292 research outputs found
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An Improved Pseudorandom Generator Based on Hardness of Factoring
We present a simple to implement and efficient pseudorandom generator based on the factoring assumption. It outputs more than pn/2 pseudorandom bits per p exponentiations, each with the same base and an exponent shorter than n/2 bits. Our generator is based on results by Hastad, Schrift and Shamir
[HSS93], but unlike their generator and its improvement by Goldreich and Rosen [GR00], it does not use hashing or extractors, and is thus simpler and somewhat more efficient.
In addition, we present a general technique that can be used to speed up pseudorandom generators based on iterating one-way permutations. We construct our generator by applying this technique to results of [HSS93]. We also show how the generator given by Gennaro [Gen00] can be simply derived from results of Patel and Sundaram [PS98a] using our technique.Engineering and Applied Science
Periodic Structure of the Exponential Pseudorandom Number Generator
We investigate the periodic structure of the exponential pseudorandom number
generator obtained from the map that acts on the set
Short Cycles in Repeated Exponentiation Modulo a Prime
Given a prime , we consider the dynamical system generated by repeated
exponentiations modulo , that is, by the map , where
and . This map is in
particular used in a number of constructions of cryptographically secure
pseudorandom generators. We obtain nontrivial upper bounds on the number of
fixed points and short cycles in the above dynamical system
On the Possibility of a Backdoor in the Micali-Schnorr Generator
In this paper, we study both the implications and potential impact of backdoored parameters for two RSA-based pseudorandom number generators: the ISO-standardized Micali-Schnorr generator and a closely related design, the RSA PRG. We observe, contrary to common understanding, that the security of the Micali-Schnorr PRG is not tightly bound to the difficulty of inverting RSA. We show that the Micali-Schnorr construction remains secure even if one replaces RSA with a publicly evaluatable PRG, or a function modeled as an efficiently invertible random permutation. This implies that any cryptographic backdoor must somehow exploit the algebraic structure of RSA, rather than an attacker\u27s ability to invert RSA or the presence of secret keys. We exhibit two such backdoors in related constructions: a family of exploitable parameters for the RSA PRG, and a second vulnerable construction for a finite-field variant of Micali-Schnorr. We also observe that the parameters allowed by the ISO standard are incompletely specified, and allow insecure choices of exponent. Several of our backdoor constructions make use of lattice techniques, in particular multivariate versions of Coppersmith\u27s method for finding small solutions to polynomials modulo integers
On the Provable Security of an Efficient RSA-Based Pseudorandom Generator
Pseudorandom Generators (PRGs) based on the RSA inversion
(one-wayness) problem have been extensively studied in the
literature over the last 25 years. These generators have the
attractive feature of provable pseudorandomness security assuming
the hardness of the RSA inversion problem. However, despite
extensive study, the most efficient provably secure RSA-based
generators output asymptotically only at most bits per
multiply modulo an RSA modulus of bitlength , and hence are too
slow to be used in many practical applications.
To bring theory closer to practice, we present a simple
modification to the proof of security by Fischlin and Schnorr of
an RSA-based PRG, which shows that one can obtain an RSA-based PRG
which outputs bits per multiply and has provable
pseudorandomness security assuming the hardness of a well-studied
variant of the RSA inversion problem, where a constant fraction of
the plaintext bits are given. Our result gives a positive answer to an open question posed by Gennaro (J. of Cryptology, 2005) regarding finding a PRG beating the rate bits per multiply at the cost of a reasonable assumption on RSA inversion
IMPROVING SMART GRID SECURITY USING MERKLE TREES
Abstract—Presently nations worldwide are starting to convert their aging electrical power infrastructures into modern, dynamic power grids. Smart Grid offers much in the way of efficiencies and robustness to the electrical power grid, however its heavy reliance on communication networks will leave it more vulnerable to attack than present day grids. This paper looks at the threat to public key cryptography systems from a fully realized quantum computer and how this could impact the Smart Grid. We argue for the use of Merkle Trees in place of public key cryptography for authentication of devices in wireless mesh networks that are used in Smart Grid applications
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