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Quadratic compact knapsack public-key cryptosystem

Baocang Wang, Yupu Hu
2010 Computers and Mathematics with Applications  
We show that the 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.  ... 
doi:10.1016/j.camwa.2009.08.031 fatcat:bvwvdczchvftzdmjwpmuzl4bhy

Criticism of Knapsack Encryption Scheme [article]

Sattar J. Aboud
2010 arXiv   pre-print
In this paper, we analyze a 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] .  ... 
arXiv:1005.4012v1 fatcat:bcuqujcsxrdqjghzh52tublgrq

Cryptanalysis of two knapsack-type public-key cryptosystems

Jingguo Bi, Xianmeng Meng, Lidong Han
2010 2010 International Conference on Computer Application and System Modeling (ICCASM 2010)  
We show that one can recover the plaintext as long as he 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.  ... 
doi:10.1109/iccasm.2010.5622956 fatcat:6u3sc2qqircp7lkrfrinkgvroa

PKCHD: Towards A Probabilistic Knapsack Public-Key Cryptosystem with High Density

Yuan Ping, Baocang Wang, Shengli Tian, Jingxian Zhou, Hui Ma
2019 Information  
Under the re-linearization attack model, PKCHD obtains a high 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.  ... 
doi:10.3390/info10020075 fatcat:bbs55j7ovjfslph6yxojd4saju

Adapting Density Attacks to Low-Weight Knapsacks [chapter]

Phong Q. Nguyễn, Jacques Stern
2005 Lecture Notes in Computer Science  
To prevent 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  ... 
doi:10.1007/11593447_3 fatcat:us7noxwnofg6lpq3qgwjxmzk6m

A knapsack public-key cryptosystem with cyclic code over $GF(2)$

Yasuyuki Murakami, Takeshi Nasako
2010 JSIAM Letters  
The proposed scheme is secure against Shamir's attack and Adleman's attack and invulnerable to the 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] .  ... 
doi:10.14495/jsiaml.2.29 fatcat:zpfwu7mczbd2bnwyyaiaslfjsa

A multiple-iterated trapdoor for dense compact knapsacks [chapter]

Glenn Orton
1995 Lecture Notes in Computer Science  
The Lagarias-Odlyzko 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] .  ... 
doi:10.1007/bfb0053429 fatcat:4prg6asq6vcjphiy4e3jhboutu

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.  ... 

New Generic Algorithms for Hard Knapsacks [chapter]

Nick Howgrave-Graham, Antoine Joux
2010 Lecture Notes in Computer Science  
In this paper 3 , we study the complexity of 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.  ... 
doi:10.1007/978-3-642-13190-5_12 fatcat:o6x7vpqjxnhpxec25dmcxge7dy

Lattice Reduction for Modular Knapsack [chapter]

Thomas Plantard, Willy Susilo, Zhenfei Zhang
2013 Lecture Notes in Computer Science  
In general, the modular 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.  ... 
doi:10.1007/978-3-642-35999-6_18 fatcat:lo5wyuulsbd5tjxgebx63fhapq

An improved knapsack public key cryptography system

Sattar J. Aboud
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 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.  ... 
doi:10.1504/ijitst.2011.041298 fatcat:afb7k7okezfbvlp6ugb3lzeblm

Cryptanalysis of a Public-key Cryptosystem Using Lattice Basis Reduction Algorithm [article]

Roohallah Rastaghi, Hamid R. Dalili Oskouei
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 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.  ... 
arXiv:1210.7417v1 fatcat:leoc6jp6xza5faz6obazian67y

Broadcast Attacks against Lattice-Based Cryptosystems [chapter]

Thomas Plantard, Willy Susilo
2009 Lecture Notes in Computer Science  
Håstad's attack was demonstrated on the RSA algorithm, where 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.  ... 
doi:10.1007/978-3-642-01957-9_28 fatcat:ht7nrvkhlnb7zb4p3nlwjbe75u

Cryptanalysis of a New Knapsack Type Public-Key Cryptosystem [article]

Roohallah Rastaghi
2013 arXiv   pre-print
By exploiting this algorithm, they attempt to increase the 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  ... 
arXiv:1210.8375v2 fatcat:tneywny3dff43aemubglidr6sy

On a knapsack based cryptosystem using real quadratic and cubic fields

Keiichiro Nishimoto, Ken Nakamula
2010 JSIAM Letters  
We further generate explicit public keys and 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.  ... 
doi:10.14495/jsiaml.2.81 fatcat:fvzqct2nczbezbzapfviygwyre
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