61 research outputs found
On Error Decoding of Locally Repairable and Partial MDS Codes
We consider error decoding of locally repairable codes (LRC) and partial MDS
(PMDS) codes through interleaved decoding. For a specific class of LRCs we
investigate the success probability of interleaved decoding. For PMDS codes we
show that there is a wide range of parameters for which interleaved decoding
can increase their decoding radius beyond the minimum distance with the
probability of successful decoding approaching , when the code length goes
to infinity
Hot exciton transport in ZnSe quantum wells
The in-plane transport of excitons in ZnSe quantum wells is investigated
directly by microphotoluminescence in combination with a solid immersion lens.
Due to the strong Froehlich coupling, the initial kinetic energy of the
excitons is well controlled by choosing the excess energy of the excitation
laser. When increasing the laser excess energy, we find a general trend of
increasing transport length and more importantly a pronounced periodic
quenching of the transport length when the excess energy corresponds to
multiples of the LO-phonon energy. Such features show the dominant role of the
kinetic energy of excitons in the transport process. Together with the
excitation intensity dependence of the transport length, we distinguish the
phonon wind driven transport of cold excitons and defect-limited hot exciton
transport.Comment: 4 pages, 4 figure
Partial MDS Codes with Local Regeneration
Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure codes
that combine locality with strong erasure correction capabilities. We construct
PMDS and SD codes where each local code is a bandwidth-optimal regenerating MDS
code. The constructions require significantly smaller field size than the only
other construction known in literature
LIGA: A Cryptosystem Based on the Hardness of Rank-Metric List and Interleaved Decoding
We propose the new rank-metric code-based cryptosystem LIGA which is based on
the hardness of list decoding and interleaved decoding of Gabidulin codes. LIGA
is an improved variant of the Faure-Loidreau (FL) system, which was broken in a
structural attack by Gaborit, Otmani, and Tal\'e Kalachi (GOT, 2018). We keep
the FL encryption and decryption algorithms, but modify the insecure key
generation algorithm. Our crucial observation is that the GOT attack is
equivalent to decoding an interleaved Gabidulin code. The new key generation
algorithm constructs public keys for which all polynomial-time interleaved
decoders fail---hence LIGA resists the GOT attack. We also prove that the
public-key encryption version of LIGA is IND-CPA secure in the standard model
and the KEM version is IND-CCA2 secure in the random oracle model, both under
hardness assumptions of formally defined problems related to list decoding and
interleaved decoding of Gabidulin codes. We propose and analyze various
exponential-time attacks on these problems, calculate their work factors, and
compare the resulting parameters to NIST proposals. The strengths of LIGA are
short ciphertext sizes and (relatively) small key sizes. Further, LIGA
guarantees correct decryption and has no decryption failure rate. It is not
based on hiding the structure of a code. Since there are efficient and
constant-time algorithms for encoding and decoding Gabidulin codes, timing
attacks on the encryption and decryption algorithms can be easily prevented.Comment: Extended version of arXiv:1801.0368
Information- and Coding-Theoretic Analysis of the RLWE Channel
Several cryptosystems based on the \emph{Ring Learning with Errors} (RLWE)
problem have been proposed within the NIST post-quantum cryptography
standardization process, e.g. NewHope. Furthermore, there are systems like
Kyber which are based on the closely related MLWE assumption. Both previously
mentioned schemes feature a non-zero decryption failure rate (DFR). The
combination of encryption and decryption for these kinds of algorithms can be
interpreted as data transmission over noisy channels. To the best of our
knowledge this paper is the first work that analyzes the capacity of this
channel. We show how to modify the encryption schemes such that the input
alphabets of the corresponding channels are increased. In particular, we
present lower bounds on their capacities which show that the transmission rate
can be significantly increased compared to standard proposals in the
literature. Furthermore, under the common assumption of stochastically
independent coefficient failures, we give lower bounds on achievable rates
based on both the Gilbert-Varshamov bound and concrete code constructions using
BCH codes. By means of our constructions, we can either increase the total
bitrate (by a factor of for Kyber and by factor of for NewHope)
while guaranteeing the same \emph{decryption failure rate} (DFR). Moreover, for
the same bitrate, we can significantly reduce the DFR for all schemes
considered in this work (e.g., for NewHope from to ).Comment: 13 pages, 4 figures, 3 table
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