form of encryption that simultaneously achieves security for weakly-random keys and key-dependent messages as special cases. Similarly, each one of the other primitives implies a certain restricted form of MBPF obfuscation. Our results carry both constructions and impossibility results from one primitive to others. In particular:
- The recent impossibility result for KDM security of Haitner and Holenstein (TCC \u2709) carries over to MBPF obfuscators.
- The Canetti-Dakdouk construction of MBPF obfuscators based on a strong variant of the DDH assumption (EC \u2708) gives an encryption scheme which is secure w.r.t. any weak key distribution of super-logarithmic
min-entropy (and in particular, also has very strong leakage resilient properties).
- All the recent constructions of encryption schemes that are secure w.r.t. weak keys imply a weak form of MBPF obfuscators
- …