3,714 research outputs found
Lattice-Based Group Signatures: Achieving Full Dynamicity (and Deniability) with Ease
In this work, we provide the first lattice-based group signature that offers
full dynamicity (i.e., users have the flexibility in joining and leaving the
group), and thus, resolve a prominent open problem posed by previous works.
Moreover, we achieve this non-trivial feat in a relatively simple manner.
Starting with Libert et al.'s fully static construction (Eurocrypt 2016) -
which is arguably the most efficient lattice-based group signature to date, we
introduce simple-but-insightful tweaks that allow to upgrade it directly into
the fully dynamic setting. More startlingly, our scheme even produces slightly
shorter signatures than the former, thanks to an adaptation of a technique
proposed by Ling et al. (PKC 2013), allowing to prove inequalities in
zero-knowledge. Our design approach consists of upgrading Libert et al.'s
static construction (EUROCRYPT 2016) - which is arguably the most efficient
lattice-based group signature to date - into the fully dynamic setting.
Somewhat surprisingly, our scheme produces slightly shorter signatures than the
former, thanks to a new technique for proving inequality in zero-knowledge
without relying on any inequality check. The scheme satisfies the strong
security requirements of Bootle et al.'s model (ACNS 2016), under the Short
Integer Solution (SIS) and the Learning With Errors (LWE) assumptions.
Furthermore, we demonstrate how to equip the obtained group signature scheme
with the deniability functionality in a simple way. This attractive
functionality, put forward by Ishida et al. (CANS 2016), enables the tracing
authority to provide an evidence that a given user is not the owner of a
signature in question. In the process, we design a zero-knowledge protocol for
proving that a given LWE ciphertext does not decrypt to a particular message
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
Server-Aided Revocable Predicate Encryption: Formalization and Lattice-Based Instantiation
Efficient user revocation is a necessary but challenging problem in many
multi-user cryptosystems. Among known approaches, server-aided revocation
yields a promising solution, because it allows to outsource the major workloads
of system users to a computationally powerful third party, called the server,
whose only requirement is to carry out the computations correctly. Such a
revocation mechanism was considered in the settings of identity-based
encryption and attribute-based encryption by Qin et al. (ESORICS 2015) and Cui
et al. (ESORICS 2016), respectively.
In this work, we consider the server-aided revocation mechanism in the more
elaborate setting of predicate encryption (PE). The latter, introduced by Katz,
Sahai, and Waters (EUROCRYPT 2008), provides fine-grained and role-based access
to encrypted data and can be viewed as a generalization of identity-based and
attribute-based encryption. Our contribution is two-fold. First, we formalize
the model of server-aided revocable predicate encryption (SR-PE), with rigorous
definitions and security notions. Our model can be seen as a non-trivial
adaptation of Cui et al.'s work into the PE context. Second, we put forward a
lattice-based instantiation of SR-PE. The scheme employs the PE scheme of
Agrawal, Freeman and Vaikuntanathan (ASIACRYPT 2011) and the complete subtree
method of Naor, Naor, and Lotspiech (CRYPTO 2001) as the two main ingredients,
which work smoothly together thanks to a few additional techniques. Our scheme
is proven secure in the standard model (in a selective manner), based on the
hardness of the Learning With Errors (LWE) problem.Comment: 24 page
PPP-Completeness with Connections to Cryptography
Polynomial Pigeonhole Principle (PPP) is an important subclass of TFNP with
profound connections to the complexity of the fundamental cryptographic
primitives: collision-resistant hash functions and one-way permutations. In
contrast to most of the other subclasses of TFNP, no complete problem is known
for PPP. Our work identifies the first PPP-complete problem without any circuit
or Turing Machine given explicitly in the input, and thus we answer a
longstanding open question from [Papadimitriou1994]. Specifically, we show that
constrained-SIS (cSIS), a generalized version of the well-known Short Integer
Solution problem (SIS) from lattice-based cryptography, is PPP-complete.
In order to give intuition behind our reduction for constrained-SIS, we
identify another PPP-complete problem with a circuit in the input but closely
related to lattice problems. We call this problem BLICHFELDT and it is the
computational problem associated with Blichfeldt's fundamental theorem in the
theory of lattices.
Building on the inherent connection of PPP with collision-resistant hash
functions, we use our completeness result to construct the first natural hash
function family that captures the hardness of all collision-resistant hash
functions in a worst-case sense, i.e. it is natural and universal in the
worst-case. The close resemblance of our hash function family with SIS, leads
us to the first candidate collision-resistant hash function that is both
natural and universal in an average-case sense.
Finally, our results enrich our understanding of the connections between PPP,
lattice problems and other concrete cryptographic assumptions, such as the
discrete logarithm problem over general groups
Algorithms on Ideal over Complex Multiplication order
We show in this paper that the Gentry-Szydlo algorithm for cyclotomic orders,
previously revisited by Lenstra-Silverberg, can be extended to
complex-multiplication (CM) orders, and even to a more general structure. This
algorithm allows to test equality over the polarized ideal class group, and
finds a generator of the polarized ideal in polynomial time. Also, the
algorithm allows to solve the norm equation over CM orders and the recent
reduction of principal ideals to the real suborder can also be performed in
polynomial time. Furthermore, we can also compute in polynomial time a unit of
an order of any number field given a (not very precise) approximation of it.
Our description of the Gentry-Szydlo algorithm is different from the original
and Lenstra- Silverberg's variant and we hope the simplifications made will
allow a deeper understanding. Finally, we show that the well-known speed-up for
enumeration and sieve algorithms for ideal lattices over power of two
cyclotomics can be generalized to any number field with many roots of unity.Comment: Full version of a paper submitted to ANT
A Generic Construction of an Anonymous Reputation System and Instantiations from Lattices
With an anonymous reputation system one can realize the process of rating sellers anonymously in an online shop. While raters can stay anonymous, sellers still have the guarantee that they can be only be reviewed by raters who bought their product.We present the first generic construction of a reputation system from basic building blocks, namely digital signatures, encryption schemes, non-interactive zero-knowledge proofs, and linking indistinguishable tags. We then show the security of the reputation system in a strong security model. Among others, we instantiate the generic construction with building blocks based on lattice problems, leading to the first module lattice-based reputation system
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
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