5,480 research outputs found
Group theory in cryptography
This paper is a guide for the pure mathematician who would like to know more
about cryptography based on group theory. The paper gives a brief overview of
the subject, and provides pointers to good textbooks, key research papers and
recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor
typographical changes. To appear in Proceedings of Groups St Andrews 2009 in
Bath, U
Quantum Cryptography Beyond Quantum Key Distribution
Quantum cryptography is the art and science of exploiting quantum mechanical
effects in order to perform cryptographic tasks. While the most well-known
example of this discipline is quantum key distribution (QKD), there exist many
other applications such as quantum money, randomness generation, secure two-
and multi-party computation and delegated quantum computation. Quantum
cryptography also studies the limitations and challenges resulting from quantum
adversaries---including the impossibility of quantum bit commitment, the
difficulty of quantum rewinding and the definition of quantum security models
for classical primitives. In this review article, aimed primarily at
cryptographers unfamiliar with the quantum world, we survey the area of
theoretical quantum cryptography, with an emphasis on the constructions and
limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference
Insecurity of Quantum Secure Computations
It had been widely claimed that quantum mechanics can protect private
information during public decision in for example the so-called two-party
secure computation. If this were the case, quantum smart-cards could prevent
fake teller machines from learning the PIN (Personal Identification Number)
from the customers' input. Although such optimism has been challenged by the
recent surprising discovery of the insecurity of the so-called quantum bit
commitment, the security of quantum two-party computation itself remains
unaddressed. Here I answer this question directly by showing that all
``one-sided'' two-party computations (which allow only one of the two parties
to learn the result) are necessarily insecure. As corollaries to my results,
quantum one-way oblivious password identification and the so-called quantum
one-out-of-two oblivious transfer are impossible. I also construct a class of
functions that cannot be computed securely in any ``two-sided'' two-party
computation. Nevertheless, quantum cryptography remains useful in key
distribution and can still provide partial security in ``quantum money''
proposed by Wiesner.Comment: The discussion on the insecurity of even non-ideal protocols has been
greatly extended. Other technical points are also clarified. Version accepted
for publication in Phys. Rev.
Letter counting: a stem cell for Cryptology, Quantitative Linguistics, and Statistics
Counting letters in written texts is a very ancient practice. It has
accompanied the development of Cryptology, Quantitative Linguistics, and
Statistics. In Cryptology, counting frequencies of the different characters in
an encrypted message is the basis of the so called frequency analysis method.
In Quantitative Linguistics, the proportion of vowels to consonants in
different languages was studied long before authorship attribution. In
Statistics, the alternation vowel-consonants was the only example that Markov
ever gave of his theory of chained events. A short history of letter counting
is presented. The three domains, Cryptology, Quantitative Linguistics, and
Statistics, are then examined, focusing on the interactions with the other two
fields through letter counting. As a conclusion, the eclectism of past
centuries scholars, their background in humanities, and their familiarity with
cryptograms, are identified as contributing factors to the mutual enrichment
process which is described here
On the Duality of Probing and Fault Attacks
In this work we investigate the problem of simultaneous privacy and integrity
protection in cryptographic circuits. We consider a white-box scenario with a
powerful, yet limited attacker. A concise metric for the level of probing and
fault security is introduced, which is directly related to the capabilities of
a realistic attacker. In order to investigate the interrelation of probing and
fault security we introduce a common mathematical framework based on the
formalism of information and coding theory. The framework unifies the known
linear masking schemes. We proof a central theorem about the properties of
linear codes which leads to optimal secret sharing schemes. These schemes
provide the lower bound for the number of masks needed to counteract an
attacker with a given strength. The new formalism reveals an intriguing duality
principle between the problems of probing and fault security, and provides a
unified view on privacy and integrity protection using error detecting codes.
Finally, we introduce a new class of linear tamper-resistant codes. These are
eligible to preserve security against an attacker mounting simultaneous probing
and fault attacks
Brief History of Quantum Cryptography: A Personal Perspective
Quantum cryptography is the only approach to privacy ever proposed that
allows two parties (who do not share a long secret key ahead of time) to
communicate with provably perfect secrecy under the nose of an eavesdropper
endowed with unlimited computational power and whose technology is limited by
nothing but the fundamental laws of nature. This essay provides a personal
historical perspective on the field. For the sake of liveliness, the style is
purposely that of a spontaneous after-dinner speech.Comment: 14 pages, no figure
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