745 research outputs found
On the parity complexity measures of Boolean functions
The parity decision tree model extends the decision tree model by allowing
the computation of a parity function in one step. We prove that the
deterministic parity decision tree complexity of any Boolean function is
polynomially related to the non-deterministic complexity of the function or its
complement. We also show that they are polynomially related to an analogue of
the block sensitivity. We further study parity decision trees in their
relations with an intermediate variant of the decision trees, as well as with
communication complexity.Comment: submitted to TCS on 16-MAR-200
Finding Significant Fourier Coefficients: Clarifications, Simplifications, Applications and Limitations
Ideas from Fourier analysis have been used in cryptography for the last three
decades. Akavia, Goldwasser and Safra unified some of these ideas to give a
complete algorithm that finds significant Fourier coefficients of functions on
any finite abelian group. Their algorithm stimulated a lot of interest in the
cryptography community, especially in the context of `bit security'. This
manuscript attempts to be a friendly and comprehensive guide to the tools and
results in this field. The intended readership is cryptographers who have heard
about these tools and seek an understanding of their mechanics and their
usefulness and limitations. A compact overview of the algorithm is presented
with emphasis on the ideas behind it. We show how these ideas can be extended
to a `modulus-switching' variant of the algorithm. We survey some applications
of this algorithm, and explain that several results should be taken in the
right context. In particular, we point out that some of the most important bit
security problems are still open. Our original contributions include: a
discussion of the limitations on the usefulness of these tools; an answer to an
open question about the modular inversion hidden number problem
Average-Case Complexity
We survey the average-case complexity of problems in NP.
We discuss various notions of good-on-average algorithms, and present
completeness results due to Impagliazzo and Levin. Such completeness results
establish the fact that if a certain specific (but somewhat artificial) NP
problem is easy-on-average with respect to the uniform distribution, then all
problems in NP are easy-on-average with respect to all samplable distributions.
Applying the theory to natural distributional problems remain an outstanding
open question. We review some natural distributional problems whose
average-case complexity is of particular interest and that do not yet fit into
this theory.
A major open question whether the existence of hard-on-average problems in NP
can be based on the PNP assumption or on related worst-case assumptions.
We review negative results showing that certain proof techniques cannot prove
such a result. While the relation between worst-case and average-case
complexity for general NP problems remains open, there has been progress in
understanding the relation between different ``degrees'' of average-case
complexity. We discuss some of these ``hardness amplification'' results
Optimal and Efficient Searchable Encryption with Single Trapdoor for Multi-Owner Data Sharing in Federated Cloud Computing
Cloud computing, an Internet based computing model, has changed the way of data owners store and manage data. In such environment, data sharing is very important with more efficient data access control. Issuing an aggregate key to users on data enables and authorizes them to search for data of select encrypted files using trapdoor or encrypted keyword. The existing schemes defined for this purpose do have certain limitations. For instance, Cui et al. scheme is elegant but lacks in flexibility in access control in presence of multiple data owners sharing data to users. Its single trapdoor approach needs transformation into individual trapdoors to access data of specific data owner. Moreover, the existing schemes including that of Cui et al. does not support federated cloud. In this paper we proposed an efficient key aggregate searchable encryption scheme which enables multiple featuressuch as support for truly single aggregate key to access data of many data owners, federated cloud support,query privacy, controlled search process and security against cross-pairing attack. It has algorithms for setup, keygen, encrypt, extract, aggregate, trapdoor, test and federator. In multi-user setting it is designed to serve data owners and users with secure data sharing through key aggregate searchable encryption The proposed scheme supports federated cloud. Experimental results revealed that the proposed scheme is provably secure withrelatively less computational overhead and time complexity when compared with the state of the art
Zero-Knowledge Arguments for Matrix-Vector Relations and Lattice-Based Group Encryption
International audienceGroup encryption (GE) is the natural encryption analogue of group signatures in that it allows verifiably encrypting messages for some anonymous member of a group while providing evidence that the receiver is a properly certified group member. Should the need arise, an opening authority is capable of identifying the receiver of any ciphertext. As introduced by Kiayias, Tsiounis and Yung (Asiacrypt'07), GE is motivated by applications in the context of oblivious retriever storage systems, anonymous third parties and hierarchical group signatures. This paper provides the first realization of group encryption under lattice assumptions. Our construction is proved secure in the standard model (assuming interaction in the proving phase) under the Learning-With-Errors (LWE) and Short-Integer-Solution (SIS) assumptions. As a crucial component of our system, we describe a new zero-knowledge argument system allowing to demonstrate that a given ciphertext is a valid encryption under some hidden but certified public key, which incurs to prove quadratic statements about LWE relations. Specifically, our protocol allows arguing knowledge of witnesses consisting of X ∈ Z m×n q , s ∈ Z n q and a small-norm e ∈ Z m which underlie a public vector b = X · s + e ∈ Z m q while simultaneously proving that the matrix X ∈ Z m×n q has been correctly certified. We believe our proof system to be useful in other applications involving zero-knowledge proofs in the lattice setting
