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Solving a class of modular polynomial equations and its relation to modular inversion hidden number problem and inversive congruential generator

Jun Xu, Santanu Sarkar, Lei Hu, Zhangjie Huang, Liqiang Peng
2017 Designs, Codes and Cryptography  
In this paper we revisit the modular inversion hidden number problem (MIHNP) and the inversive congruential generator (ICG) and consider how to attack them more efficiently.  ...  In the first strategy, we use the polynomial number of samples and get the same asymptotic bound on attacking ICG proposed in PKC 2012, which is the best result so far.  ...  The authors would like to thank anonymous reviewers for their helpful comments and suggestions.  ... 
doi:10.1007/s10623-017-0435-4 fatcat:r4zq2hloubgkxhudpnzwjmcrgq

"Pseudo-random" number generation within cryptographic algorithms: The DDS case [chapter]

Mihir Bellare, Shafi Goldwasser, Daniele Micciancio
1997 Lecture Notes in Computer Science  
The attack we present applies to truncated linear congruential generators as well, and can be extended to any pseudo random generator that can be described via modular linear equations.  ...  The DSS signature algorithm requires the signer to generate a new random number with every signature.  ...  Acknowledgments The first author is supported in part by a 1996 Packard Foundation Fellowship in Science and Engineering, and NSF CAREER award CCR-9624439.  ... 
doi:10.1007/bfb0052242 fatcat:p4ksnljbyjcsrbw2j3ie34wf2i

Good random number generators are (not so) easy to find

P. Hellekalek
1998 Mathematics and Computers in Simulation  
Every random number generator has its advantages and deficiencies. There are no"safe" generators. The practitioner's problem is how to decide which random number generator will suit his needs best.  ...  We will compare the different methods and supply numerical results as well as selected pointers and links to important literature and other sources.  ...  Acknowledgements I would like to thank my research assistants Stefan Wegenkittl, who has carried out the necessary computations for the figures in Section 7, and Karl Entacher, who has calculated Table  ... 
doi:10.1016/s0378-4754(98)00078-0 fatcat:cqaxq742ezeqlcmnx77mezudra

Non-injective knapsack public-key cryptosystems

Jukka A. Koskinen
2001 Theoretical Computer Science  
The speciÿc form of the proposal uses also one large non-injective component, which is generated and decrypted in a way that resembles superincrease.  ...  Two public-key 0-1 knapsack cryptosystems are proposed, that have so high a density and use so weak a modular multiplication as a trapdoor, that known attacks can be avoided.  ...  Generation algorithm This algorithm creates a dense trapdoor knapsack based on the congruential construction and using one large non-injective covering knapsack.  ... 
doi:10.1016/s0304-3975(99)00297-2 fatcat:obysbpyseve4dluzllwmrg6bpu

Random Numbers in Scientific Computing: An Introduction [article]

Helmut G. Katzgraber
2010 arXiv   pre-print
The differences, advantages and disadvantages of true and pseudo random number generators are discussed with an emphasis on the intrinsic details of modern and fast pseudo random number generators.  ...  Potential problems that one might encounter when using large parallel machines are discussed.  ...  Acknowledgments I would like to thank Juan Carlos Andresen, Ruben Andrist and Creighton K. Thomas for critically reading the manuscript.  ... 
arXiv:1005.4117v1 fatcat:pzuxb2kpbfbxzizxx2votqhkvm

Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related Schemes [chapter]

Dan Boneh, Ramarathnam Venkatesan
1996 Lecture Notes in Computer Science  
This is done by studying the following hidden number problem: Given an oracle O ; (x) that on input x computes the k most signicant bits of g x + mod p, nd ; mod p.  ...  Our results lead us to suggest a new variant of Die-Hellman key exchange, for which we prove the most signicant bit is hard to compute.  ...  The proof relies on a new lattice rounding technique to solve the hidden number problem. We intend to query the oracle O at uniformly and independently chosen inputs r 1 ; : : : ; r d .  ... 
doi:10.1007/3-540-68697-5_11 fatcat:s32fy6mjx5donfnt5sdkpwcayq

The Two Faces of Lattices in Cryptology [chapter]

Phong Q. Nguyen
2001 Lecture Notes in Computer Science  
Paradoxically, several positive cryptographic applications of lattices have emerged in the past ve years: there now exist public-key cryptosystems based on the hardness of lattice problems, and lattices  ...  Lattices are regular arrangements of points in n-dimensional space, whose study appeared in the 19th century in both number theory and crystallography.  ...  We thank Dan Boneh, Don Coppersmith, Glenn Durfee, Arjen and Hendrik Lenstra, L aszl o Lov asz, Daniele Micciancio, Igor Shparlinski and Joe Silverman for helpful discussions and comments.  ... 
doi:10.1007/3-540-45537-x_24 fatcat:6gnzxzvjuvftvov3quwup6dg2e

A new class of scalable parallel pseudorandom number generators based on Pohlig-Hellman exponentiation ciphers [article]

