64 research outputs found
Anonymous quantum communication
We present the first protocol for the anonymous transmission of a quantum
state that is information-theoretically secure against an active adversary,
without any assumption on the number of corrupt participants. The anonymity of
the sender and receiver is perfectly preserved, and the privacy of the quantum
state is protected except with exponentially small probability. Even though a
single corrupt participant can cause the protocol to abort, the quantum state
can only be destroyed with exponentially small probability: if the protocol
succeeds, the state is transferred to the receiver and otherwise it remains in
the hands of the sender (provided the receiver is honest).Comment: 11 pages, to appear in Proceedings of ASIACRYPT, 200
On Albanese torsors and the elementary obstruction
We show that the elementary obstruction to the existence of 0-cycles of
degree 1 on an arbitrary variety X (over an arbitrary field) can be expressed
in terms of the Albanese 1-motives associated with dense open subsets of X.
Arithmetic applications are given
Sur la p-dimension des corps
Let A be an excellent integral henselian local noetherian ring, k its residue
field of characteristic p>0 and K its fraction field. Using an algebraization
technique introduced by the first named author, and the one-dimension case
already proved by Kazuya KATO, we prove the following formula: cd_p(K) = dim(A)
+ p-rank(k), if k is separably closed and K of characteristic zero. A similar
statement is valid without those assumptions on k and K
On the -supports of a holonomic -module
For a smooth variety over a perfect field of positive characteristic, the
sheaf of crystalline differential operators on (also called the sheaf
of -differential operators) is known to be an Azumaya algebra over
the cotangent space of the Frobenius twist of Thus to a
sheaf of modules over one can assign a closed subvariety of
called the -support, namely the support of seen as a sheaf
on We study here the family of -supports assigned to the
reductions modulo primes of a holonomic -module. We prove that
the Azumaya algebra of differential operators splits on the regular locus of
the -support and that the -support is a Lagrangian subvariety of the
cotangent space, for large enough. The latter was conjectured by
Kontsevich. Our approach also provides a new proof of the involutivity of the
singular support of a holonomic -module, by reduction modulo Comment: The article has been rewritten with much improved exposition as well
as some additional results, e.g. Corollary 6.3.1. This is the final version,
accepted for publication in Inventiones Mathematica
Unitary structure in representations of infinite-dimensional groups and a convexity theorem
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46611/1/222_2005_Article_BF01388487.pd
CommitCoin: Carbon Dating Commitments with Bitcoin
Abstract. In the standard definition of a commitment scheme, the sender commits to a message and immediately sends the commitment to the recipient interested in it. However the sender may not always know at the time of commitment who will become interested in verifying it. Further, when the interested party does emerge, it could be critical to establish when the commitment was made. Employing a proof of work protocol at commitment time will later allow anyone to “carbon date ” when the commitment was made, approximately, without trusting any external parties. We present CommitCoin, an instantiation of this approach that harnesses the existing processing power of the Bitcoin peer-to-peer network; a network used to mint and trade digital cash. 1 Introductory Remarks Consider the scenario where Alice makes an important discovery. It is important to her that she receives recognition for her breakthrough, however she would also like to keep it a secret until she can establish a suitable infrastructure for monetizing it. By forgoing publication of her discovery, she risks Bob independently making the same discovery and publicizing it as his own. Folklore suggests that Alice might mail herself a copy of her discovery and leave the letter sealed, with the postal service’s timestamp intact, for a later resolution time. If Bob later claims the same discovery, th
Securing Abe\u27s Mix-net Against Malicious Verifiers via Witness Indistinguishability
We show that the simple and appealing unconditionally sound mix-net due to Abe (Asiacrypt\u2799) can be augmented to further guarantee anonymity against malicious verifiers. This additional guarantee implies, in particular, that when applying the Fiat-Shamir transform to the mix-net\u27s underlying sub-protocols, anonymity is provably guaranteed for {\em any} hash function.
As our main contribution, we demonstrate how anonymity can be attained, even if most sub-protocols of a mix-net are merely witness indistinguishable (WI). We instantiate our framework with two variants of Abe\u27s mix-net. In the first variant, ElGamal ciphertexts are replaced by an alternative, yet equally efficient, lossy encryption scheme. In the second variant, new dummy vote ciphertexts are injected prior to the mixing process, and then removed.
Our techniques center on new methods to introduce additional witnesses to the sub-protocols within the proof of security. This, in turn, enables us to leverage the WI guarantees against malicious verifiers. In our first instantiation, these witnesses follow somewhat naturally from the lossiness of the encryption scheme, whereas in our second instantiation they follow from leveraging combinatorial properties of the Benes-network. These approaches may be of independent interest.
Finally, we demonstrate cases in Abe\u27s original mix-net (without modification) where only one witness exists, such that if the WI proof leaks information on the (single) witness in these cases, then the system will not be anonymous against malicious verifiers
On Eigenvalues of Random Complexes
We consider higher-dimensional generalizations of the normalized Laplacian
and the adjacency matrix of graphs and study their eigenvalues for the
Linial-Meshulam model of random -dimensional simplicial complexes
on vertices. We show that for , the eigenvalues of
these matrices are a.a.s. concentrated around two values. The main tool, which
goes back to the work of Garland, are arguments that relate the eigenvalues of
these matrices to those of graphs that arise as links of -dimensional
faces. Garland's result concerns the Laplacian; we develop an analogous result
for the adjacency matrix. The same arguments apply to other models of random
complexes which allow for dependencies between the choices of -dimensional
simplices. In the second part of the paper, we apply this to the question of
possible higher-dimensional analogues of the discrete Cheeger inequality, which
in the classical case of graphs relates the eigenvalues of a graph and its edge
expansion. It is very natural to ask whether this generalizes to higher
dimensions and, in particular, whether the higher-dimensional Laplacian spectra
capture the notion of coboundary expansion - a generalization of edge expansion
that arose in recent work of Linial and Meshulam and of Gromov. We show that
this most straightforward version of a higher-dimensional discrete Cheeger
inequality fails, in quite a strong way: For every and , there is a -dimensional complex on vertices that
has strong spectral expansion properties (all nontrivial eigenvalues of the
normalised -dimensional Laplacian lie in the interval
) but whose coboundary expansion is bounded
from above by and so tends to zero as ;
moreover, can be taken to have vanishing integer homology in dimension
less than .Comment: Extended full version of an extended abstract that appeared at SoCG
2012, to appear in Israel Journal of Mathematic
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