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Breaking Iterated Knapsacks [chapter]

Ernest F. Brickell
Advances in Cryptology  
This paper presents an outline of an attack that we have used successfully to break iterated knapsacks.  ...  Since each iteration lowers the information rate, these methods will break a knapsack cryptosystem if it has been iterated too many times .  ...  Since a knapsack of this size would require This algorithm will also break Shamir's ultimate knapsack [ I 4 1 It appears that the algorithm can be modified to break the knapsackthat Brickell presented  ... 
doi:10.1007/3-540-39568-7_27 dblp:conf/crypto/Brickell84 fatcat:oyo2txmemfawbdhhukkgtgujcm

Page 1660 of Mathematical Reviews Vol. , Issue 87c [page]

1987 Mathematical Reviews  
Author summary: “We present an outline of an attack that we have used successfully to break iterated knapsacks.  ...  Lieberman (Princeton, N.J.) 87c:94035 Brickell, Ernest F. (1-SAND) Breaking iterated knapsacks. Advances in cryptology (Santa Barbara, Calif., 1984), 342-358, Lecture Notes in Comput.  ... 

An experimental study of random knapsack problems

Rene Beier, Berthold Vöcking
2006 Algorithmica  
We experimentally investigate the number of Pareto optimal knapsack fillings.  ...  In the second part we study advanced algorithmic techniques for the knapsack problem.  ...  This item is called break item and the computed knapsack filling, not including the break item, is called the break solution.  ... 
doi:10.1007/s00453-005-1193-7 fatcat:nsqmma6n3zhodlbuqkidrmujd4

An Experimental Study of Random Knapsack Problems [chapter]

Rene Beier, Berthold Vöcking
2004 Lecture Notes in Computer Science  
We experimentally investigate the number of Pareto optimal knapsack fillings.  ...  In the second part we study advanced algorithmic techniques for the knapsack problem.  ...  This item is called break item and the computed knapsack filling, not including the break item, is called the break solution.  ... 
doi:10.1007/978-3-540-30140-0_55 fatcat:ernwloz6qfebrcbvab2znou5hu

Hiding information and signatures in trapdoor knapsacks

R. Merkle, M. Hellman
1978 IEEE Transactions on Information Theory  
Ahwcz--The knapsack problem is aa Np-complete combinatorial problem that is strongly believed to be computationally difficult to solve in general.  ...  with each iteration.  ...  It is possible, however, to use the iterative method of Section IV to obtain a solution density of approximately l/l@ with two iterations or l/lo6 with three iterations when n = 100.  ... 
doi:10.1109/tit.1978.1055927 fatcat:j7vrf6sfbrfjjplfrs7wt3v4fq

Accelerating Greenberg's metho̧d for the computation of knapsack functions

Jonathan S Yormark
1975 Journal of Mathematical Analysis and Applications  
Submitted by Richard Bellman Greenberg [4] described an interesting procedure based on dynamic programming for generating the knapsack function @p(s) = max{cx: ax < s, x > 0, integer) for all arguments  ...  In such a case the payoffs corresponding to the alternative minima must also be examined in order to break ties.  ...  At any iteration K of the procedure as many as Kn sums yl-r + ui may have to be examined to determine the minimum, the K-th knapsack point.  ... 
doi:10.1016/0022-247x(75)90202-4 fatcat:33rfnukl2rhppkldvn7tush5om

LATTICE BASED TOOLS IN CRYPTANALYSIS FOR PUBLIC KEY CRYPTOGRAPHY

R. Santosh Kumar, C. Narasimham, S. Pallam Setty
2012 Zenodo  
Similar techniques have since been used to break most knapsacks schemes that have been proposed, including the multiple-iterated Merkle-Hellman scheme.  ...  This technique, in turn can be applied to break knapsack cryptosystems like Merkle-Hellman knapsack cryptosystem.  ... 
doi:10.5281/zenodo.3351415 fatcat:rttkitq545cs5aio7nsgg4cmfu

A fast algorithm for strongly correlated knapsack problems

David Pisinger
1998 Discrete Applied Mathematics  
We consider a variant of the O-1 Knapsack Problem, where the profit of each item corresponds to its weight plus a fixed constant.  ...  These so-called Strongly Correlated Knapsack Problems have attained much interest due to their apparent hardness and wide applicability in several fixedcharge problems.  ...  The weight of the break solution is L" = cj:i wj and the residual capacity of the knapsack is r = c -v'.  ... 
doi:10.1016/s0166-218x(98)00127-9 fatcat:yzhqziok6vhfhd72dxzm2fkiv4

