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Knapsack Public Key Cryptosystems and Diophantine Approximation
[chapter]

1984
*
Advances in Cryptology
*

This paper presents

doi:10.1007/978-1-4684-4730-9_1
fatcat:mcbyfnxigza4tplfm3gcekxdpy
*and*analyzes cryptanalytic attacks on*knapsack**public**key**cryptosystems*that are based on ideas from*Diophantine**approximation*. ... Shamir's attack on the basic Merkle-Hellman*knapsack**cryptosystem*is shown to depend on the existence of "unusually good" simultaneous*Diophantine**approximations*to a vector constructed from the*public*... Introduction In 1978 Merkle*and*Hellman [14] proposed a*public**key**cryptosystem*based on the idea of a ''trapdoor''*knapsack*. ...##
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Page 4939 of Mathematical Reviews Vol. , Issue 86j
[page]

1986
*
Mathematical Reviews
*

Author summary: “We present

*and*analyze cryptanalytic attacks on*knapsack**public**key**cryptosystems*that are based on ideas from*Diophantine**approximation*. A. ... These probabilities are analyzed*and*shown to be negligibly small.” Lagarias, J. C. (1-BELL) 86j:94050*Knapsack**public**key**cryptosystems**and**Diophantine**approximation*(extended abstract). ...##
###
Cryptanalysis of a Public-key Cryptosystem Using Lattice Basis Reduction Algorithm
[article]

2012
*
arXiv
*
pre-print

Sattar, "An improved

arXiv:1210.7417v1
fatcat:leoc6jp6xza5faz6obazian67y
*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 super-increasing sequence as private*key**and*the authors investigate a new algorithm called permutation combination algorithm to enhance density of*knapsack*to avoid the low-density ... Conclusion We considered cryptanalysis of a*knapsack*-type*public**key**cryptosystem*. ...##
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An improved knapsack public key cryptography system

2011
*
International Journal of Internet Technology and Secured Transactions
*

This

doi:10.1504/ijitst.2011.041298
fatcat:afb7k7okezfbvlp6ugb3lzeblm
*cryptosystem*uses a super-increasing sequence as private*key**and*the authors investigate a new algorithm called permutation combination algorithm to enhance density of*knapsack*to avoid the low-density ... s*cryptosystem*. ... Introduction The first*knapsack*-type*public**key**cryptosystem*(PKC) was introduced by Merkle*and*Hellman [12] . ...##
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Quadratic compact knapsack public-key cryptosystem

2010
*
Computers and Mathematics with Applications
*

It is shown that the proposed

doi:10.1016/j.camwa.2009.08.031
fatcat:bvwvdczchvftzdmjwpmuzl4bhy
*cryptosystem*is also secure against some brute-force attacks*and*some known*key*-recovery attacks including the simultaneous*Diophantine**approximation*attack*and*the orthogonal ... In this paper, additive*knapsack*-type*public*-*key*cryptography is reconsidered. We propose a*knapsack*-type*public*-*key**cryptosystem*by introducing an easy quadratic compact*knapsack*problem. ... Introduction*Knapsack*cryptography [1] is an important class of*public*-*key**cryptosystems*in the area of*public*-*key*cryptography. ...##
###
PKCHD: Towards A Probabilistic Knapsack Public-Key Cryptosystem with High Density

2019
*
Information
*

By introducing an easy

doi:10.3390/info10020075
fatcat:bbs55j7ovjfslph6yxojd4saju
*knapsack*-type problem, a probabilistic*knapsack*-type*public**key**cryptosystem*(PKCHD) is proposed. It uses a Chinese remainder theorem to disguise the easy*knapsack*sequence. ... Meanwhile, it can use the hardest*knapsack*vector as the*public**key*if its density evaluates the hardness of a*knapsack*instance. ... Acknowledgments: The authors would like to thank the anonymous reviewers for their carefulness*and*patience,*and*thank Sheng Tong for the proof of Theorem 8*and*Fagen Li for paper preparation. ...##
###
LATTICE BASED TOOLS IN CRYPTANALYSIS FOR PUBLIC KEY CRYPTOGRAPHY

2012
*
Zenodo
*

Not only the existence of lattice based

doi:10.5281/zenodo.3351415
fatcat:rttkitq545cs5aio7nsgg4cmfu
*cryptosystems*of hard in nature, but also has vulnerabilities by lattice reduction techniques. ... In this survey paper, we are focusing on point lattices*and*then describing an introduction to the theoretical*and*practical aspects of lattice reduction. ... Algorithms for finding simultaneous*Diophantine**approximation*have been used to break some*knapsack**public**key**cryptosystems*. is said to be a simultaneous*Diophantine**approximation*of ߜ-quality to the ...##
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Diophantine Approximation Attack on a Fast Public Key Cryptosystem
[chapter]