Identity-Based Encryption with Security against the KGC: A Formal Model and Its Instantiations
The key escrow problem is one of the main barriers to the widespread real-world use of identity-based encryption (IBE). Specifically, a key generation center (KGC), which generates secret keys for a given identity, has the power to decrypt all ciphertexts. At PKC 2009, Chow defined a notion of security against the KGC, that relies on assuming that it cannot discover the underlying identities behind ciphertexts. However, this is not a realistic assumption since, in practice, the KGC manages an identity list, and hence it can easily guess the identities corresponding to given ciphertexts. Chow later amended this issue by introducing a new entity called an identity-certifying authority (ICA) and proposed an anonymous key-issuing protocol. Essentially, this allows the users, KGC, and ICA to interactively generate secret keys without users ever having to reveal their identities to the KGC. Unfortunately, since Chow separately defined the security of IBE and that of the anonymous key-issuing protocol, his IBE definition did not provide any formal treatment when the ICA is used to authenticate the users. Effectively, all of the subsequent works following Chow lack the formal proofs needed to determine whether or not it delivers a secure solution to the key escrow problem.
In this paper, based on Chow\u27s work, we formally define an IBE scheme that resolves the key escrow problem and provide formal definitions of security against corrupted users, KGC, and ICA. Along the way, we observe that if we are allowed to assume a fully trusted ICA, as in Chow\u27s work, then we can construct a trivial (and meaningless) IBE scheme that is secure against the KGC. Finally, we present two instantiations in our new security model: a lattice-based construction based on the Gentry--Peikert--Vaikuntanathan IBE scheme (STOC 2008) and R{ü}ckert\u27s lattice-based blind signature scheme (ASIACRYPT 2010), and a pairing-based construction based on the Boneh--Franklin IBE scheme (CRYPTO 2001) and Boldyreva\u27s blind signature scheme (PKC 2003)
Formal security analysis of registration protocols for interactive systems: a methodology and a case of study
In this work we present and formally analyze CHAT-SRP (CHAos based
Tickets-Secure Registration Protocol), a protocol to provide interactive and
collaborative platforms with a cryptographically robust solution to classical
security issues. Namely, we focus on the secrecy and authenticity properties
while keeping a high usability. In this sense, users are forced to blindly
trust the system administrators and developers. Moreover, as far as we know,
the use of formal methodologies for the verification of security properties of
communication protocols isn't yet a common practice. We propose here a
methodology to fill this gap, i.e., to analyse both the security of the
proposed protocol and the pertinence of the underlying premises. In this
concern, we propose the definition and formal evaluation of a protocol for the
distribution of digital identities. Once distributed, these identities can be
used to verify integrity and source of information. We base our security
analysis on tools for automatic verification of security protocols widely
accepted by the scientific community, and on the principles they are based
upon. In addition, it is assumed perfect cryptographic primitives in order to
focus the analysis on the exchange of protocol messages. The main property of
our protocol is the incorporation of tickets, created using digests of chaos
based nonces (numbers used only once) and users' personal data. Combined with a
multichannel authentication scheme with some previous knowledge, these tickets
provide security during the whole protocol by univocally linking each
registering user with a single request. [..]Comment: 32 pages, 7 figures, 8 listings, 1 tabl
Forward Secure Efficient Group Signature in Dynamic Setting using Lattices
Secret key exposure is at high risk in the computing infrastructure due to the increase in use of harmful devices. As a result, achieving forward secrecy is a preferable feature for any cryptosystem where the lifetime of a user is divided into discrete time periods. Forward secrecy preserves the security of past periods even if the secret key is exposed. In this work, we introduce the first lattice based forward secure dynamic group signature scheme. The existing forward secure group signature schemes are secure in the bilinear setting, and becomes insecure in the quantum computer period. We employ a complete binary tree whose leaves are associated with discrete time periods and label the nodes in a unique way that enables each node of the same depth to have different hamming weight. This helps the group manager to produce distinct certificates to distinct users. Our scheme withstand framing attacks, mis-identification attack and preserves anonymity under the learning with errors (LWE) and short integer solution (SIS) assumptions
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