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Quadratic compact knapsack public-key cryptosystem

2010
*
Computers and Mathematics with Applications
*

We show that the

doi:10.1016/j.camwa.2009.08.031
fatcat:bvwvdczchvftzdmjwpmuzl4bhy
*knapsack*cryptosystem is secure against the*low*-*density*subset-sum attacks by observing that the underlying compact*knapsack*problem has exponentially many solutions. ... However, these cryptosystems were shown to be vulnerable to the*low*-*density*subset-sum attacks or some key-recovery attacks. ...*Low*-*density*subset-sum attacks The basic idea of*low*-*density*attacks is to*solve*the*knapsack*problem with lattice basis reduction algorithms. ...##
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Criticism of Knapsack Encryption Scheme
[article]

2010
*
arXiv
*
pre-print

In this paper, we analyze a

arXiv:1005.4012v1
fatcat:bcuqujcsxrdqjghzh52tublgrq
*knapsack*schemes. The one is suggested by Su, which is relied on a new method entitled permutation combination method. ... We demonstrate that the permutation method is useless to avoid the*low*-*density*attack and the*density*of*knapsack*sequence is lesser than 9408 . 0 . ...*LOW**DENSITY*ATTACKS In this section, we will present the*low**density*attack suggested by Coster [5] which is the modification of Lagarias and Odlyzko attack [4] . ...##
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Cryptanalysis of two knapsack-type public-key cryptosystems

2010
*
2010 International Conference on Computer Application and System Modeling (ICCASM 2010)
*

We show that one can recover the plaintext as long as he

doi:10.1109/iccasm.2010.5622956
fatcat:6u3sc2qqircp7lkrfrinkgvroa
*solve*a*knapsack*problem.Unfounately, this*knapsack*problem can be*solved*by Shamir's method or the*low**density*attack. ... The second one is provided by Su et al [16] , which is based on the elliptic curve discrete logarithm and*knapsack*problem. ... We show that the permutation algorithm is useless to avoid the*low*-*density*attack and the*density*of*knapsack*vector is smaller than 0.9408. ...##
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PKCHD: Towards A Probabilistic Knapsack Public-Key Cryptosystem with High Density

2019
*
Information
*

Under the re-linearization attack model, PKCHD obtains a high

doi:10.3390/info10020075
fatcat:bbs55j7ovjfslph6yxojd4saju
*density*and is secure against the*low*-*density*subset sum attacks, and the success probability for an attacker to recover the message vector ... Meanwhile, it can use the hardest*knapsack*vector as the public key if its*density*evaluates the hardness of a*knapsack*instance. ... When applied to a specific*knapsack*instance, the*low*-*density*attacks depend on the*density*of the*knapsack*. ...##
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Adapting Density Attacks to Low-Weight Knapsacks
[chapter]

2005
*
Lecture Notes in Computer Science
*

To prevent

doi:10.1007/11593447_3
fatcat:us7noxwnofg6lpq3qgwjxmzk6m
*low*-*density*attacks, several designers found a subtle way to increase the*density*beyond the critical*density*by decreasing the weight of the*knapsack*, and possibly allowing non-binary coefficients ... Our results also explain why Schnorr and Hörner were able to*solve*at Eurocrypt '95 certain high-*density**knapsacks*related to the Chor-Rivest cryptosystem, using lattice reduction. n i=1 m i a i , where ... This shows that if the pseudo-*density*κ is ≤ 1, then the right-hand term will be bounded, and therefore the*low*-weight*knapsack*can be*solved*with high probability by a single call to either a SVP-oracle ...##
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A knapsack public-key cryptosystem with cyclic code over $GF(2)$

2010
*
JSIAM Letters
*

The proposed scheme is secure against Shamir's attack and Adleman's attack and invulnerable to the

doi:10.14495/jsiaml.2.29
fatcat:zpfwu7mczbd2bnwyyaiaslfjsa
*low*-*density*attack. ... The*knapsack*PKC is based on the subset sum problem which is NP -hard. In this paper, we propose a*knapsack*PKC with a cyclic code over GF (2) using the Chinese remainder theorem. ... LDA was proposed by Lagarias and Odlyzko for*solving*the subset sum problem of*low**density*[5] . ...##
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A multiple-iterated trapdoor for dense compact knapsacks
[chapter]

1995
*
Lecture Notes in Computer Science
*

The Lagarias-Odlyzko

doi:10.1007/bfb0053429
fatcat:4prg6asq6vcjphiy4e3jhboutu
*low*-*density*attack can*solve*"almost all"*knapsacks*of*density*below 0.94 [36],[37] (*density*is defined in w ffthe shortest vector in a lattice can be found. ... A modification to the multiple-iterated Merkle-Hellman trapdoor is described that permits a*knapsack**density*exceeding the critical*density*0.94 of the Lagarias-Odlyzko*low*-*density*attack. ... The*density*approaches I + (r -l)(s + Iogn)/ns, well beyond the critical*density*of*low*-*density*attacks [30] - [38] . ...##
###
Page 4385 of Mathematical Reviews Vol. , Issue 86i
[page]