2006
*
Lecture Notes in Computer Science
*

Yoo etc. proposed a

doi:10.1007/11689522_3
fatcat:wfympgoumbcinhdfkelr2mop54
*public**key**cryptosystem*using matrices over a ring, which was analyzed using lattice basis reduction algorithms by Youssef etc. at ACISP 2001. ... It is shown that the decryption of the*cryptosystem*can be transformed into solving the simultaneous*Diophantine**approximation*problem, which can be*approximated*by lattice basis reduction algorithms. ... At ACISP 2000, Yoo etc. proposed a fast*public**key**cryptosystem*using matrices over a ring [9] . ...##
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Cryptanalysis of a New Knapsack Type Public-Key Cryptosystem
[article]

2013
*
arXiv
*
pre-print

Recently, Hwang et al. introduced a

arXiv:1210.8375v2
fatcat:tneywny3dff43aemubglidr6sy
*knapsack*type*public*-*key**cryptosystem*. They proposed a new algorithm called permutation combination algorithm. ... We show that this*cryptosystem*is not secure, as it based on basic Merkel-Hellman*knapsack**cryptosystem**and*because of the superincreasing structure, we can use shamir's attack on the basic Merkel-Hellman ... attack [14]*and**diophantine**approximation*attack [17] . ...##
###
Performance analysis of Shamir's attack on the basic Merkle-Hellman knapsack cryptosystem
[chapter]

1984
*
Lecture Notes in Computer Science
*

Let R = maximum # cipher text bits # plain text bits _ ________________________ denote the rate at which a

doi:10.1007/3-540-13345-3_28
fatcat:2jvpnnb3tnb2lhmcnvawesvnoa
*knapsack**cryptosystem*transmits information,*and*let n denote the number of items in a*knapsack*... This paper gives a performance analysis of one variant of Shamir's attack on the basic Merkle-Hellman*knapsack**cryptosystem*, which we call Algorithm S. ... Introduction In 1978 Merkle*and*Hellman [11] proposed*public**key**cryptosystems*based on the*knapsack*problem. The simplest of these*cryptosystems*, the basic*knapsack**cryptosystem*, works as follows. ...##
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Preimage Selective Trapdoor Function: How to Repair an Easy Problem

2014
*
Mathematical Problems in Engineering
*

*Public*

*key*

*cryptosystems*are constructed by embedding a trapdoor into a one-way function. So, the one-wayness

*and*the trapdoorness are vital to

*public*

*key*cryptography. ... The compact

*knapsack*problem is used to construct a probabilistic

*public*

*key*

*cryptosystem*, the underlying encryption function of which is proven to be preimage selective trapdoor one-way functions under ... See [6, 7] for more details about the relation between the simultaneous

*Diophantine*

*approximation*problem

*and*

*knapsack*

*public*

*key*cryptanalytics. ...

##
###
Page 4386 of Mathematical Reviews Vol. , Issue 86i
[page]

1986
*
Mathematical Reviews
*

The basic Merkle- Hellman additive trapdoor

*knapsack**public*-*key**cryptosystem*has already been shown to be insecure by many re- searchers. ... The corresponding*public**key*is A,m with A=T'T. A signature y of a message z € Z,, is any y €(Z,,)” such that y’ Ay*approximates*z, e.g. |z — y" Ay| < 4m?”". ...##
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A new public-key cipher system based upon the diophantine equations

1995
*
IEEE transactions on computers
*

Index Terms-

doi:10.1109/12.368013
fatcat:w6xo3miz2bgfzarntvkqagprya
*Public**keys*, private*keys*,*cryptosystems*,*Diophantine*equation problems, integer*knapsack*problems, one-way functions, trapdoor one-way functions, NP-complete. ... A b~t r~~t - A new*public*-*key*(two-*key*) cipher scheme is proposed in this paper. In our scheme,*keys*can be easily generated. In addition, both encryption*and*decryption procedures are simple. ... ACKNOWLEDGMENT The authors thank the referees for many helpful suggestions*and*comments. 1989 ...##
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Cryptanalysis of a quadratic knapsack cryptosystem

2011
*
Computers and Mathematics with Applications
*

Wang

doi:10.1016/j.camwa.2011.01.006
fatcat:d76l4d4n6fcofhe2gr3u73fpsq
*and*Hu [B. Wang*and*Y. Hu, Quadratic compact*knapsack**public*-*key**cryptosystem*, Comput. Math. ... Appl. 59 (1) (2010) 194-206] proposed a*knapsack*-type*public*-*key**cryptosystem*by introducing an easy quadratic compact*knapsack*problem*and*then using the Chinese remainder theorem to disguise the easy ... Introduction*Knapsack*-based*cryptosystems*[1, 2] were among the first*public*-*key*systems to be invented. ...##
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Page 3308 of Mathematical Reviews Vol. , Issue 86g
[page]

1986
*
Mathematical Reviews
*

Theory 30 (1984), no. 5, 699-704], who showed how to break the basic Merkle-Hellman

*knapsack**public**key**cryptosystem*[R. C. Merkle*and*M. E. Hellman, ibid. 24 (1978), no. 5, 525-530]. ... He then goes on to discuss Shamir’s attack on the basic Merkle- Hellman*cryptosystem*which derives a set of*Diophantine**approximation*inequalities*and*solves them using the author’s integer programming ...
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