104 research outputs found
URDP: General Framework for Direct CCA2 Security from any Lattice-Based PKE Scheme
Design efficient lattice-based cryptosystem secure against adaptive chosen
ciphertext attack (IND-CCA2) is a challenge problem. To the date, full
CCA2-security of all proposed lattice-based PKE schemes achieved by using a
generic transformations such as either strongly unforgeable one-time signature
schemes (SU-OT-SS), or a message authentication code (MAC) and weak form of
commitment. The drawback of these schemes is that encryption requires "separate
encryption". Therefore, the resulting encryption scheme is not sufficiently
efficient to be used in practice and it is inappropriate for many applications
such as small ubiquitous computing devices with limited resources such as smart
cards, active RFID tags, wireless sensor networks and other embedded devices.
In this work, for the first time, we introduce an efficient universal random
data padding (URDP) scheme, and show how it can be used to construct a "direct"
CCA2-secure encryption scheme from "any" worst-case hardness problems in
(ideal) lattice in the standard model, resolving a problem that has remained
open till date. This novel approach is a "black-box" construction and leads to
the elimination of separate encryption, as it avoids using general
transformation from CPA-secure scheme to a CCA2-secure one. IND-CCA2 security
of this scheme can be tightly reduced in the standard model to the assumption
that the underlying primitive is an one-way trapdoor function.Comment: arXiv admin note: text overlap with arXiv:1302.0347, arXiv:1211.6984;
and with arXiv:1205.5224 by other author
Learning with Errors is easy with quantum samples
Learning with Errors is one of the fundamental problems in computational
learning theory and has in the last years become the cornerstone of
post-quantum cryptography. In this work, we study the quantum sample complexity
of Learning with Errors and show that there exists an efficient quantum
learning algorithm (with polynomial sample and time complexity) for the
Learning with Errors problem where the error distribution is the one used in
cryptography. While our quantum learning algorithm does not break the LWE-based
encryption schemes proposed in the cryptography literature, it does have some
interesting implications for cryptography: first, when building an LWE-based
scheme, one needs to be careful about the access to the public-key generation
algorithm that is given to the adversary; second, our algorithm shows a
possible way for attacking LWE-based encryption by using classical samples to
approximate the quantum sample state, since then using our quantum learning
algorithm would solve LWE
Making Existential-Unforgeable Signatures Strongly Unforgeable in the Quantum Random-Oracle Model
Strongly unforgeable signature schemes provide a more stringent security
guarantee than the standard existential unforgeability. It requires that not
only forging a signature on a new message is hard, it is infeasible as well to
produce a new signature on a message for which the adversary has seen valid
signatures before. Strongly unforgeable signatures are useful both in practice
and as a building block in many cryptographic constructions.
This work investigates a generic transformation that compiles any
existential-unforgeable scheme into a strongly unforgeable one, which was
proposed by Teranishi et al. and was proven in the classical random-oracle
model. Our main contribution is showing that the transformation also works
against quantum adversaries in the quantum random-oracle model. We develop
proof techniques such as adaptively programming a quantum random-oracle in a
new setting, which could be of independent interest. Applying the
transformation to an existential-unforgeable signature scheme due to Cash et
al., which can be shown to be quantum-secure assuming certain lattice problems
are hard for quantum computers, we get an efficient quantum-secure strongly
unforgeable signature scheme in the quantum random-oracle model.Comment: 15 pages, to appear in Proceedings TQC 201
Bounded-Collusion IBE from Key Homomorphism
In this work, we show how to construct IBE schemes that are secure against a bounded number of collusions, starting with underlying PKE schemes which possess linear homomorphisms over their keys. In particular, this enables us to exhibit a new (bounded-collusion) IBE construction based on the quadratic residuosity assumption, without any need to assume the existence of random oracles. The new IBE’s public parameters are of size O(tλlogI) where I is the total number of identities which can be supported by the system, t is the number of collusions which the system is secure against, and λ is a security parameter. While the number of collusions is bounded, we note that an exponential number of total identities can be supported.
More generally, we give a transformation that takes any PKE satisfying Linear Key Homomorphism, Identity Map Compatibility, and the Linear Hash Proof Property and translates it into an IBE secure against bounded collusions. We demonstrate that these properties are more general than our quadratic residuosity-based scheme by showing how a simple PKE based on the DDH assumption also satisfies these properties.National Science Foundation (U.S.) (NSF CCF-0729011)National Science Foundation (U.S.) (NSF CCF-1018064)United States. Defense Advanced Research Projects Agency (DARPA FA8750-11-2-0225
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