7,481 research outputs found
Finding Significant Fourier Coefficients: Clarifications, Simplifications, Applications and Limitations
Ideas from Fourier analysis have been used in cryptography for the last three
decades. Akavia, Goldwasser and Safra unified some of these ideas to give a
complete algorithm that finds significant Fourier coefficients of functions on
any finite abelian group. Their algorithm stimulated a lot of interest in the
cryptography community, especially in the context of `bit security'. This
manuscript attempts to be a friendly and comprehensive guide to the tools and
results in this field. The intended readership is cryptographers who have heard
about these tools and seek an understanding of their mechanics and their
usefulness and limitations. A compact overview of the algorithm is presented
with emphasis on the ideas behind it. We show how these ideas can be extended
to a `modulus-switching' variant of the algorithm. We survey some applications
of this algorithm, and explain that several results should be taken in the
right context. In particular, we point out that some of the most important bit
security problems are still open. Our original contributions include: a
discussion of the limitations on the usefulness of these tools; an answer to an
open question about the modular inversion hidden number problem
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
A Contribution to Secure the Routing Protocol "Greedy Perimeter Stateless Routing" Using a Symmetric Signature-Based AES and MD5 Hash
This work presents a contribution to secure the routing protocol GPSR (Greedy
Perimeter Stateless Routing) for vehicular ad hoc networks, we examine the
possible attacks against GPSR and security solutions proposed by different
research teams working on ad hoc network security. Then, we propose a solution
to secure GPSR packet by adding a digital signature based on symmetric
cryptography generated using the AES algorithm and the MD5 hash function more
suited to a mobile environment
Review on DNA Cryptography
Cryptography is the science that secures data and communication over the
network by applying mathematics and logic to design strong encryption methods.
In the modern era of e-business and e-commerce the protection of
confidentiality, integrity and availability (CIA triad) of stored information
as well as of transmitted data is very crucial. DNA molecules, having the
capacity to store, process and transmit information, inspires the idea of DNA
cryptography. This combination of the chemical characteristics of biological
DNA sequences and classical cryptography ensures the non-vulnerable
transmission of data. In this paper we have reviewed the present state of art
of DNA cryptography.Comment: 31 pages, 12 figures, 6 table
Discrete Logarithms on Elliptic Curves
Cryptographic protocols often make use of the inherent hardness of the classical discrete logarithm problem, which is to solve gx ≈ y ( mod p ) for x. The hardness of this problem has been exploited in the Diffie-Hellman key exchange, as well as in cryptosystems such as ElGamal. There is a similar discrete logarithm problem on elliptic curves: solve kB = P for k. Therefore, Diffie-Hellman and ElGamal have been adapted for elliptic curves. There is an abundance of evidence suggesting that elliptic curve cryptography is even more secure, which means that we can obtain the same security with fewer bits. In this paper, we investigate the discrete logarithm for elliptic curves over Fp for p ≥ 5 by constructing a function and considering the induced functional graph and the implications for cryptography
A kilobit hidden SNFS discrete logarithm computation
We perform a special number field sieve discrete logarithm computation in a
1024-bit prime field. To our knowledge, this is the first kilobit-sized
discrete logarithm computation ever reported for prime fields. This computation
took a little over two months of calendar time on an academic cluster using the
open-source CADO-NFS software. Our chosen prime looks random, and
has a 160-bit prime factor, in line with recommended parameters for the Digital
Signature Algorithm. However, our p has been trapdoored in such a way that the
special number field sieve can be used to compute discrete logarithms in
, yet detecting that p has this trapdoor seems out of reach.
Twenty-five years ago, there was considerable controversy around the
possibility of back-doored parameters for DSA. Our computations show that
trapdoored primes are entirely feasible with current computing technology. We
also describe special number field sieve discrete log computations carried out
for multiple weak primes found in use in the wild. As can be expected from a
trapdoor mechanism which we say is hard to detect, our research did not reveal
any trapdoored prime in wide use. The only way for a user to defend against a
hypothetical trapdoor of this kind is to require verifiably random primes
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