Comparative Study of Several Intelligent Algorithms for Knapsack Problem

Jing Zhang
2011 Procedia Environmental Sciences  
Imitation of nature in the current algorithm used for the study of knapsack problem, solutions that approach seems to have become a bottleneck limit break, if we can design a new solution easier to produce  ...  Increase the number of iterations k, if k reaches the maximum number of iterations, stop iteration; otherwise return to Step (3).  ... 
doi:10.1016/j.proenv.2011.12.025 fatcat:mvzg7up5jve5tnwo5rftpy74re

An Efficient Hybrid Algorithm for the Separable Convex Quadratic Knapsack Problem

Timothy A. Davis, William W. Hager, James T. Hungerford
2016 ACM Transactions on Mathematical Software  
This paper considers the problem of minimizing a convex, separable quadratic function subject to a knapsack constraint and a box constraint.  ...  A key innovation in our algorithm is the implementation of a heap data structure for storing the break points of the dual function, and computing the solution of the dual problem.  ...  Given an interval (α, β) containing an optimal dual multiplier λ * associated with the knapsack constraint, the break points on (α, β) are arranged in a heap.  ... 
doi:10.1145/2828635 fatcat:mkkmbrxhxncsjlyxlkm3bfmuuy

Knapsack Public Key Cryptosystems and Diophantine Approximation [chapter]

J. C. Lagarias
1984 Advances in Cryptology  
These "unusually good" simultaneous Diophantine approximations can be used to break multiply iterated knapsack cryptosystems provided one can solve a certain nonlinear Diophantine approximation problem  ...  This nonlinear problem is solved in the simplest case and then used to give a new cryptanalytic attack on doubly iterated knapsack cryptosystems.  ...  is an analogue of Theorem B for multiply iterated knapsacks.  ... 
doi:10.1007/978-1-4684-4730-9_1 fatcat:mcbyfnxigza4tplfm3gcekxdpy

Cryptology: From Caesar Ciphers to Public-Key Cryptosystems

Dennis Luciano, Gordon Prichett
1987 The College Mathematics Journal  
This technique is expected to break a 1000-weights, 40-iterations cipher in 750 hours on the same computer [3] .  ...  He found a way to use a single function to change the multiple iterations into an easy knapsack problem.  ... 
doi:10.2307/2686311 fatcat:wgfuylucpjaavgrrewnzxipj7q

Cryptology: From Caesar Ciphers to Public-key Cryptosystems

Dennis Luciano, Gordon Prichett
1987 The College Mathematics Journal  
This technique is expected to break a 1000-weights, 40-iterations cipher in 750 hours on the same computer [3] .  ...  He found a way to use a single function to change the multiple iterations into an easy knapsack problem.  ... 
doi:10.1080/07468342.1987.11973000 fatcat:jq2reew24zh7hcmeam4xxvwguu

A Heuristic Algorithm Based on Expectation Efficiency for 0-1 Knapsack Problem

Lingling Zhang, Jianhui Lv
2018 International Journal of Innovative Computing, Information and Control  
(i) Some items are selected with greedy strategy and put into knapsack.  ...  0-1 Knapsack Problem (KP01) is a classical NP-hard problem and it plays an important role in real-world applications.  ...  into knapsack; the 20th iteration represents that item 7 is loaded into knapsack; the 21st iteration represents that item 11 is loaded into knapsack.  ... 
doi:10.24507/ijicic.14.05.1833 fatcat:op6i7rijafgttd6kjn6hjvyik4

Page 4939 of Mathematical Reviews Vol. , Issue 86j [page]

1986 Mathematical Reviews  
These ‘unusually good’ simultaneous Diophantine approximations can be used to break multiply iterated knapsack cryptosystems, provided one can solve a certain nonlinear Diophantine approximation problem  ...  This nonlinear problem is solved in the simplest case and then used to give a new cryptanalytic attack on doubly iterated knapsack cryptosystems.” {For the entire collection see MR 86f:94001.}  ... 
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