Paul D. Beale
2015 arXiv   pre-print
We propose a new scalable class of parallel pseudorandom number generators based on Pohlig--Hellman exponentiation ciphers.  ...  Parallel supercomputer-based Monte Carlo applications depend on pseudorandom number generators that produce independent pseudorandom streams across many separate processes.  ...  This work utilized the Janus supercomputer, which is supported by the National Science Foundation (award number CNS-0821794) and the University of Colorado Boulder.  ... 
arXiv:1411.2484v4 fatcat:xx6wrmjbybhlvmqplzl2mhgaz4

Security Improvement in Elliptic Curve Cryptography

Kawther Esaa Abdullah, Nada Hussein
2018 International Journal of Advanced Computer Science and Applications  
The gained results show the positive effect of the dual elliptic curve system in terms of speed and confidentiality without needing any extra time for encryption.  ...  This paper presents a new generator function to produce the domain parameters for creating the elliptic curve; a secure mechanism is used in the proposed function to avoid all possible known attacks that  ...  So, the subtraction operation is the same addition operation, just take the inverse of i.e, the inverse of ( ) ( ) ( ). RESULTS AND DISCUSSION VII.  ... 
doi:10.14569/ijacsa.2018.090516 fatcat:rly44n3yizfbjlzj6dbc4ch44y

The Insecurity of Esign in Practical Implementations [chapter]

Pierre-Alain Fouque, Nick Howgrave-Graham, Gwenaëlle Martinet, Guillaume Poupard
2003 Lecture Notes in Computer Science  
As an independent result, we show that the factorization problem is equivalent to the existence of an oracle returning the most or least significant bits of S mod p, on input S randomly chosen in Zpq.  ...  However, our results show that random data used to generate signatures must be very carefully produced and protected against any kind of exposure, even partial.  ...  The first problem is that a true random number generator must be based on some kind of physical noise source. Such a generator is not commonly accessible on standard computers.  ... 
doi:10.1007/978-3-540-40061-5_31 fatcat:uqvwollwgjejlf64dp3yqglu24

Inferring Sequences Produced by Nonlinear Pseudorandom Number Generators Using Coppersmith's Methods [chapter]

Aurélie Bauer, Damien Vergnaud, Jean-Christophe Zapalowicz
2012 Lecture Notes in Computer Science  
In 2005, Blackburn, Gomez-Perez, Gutierrez and Shparlinski proposed a deep analysis on the security of such generators.  ...  In this paper, we revisit the security of number-theoretic generators by proposing better attacks based on Coppersmith's techniques for finding small roots on polynomial equations.  ...  Introduction This paper aims to present new cryptanalytic results on some nonlinear numbertheoretic pseudorandom number generators.  ... 
doi:10.1007/978-3-642-30057-8_36 fatcat:jugiuj2oa5andapd76odsqy5ti

Algebraic and Model Theoretic Techniques for Fusion Decidability in Modal Logics [chapter]

Silvio Ghilardi, Luigi Santocanale
2003 Lecture Notes in Computer Science  
We introduce a new method (derived from model theoretic general combination procedures in automated deduction) for proving fusion decidability in modal systems.  ...  Goranko for suggestions on an earlier version of this paper.  ...  We list, among them, extensions with transitive roles [25] , least or greatest fixed point semantics of cyclic terminologies [23] , number restrictions [7] , functional and inverse roles -which we are  ... 
doi:10.1007/978-3-540-39813-4_10 fatcat:xzdq5kc4cra45odldifu3drn4y

Some lattice attacks on DSA and ECDSA

Dimitrios Poulakis
2011 Applicable Algebra in Engineering, Communication and Computing  
In this paper, using the LLL reduction method and computing the integral points of two classes of conics, we develop attacks on DSA and ECDSA in case where the secret and the ephemeral key and their modular  ...  inverse are quite small or quite large.  ...  In [1] it was shown that one can recover the DSA secret key a, if the ephemeral key k is produced by Knuth's linear congruential generator with known parameters, or variants.  ... 
doi:10.1007/s00200-011-0154-4 fatcat:zf34i5utafcv3jsjklid6hjwn4

Towards Practical Implementation of Deep Random Secrecy [article]

Thibault de Valroger
2019 arXiv   pre-print
This article is presenting an optimization technique, based on recombination and reuse of random bits; this technique enables to dramatically increase the bandwidth performance of formerly introduced protocols  ...  The article also summarizes former results in the perspective of a comprehensive implementation.  ...  One can thus apply the result of lemma AII below, and get: [ ([ ] ) ( ) ] √ ( ) ( ) Eventually, the average number of solution [ ] for the linear system: { ( ) ( )} { } is lower bounded by √ ( ) ( ) The  ... 
arXiv:1805.00337v3 fatcat:q3oldikxtzaedlgvtdjdedhhkq

On Zaremba's Conjecture [article]

Jean Bourgain, Alex Kontorovich
2013 arXiv   pre-print
We confirm this conjecture for a set of density one.  ...  We thank Curt McMullen for bringing this problem to our attention, and Doug Hensley and Peter Sarnak for many helpful comments regarding this work.  ...  In particular as mentioned in Remark 1.6, McMullen [McM09] made progress on the problem of producing many closed geodesics on the modular surface defined over a fixed real quadratic number field Q( √  ... 
arXiv:1107.3776v2 fatcat:cumyi4mdzff4zcy6fj3fcg3kha
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