1986
*
Mathematical Reviews
*

We define the

*density*of a*knapsack*problem with weights a;,---,a@,, to be n/ log, A. In this paper, we describe two methods for*solving**knapsacks*of*low**density*. ... Brickell, Ernest F. (1-SAND)*Solving**low**density**knapsacks*. Advances in cryptology (Santa Barbara, Calif., 1983), 25-37, Plenum, New York-London, 1984. ...##
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New Generic Algorithms for Hard Knapsacks
[chapter]

2010
*
Lecture Notes in Computer Science
*

In this paper 3 , we study the complexity of

doi:10.1007/978-3-642-13190-5_12
fatcat:o6x7vpqjxnhpxec25dmcxge7dy
*solving*hard*knapsack*problems, i.e.,*knapsacks*with a*density*close to 1 where latticebased*low**density*attacks are not an option. ... We propose here two new algorithms which improve on this bound, finally lowering the running time down toÕ(2 0.3113 n ) for almost all*knapsacks*of*density*1. ... We would like to thank Igor Shparlinski for useful discussions about exponential sums and distributions of*knapsack*outputs. ...##
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Lattice Reduction for Modular Knapsack
[chapter]

2013
*
Lecture Notes in Computer Science
*

In general, the modular

doi:10.1007/978-3-642-35999-6_18
fatcat:lo5wyuulsbd5tjxgebx63fhapq
*knapsack*problem can be*solved*using a lattice reduction algorithm, when its*density*is*low*. ... In general, the modular*knapsack*problem can be*solved*using a lattice reduction algorithm, when its*density*is*low*. ... Finding one with exponential distance to the shortest one is already useful, for instance, to*solve*a*low**density**knapsack*problem or a*low**density*modular*knapsack*problem. ...##
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An improved knapsack public key cryptography system

2011
*
International Journal of Internet Technology and Secured Transactions
*

This cryptosystem uses a super-increasing sequence as private key and the authors investigate a new algorithm called permutation combination algorithm to enhance

doi:10.1504/ijitst.2011.041298
fatcat:afb7k7okezfbvlp6ugb3lzeblm
*density*of*knapsack*to avoid the*low*-*density*... By exploiting this algorithm, the authors attempted to enhance*density*of*knapsack*to avoid the*low*-*density*attack. Hwang et al.*knapsack*-type cryptosystem was attacked by Aboud [1] . ... By exploiting this algorithm, they attempted to enhance*density*of*knapsack*to avoid the*low*-*density*attack [2, 8] . The permutation algorithm is as follows: 1. ...##
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Cryptanalysis of a Public-key Cryptosystem Using Lattice Basis Reduction Algorithm
[article]

2012
*
arXiv
*
pre-print

This cryptosystem uses a super-increasing sequence as private key and the authors investigate a new algorithm called permutation combination algorithm to enhance

arXiv:1210.7417v1
fatcat:leoc6jp6xza5faz6obazian67y
*density*of*knapsack*to avoid the*low*-*density*... Sattar, "An improved*knapsack*public key cryptography system", International Journal of Internet Technology and Secured Transactions, Vol.3 (3), pp.310-319, 2011] used Shamir's attack on the basic Merkle-Hellman ... This cryptosystem uses a combination permutation algorithm in the encryption phase to avoid the*low**density*attack by keeping the*density*high. ...##
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Broadcast Attacks against Lattice-Based Cryptosystems
[chapter]

2009
*
Lecture Notes in Computer Science
*

Håstad's attack was demonstrated on the RSA algorithm, where

doi:10.1007/978-3-642-01957-9_28
fatcat:ht7nrvkhlnb7zb4p3nlwjbe75u
*low*exponents are used. ... These problems are used in lattice based cryptography and to model attack on*knapsack*cryptosystems. In this work, we are able to present some attacks against both lattice and*knapsack*cryptosystems. ... For instance, in [12] , the authors successfully cryptanalyzed*knapsack*cryptosystems with*density*less than 0.9408. These*low**density*attacks use lattice reduction tools. ...##
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Cryptanalysis of a New Knapsack Type Public-Key Cryptosystem
[article]

2013
*
arXiv
*
pre-print

By exploiting this algorithm, they attempt to increase the

arXiv:1210.8375v2
fatcat:tneywny3dff43aemubglidr6sy
*density*of*knapsack*to avoid the*low*-*density*attack. ...*knapsack*to break this cryptosystem. ... Although the underlying problem is NP-complete, but almost all*knapsack*cryptosystems were shown insecure in that they are vulnerable to some known attacks such as:*low**density*attack [2, 6] , Shamir's ...##
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On a knapsack based cryptosystem using real quadratic and cubic fields

2010
*
JSIAM Letters
*

We further generate explicit public keys and

doi:10.14495/jsiaml.2.81
fatcat:fvzqct2nczbezbzapfviygwyre
*knapsack*problems for several special cases and test the resistance against*low*-*density*attacks. ... We then estimate various*densities*of the generated*knapsack*problems for these cases and for the imaginary quadratic case. ... In Section 4, we show experimental results about various*densities*of the generated*knapsack*problem and study the resistance against*low*-*density*attacks. ...
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