2,345 research outputs found
An efficient and secure RSA--like cryptosystem exploiting R\'edei rational functions over conics
We define an isomorphism between the group of points of a conic and the set
of integers modulo a prime equipped with a non-standard product. This product
can be efficiently evaluated through the use of R\'edei rational functions. We
then exploit the isomorphism to construct a novel RSA-like scheme. We compare
our scheme with classic RSA and with RSA-like schemes based on the cubic or
conic equation. The decryption operation of the proposed scheme turns to be two
times faster than RSA, and involves the lowest number of modular inversions
with respect to other RSA-like schemes based on curves. Our solution offers the
same security as RSA in a one-to-one communication and more security in
broadcast applications.Comment: 18 pages, 1 figur
Ring-LWE Cryptography for the Number Theorist
In this paper, we survey the status of attacks on the ring and polynomial
learning with errors problems (RLWE and PLWE). Recent work on the security of
these problems [Eisentr\"ager-Hallgren-Lauter, Elias-Lauter-Ozman-Stange] gives
rise to interesting questions about number fields. We extend these attacks and
survey related open problems in number theory, including spectral distortion of
an algebraic number and its relationship to Mahler measure, the monogenic
property for the ring of integers of a number field, and the size of elements
of small order modulo q.Comment: 20 Page
An Experiment in Ping-Pong Protocol Verification by Nondeterministic Pushdown Automata
An experiment is described that confirms the security of a well-studied class
of cryptographic protocols (Dolev-Yao intruder model) can be verified by
two-way nondeterministic pushdown automata (2NPDA). A nondeterministic pushdown
program checks whether the intersection of a regular language (the protocol to
verify) and a given Dyck language containing all canceling words is empty. If
it is not, an intruder can reveal secret messages sent between trusted users.
The verification is guaranteed to terminate in cubic time at most on a
2NPDA-simulator. The interpretive approach used in this experiment simplifies
the verification, by separating the nondeterministic pushdown logic and program
control, and makes it more predictable. We describe the interpretive approach
and the known transformational solutions, and show they share interesting
features. Also noteworthy is how abstract results from automata theory can
solve practical problems by programming language means.Comment: In Proceedings MARS/VPT 2018, arXiv:1803.0866
Scalable and Secure Aggregation in Distributed Networks
We consider the problem of computing an aggregation function in a
\emph{secure} and \emph{scalable} way. Whereas previous distributed solutions
with similar security guarantees have a communication cost of , we
present a distributed protocol that requires only a communication complexity of
, which we prove is near-optimal. Our protocol ensures perfect
security against a computationally-bounded adversary, tolerates
malicious nodes for any constant (not
depending on ), and outputs the exact value of the aggregated function with
high probability
Quantum cryptography over non-Markovian channels
A set of schemes for secure quantum communication are analyzed under the
influence of non-Markovian channels. By comparing with the corresponding
Markovian cases, it is seen that the average fidelity in all these schemes can
be maintained for relatively longer periods of time. The effects of
non-Markovian noise on a number of facets of quantum cryptography, such as
quantum secure direct communication, deterministic secure quantum communication
and their controlled counterparts, quantum dialogue, quantum key distribution,
quantum key agreement, etc., have been extensively investigated. Specifically,
a scheme for controlled quantum dialogue (CQD) is analyzed over damping,
dephasing and depolarizing non-Markovian channels, and subsequently, the effect
of these non-Markovian channels on the other schemes of secure quantum
communication is deduced from the results obtained for CQD. The damped
non-Markovian channel causes, a periodic revival in the fidelity; while
fidelity is observed to be sustained under the influence of the dephasing
non-Markovian channel. The depolarizing channel, as well as the other
non-Markovian channels discussed here, show that the obtained average fidelity
subjected to noisy environment depends on the strength of coupling between the
quantum system with its surroundings and the number of rounds of quantum
communication involved in a particular scheme.Comment: 11 pages, 6 figure
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