3,387 research outputs found
Combinatorial Bounds and Characterizations of Splitting Authentication Codes
We present several generalizations of results for splitting authentication
codes by studying the aspect of multi-fold security. As the two primary
results, we prove a combinatorial lower bound on the number of encoding rules
and a combinatorial characterization of optimal splitting authentication codes
that are multi-fold secure against spoofing attacks. The characterization is
based on a new type of combinatorial designs, which we introduce and for which
basic necessary conditions are given regarding their existence.Comment: 13 pages; to appear in "Cryptography and Communications
Information Theoretic Authentication and Secrecy Codes in the Splitting Model
In the splitting model, information theoretic authentication codes allow
non-deterministic encoding, that is, several messages can be used to
communicate a particular plaintext. Certain applications require that the
aspect of secrecy should hold simultaneously. Ogata-Kurosawa-Stinson-Saido
(2004) have constructed optimal splitting authentication codes achieving
perfect secrecy for the special case when the number of keys equals the number
of messages. In this paper, we establish a construction method for optimal
splitting authentication codes with perfect secrecy in the more general case
when the number of keys may differ from the number of messages. To the best
knowledge, this is the first result of this type.Comment: 4 pages (double-column); to appear in Proc. 2012 International Zurich
Seminar on Communications (IZS 2012, Zurich
Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes
It is a standard result in the theory of quantum error-correcting codes that
no code of length n can fix more than n/4 arbitrary errors, regardless of the
dimension of the coding and encoded Hilbert spaces. However, this bound only
applies to codes which recover the message exactly. Naively, one might expect
that correcting errors to very high fidelity would only allow small violations
of this bound. This intuition is incorrect: in this paper we describe quantum
error-correcting codes capable of correcting up to (n-1)/2 arbitrary errors
with fidelity exponentially close to 1, at the price of increasing the size of
the registers (i.e., the coding alphabet). This demonstrates a sharp
distinction between exact and approximate quantum error correction. The codes
have the property that any components reveal no information about the
message, and so they can also be viewed as error-tolerant secret sharing
schemes.
The construction has several interesting implications for cryptography and
quantum information theory. First, it suggests that secret sharing is a better
classical analogue to quantum error correction than is classical error
correction. Second, it highlights an error in a purported proof that verifiable
quantum secret sharing (VQSS) is impossible when the number of cheaters t is
n/4. More generally, the construction illustrates a difference between exact
and approximate requirements in quantum cryptography and (yet again) the
delicacy of security proofs and impossibility results in the quantum model.Comment: 14 pages, no figure
Multiply Constant-Weight Codes and the Reliability of Loop Physically Unclonable Functions
We introduce the class of multiply constant-weight codes to improve the
reliability of certain physically unclonable function (PUF) response. We extend
classical coding methods to construct multiply constant-weight codes from known
-ary and constant-weight codes. Analogues of Johnson bounds are derived and
are shown to be asymptotically tight to a constant factor under certain
conditions. We also examine the rates of the multiply constant-weight codes and
interestingly, demonstrate that these rates are the same as those of
constant-weight codes of suitable parameters. Asymptotic analysis of our code
constructions is provided
Leakage-resilient Algebraic Manipulation Detection Codes with Optimal Parameters
Algebraic Manipulation Detection (AMD) codes [CDF+08] are keyless message
authentication codes that protect messages against additive tampering by the
adversary assuming that the adversary cannot see the codeword. For certain
applications, it is unreasonable to assume that the adversary computes the
added offset without any knowledge of the codeword c. Recently, Ahmadi and
Safavi-Naini [AS13], and then Lin, Safavi-Naini, and Wang [LSW16] gave a construction
of leakage-resilient AMD codes where the adversary has some partial
information about the codeword before choosing added offset, and the scheme
is secure even conditioned on this partial information.
In this paper we show the bounds on the leakage rate r and the code rate k
for leakage-resilient AMD codes. In particular we prove that 2r + k < 1 and for
the weak case (security is averaged over a uniformly random message) r + k < 1.
These bounds hold even if adversary is polynomial-time bounded, as long as we
allow leakage function to be arbitrary.
We present the constructions of AMD codes that (asymptotically) fulfill
above bounds for almost full range of parameters r and k. This shows that
above bounds and constructions are in-fact optimal.
In the last section we show that if a leakage function is computationally
bounded (we use Ideal Cipher Model) then it is possible to break these bounds
Constructing Optimal Authentication Codes with Perfect Multi-fold Secrecy
We establish a construction of optimal authentication codes achieving perfect
multi-fold secrecy by means of combinatorial designs. This continues the
author's work (ISIT 2009) and answers an open question posed therein. As an
application, we present the first infinite class of optimal codes that provide
two-fold security against spoofing attacks and at the same time perfect two-
fold secrecy.Comment: 4 pages (double-column); to appear in Proc. 2010 International Zurich
Seminar on Communications (IZS 2010, Zurich
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