475 research outputs found
Still Wrong Use of Pairings in Cryptography
Several pairing-based cryptographic protocols are recently proposed with a
wide variety of new novel applications including the ones in emerging
technologies like cloud computing, internet of things (IoT), e-health systems
and wearable technologies. There have been however a wide range of incorrect
use of these primitives. The paper of Galbraith, Paterson, and Smart (2006)
pointed out most of the issues related to the incorrect use of pairing-based
cryptography. However, we noticed that some recently proposed applications
still do not use these primitives correctly. This leads to unrealizable,
insecure or too inefficient designs of pairing-based protocols. We observed
that one reason is not being aware of the recent advancements on solving the
discrete logarithm problems in some groups. The main purpose of this article is
to give an understandable, informative, and the most up-to-date criteria for
the correct use of pairing-based cryptography. We thereby deliberately avoid
most of the technical details and rather give special emphasis on the
importance of the correct use of bilinear maps by realizing secure
cryptographic protocols. We list a collection of some recent papers having
wrong security assumptions or realizability/efficiency issues. Finally, we give
a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page
Resolvents of R-Diagonal Operators
We consider the resolvent of any -diagonal operator
in a -factor. Our main theorem gives a universal asymptotic
formula for the norm of such a resolvent. En route to its proof, we calculate
the -transform of the operator where is Voiculescu's
circular operator, and give an asymptotic formula for the negative moments of
for any -diagonal . We use a mixture of complex analytic
and combinatorial techniques, each giving finer information where the other can
give only coarse detail. In particular, we introduce {\em partition structure
diagrams}, a new combinatorial structure arising in free probability.Comment: 29 pages, 12 figures, used gastex.st
A Practical Second-Order Fault Attack against a Real-World Pairing Implementation
Several fault attacks against pairing-based
cryptography have been described theoretically in recent
years. Interestingly, none of these have been practically
evaluated. We accomplished this task and prove that fault
attacks against pairing-based cryptography are indeed
possible and are even practical — thus posing a serious
threat. Moreover, we successfully conducted a second-order fault attack against an open source implementation
of the eta pairing on an AVR XMEGA A1. We injected
the first fault into the computation of the Miller Algorithm
and applied the second fault to skip the final exponentiation completely. We introduce a low-cost setup that
allowed us to generate multiple independent faults in one
computation. The setup implements these faults by clock
glitches which induce instruction skips. With this setup we
conducted the first practical fault attack against a complete
pairing computation
Topological phase transitions in multi-component superconductors
We study the phase transition between a trivial and a time-reversal-invariant
topological superconductor in a single-band system. By analyzing the interplay
of symmetry, topology and energetics, we show that for a generic normal state
band structure, the phase transition occurs via extended intermediate phases in
which even- and odd-parity pairing components coexist. For inversion-symmetric
systems, the coexistence phase spontaneously breaks time-reversal symmetry. For
noncentrosymmetric superconductors, the low-temperature intermediate phase is
time-reversal breaking, while the high-temperature phase preserves
time-reversal symmetry and has topologically protected line nodes. Furthermore,
with approximate rotational invariance, the system has an emergent symmetry, and novel topological defects, such as half vortex lines
binding Majorana fermions, can exist. We analytically solve for the dispersion
of the Majorana fermion and show that it exhibit small and large velocities at
low and high energies. Relevance of our theory to superconducting pyrochlore
oxide CdReO and half-Heusler materials is discussed.Comment: 14 pages, 7 figures; to appear on Phys. Rev. Let
Still Wrong Use of Pairings in Cryptography
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Several pairing-based cryptographic protocols are recently
proposed with a wide variety of new novel applications including the ones
in emerging technologies like cloud computing, internet of things (IoT),
e-health systems and wearable technologies. There have been however a
wide range of incorrect use of these primitives. The paper of Galbraith,
Paterson, and Smart (2006) pointed out most of the issues related to the
incorrect use of pairing-based cryptography. However, we noticed that
some recently proposed applications still do not use these primitives correctly.
This leads to unrealizable, insecure or too ine cient designs of
pairing-based protocols. We observed that one reason is not being aware
of the recent advancements on solving the discrete logarithm problems in
some groups. The main purpose of this article is to give an understandable,
informative, and the most up-to-date criteria for the correct use of
pairing-based cryptography. We thereby deliberately avoid most of the
technical details and rather give special emphasis on the importance of
the correct use of bilinear maps by realizing secure cryptographic protocols.
We list a collection of some recent papers having wrong security
assumptions or realizability/e ciency issues. Finally, we give a compact
and an up-to-date recipe of the correct use of pairings
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