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Breaking Iterated Knapsacks
[chapter]

*
Advances in Cryptology
*

This paper presents an outline of an attack that we have used successfully to

doi:10.1007/3-540-39568-7_27
dblp:conf/crypto/Brickell84
fatcat:oyo2txmemfawbdhhukkgtgujcm
*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 ...##
###
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. ...##
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An experimental study of random knapsack problems

2006
*
Algorithmica
*

We experimentally investigate the number of Pareto optimal

doi:10.1007/s00453-005-1193-7
fatcat:nsqmma6n3zhodlbuqkidrmujd4
*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. ...##
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An Experimental Study of Random Knapsack Problems
[chapter]

2004
*
Lecture Notes in Computer Science
*

We experimentally investigate the number of Pareto optimal

doi:10.1007/978-3-540-30140-0_55
fatcat:ernwloz6qfebrcbvab2znou5hu
*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. ...##
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Hiding information and signatures in trapdoor knapsacks

1978
*
IEEE Transactions on Information Theory
*

Ahwcz--The

doi:10.1109/tit.1978.1055927
fatcat:j7vrf6sfbrfjjplfrs7wt3v4fq
*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. ...##
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Accelerating Greenberg's metho̧d for the computation of knapsack functions

1975
*
Journal of Mathematical Analysis and Applications
*

Submitted by Richard Bellman Greenberg [4] described an interesting procedure based on dynamic programming for generating the

doi:10.1016/0022-247x(75)90202-4
fatcat:33rfnukl2rhppkldvn7tush5om
*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. ...##
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LATTICE BASED TOOLS IN CRYPTANALYSIS FOR PUBLIC KEY CRYPTOGRAPHY

2012
*
Zenodo
*

Similar techniques have since been used to

doi:10.5281/zenodo.3351415
fatcat:rttkitq545cs5aio7nsgg4cmfu
*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. ...##
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A fast algorithm for strongly correlated knapsack problems

1998
*
Discrete Applied Mathematics
*

We consider a variant of the O-1

doi:10.1016/s0166-218x(98)00127-9
fatcat:yzhqziok6vhfhd72dxzm2fkiv4
*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'. ...##
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Comparative Study of Several Intelligent Algorithms for Knapsack Problem

2011
*
Procedia Environmental Sciences
*

Imitation of nature in the current algorithm used for the study of

doi:10.1016/j.proenv.2011.12.025
fatcat:mvzg7up5jve5tnwo5rftpy74re
*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). ...##
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An Efficient Hybrid Algorithm for the Separable Convex Quadratic Knapsack Problem

2016
*
ACM Transactions on Mathematical Software
*

This paper considers the problem of minimizing a convex, separable quadratic function subject to a

doi:10.1145/2828635
fatcat:mkkmbrxhxncsjlyxlkm3bfmuuy
*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. ...##
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Knapsack Public Key Cryptosystems and Diophantine Approximation
[chapter]

1984
*
Advances in Cryptology
*

These "unusually good" simultaneous Diophantine approximations can be used to

doi:10.1007/978-1-4684-4730-9_1
fatcat:mcbyfnxigza4tplfm3gcekxdpy
*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*. ...##
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Cryptology: From Caesar Ciphers to Public-Key Cryptosystems

1987
*
The College Mathematics Journal
*

This technique is expected to

doi:10.2307/2686311
fatcat:wgfuylucpjaavgrrewnzxipj7q
*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. ...##
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Cryptology: From Caesar Ciphers to Public-key Cryptosystems

1987
*
The College Mathematics Journal
*

This technique is expected to

doi:10.1080/07468342.1987.11973000
fatcat:jq2reew24zh7hcmeam4xxvwguu
*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. ...##
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A Heuristic Algorithm Based on Expectation Efficiency for 0-1 Knapsack Problem

2018
*
International Journal of Innovative Computing, Information and Control
*

(i) Some items are selected with greedy strategy and put into

doi:10.24507/ijicic.14.05.1833
fatcat:op6i7rijafgttd6kjn6hjvyik4
*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*. ...##
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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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