A knapsack-based probabilistic encryption scheme

Wang, Baocang; Wu, Qianhong; Hu, Yupu

doi:10.1016/j.ins.2007.03.010

Cited by 42 publications

(33 citation statements)

References 30 publications

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“…Due to these properties, chaotic systems have become a very good candidate for use in the field of cryptography. The existing related research progress includes chaos-based symmetric encryptions [1][2][3][4][5][6][7], security protocols [8,9], asymmetric encryptions [10,11], and hash functions [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A novel parallel hash function based on 3D chaotic map

Akhavan

Samsudin

Akhshani

2013

EURASIP J. Adv. Signal Process.

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As the core of cryptography, hash function is one of the basic techniques for information security. During the last few years, considerable effort has been devoted to research on chaos-based hash functions. Nevertheless, the corresponding analysis of them lag far behind. In this paper, a new efficient scheme for parallel hash function based on high-dimensional chaotic map is proposed. In the proposed scheme, the confusion as well as the diffusion effect is enhanced significantly by utilizing two nonlinear coupling parameters. Theoretical and experimental results indicate that the proposed scheme can satisfy all performance requirements of hash function such as desired statistical properties and strong collision resistance. At the same time, the proposed scheme can keep the parallel merit and message sensitivity with high potential to be adopted for network security.

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Section: Introductionmentioning

confidence: 99%

A novel parallel hash function based on 3D chaotic map

Akhavan

Samsudin

Akhshani

2013

EURASIP J. Adv. Signal Process.

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“…, x n ), x i ∈ {0, 1}, and A is an n-dimensional square matrix. These problems had been used to construct knapsacktype public-key cryptosystems [1,4,31,9,14]. In this paper, we will define a new knapsack problem, simultaneous quadratic compact knapsack problem.…”

Section: Knapsack Problems and Densitymentioning

confidence: 99%

“…In this section, we give an easy quadratic knapsack problem. The cargo vector defined in the easy knapsack problem is different from the super-increasing sequences [1], the cargo vectors used in Graham-Shamir cryptosystem [34], and the knapsack sequences [35] used for attacking a knapsack-type cryptosystem [12] based on Diophantine equations, and it can be thought as the generalization of the cargo vectors given in [31,14].…”

Section: An Easy Simultaneous Quadratic Knapsack Problemmentioning

confidence: 99%

“…For a long time, knapsack-type cryptosystems were considered to be the most attractive and the most promising due to their high speed of encryption and decryption and NP-completeness nature. Many knapsack-type cryptosystems were developed in the history of knapsack public-key cryptography especially in the 1980s, and the cryptographic applications of some variants of the knapsack problem were also investigated [4][5][6][7][8][9][10][11][12][13][14]. However, almost all additive knapsack-type cryptosystems were shown to be vulnerable to lowdensity subset-sum attacks [15][16][17], GCD attack [18], simultaneous Diophantine approximation attack [19,20] or orthogonal lattice attack [21].…”

Section: Introductionmentioning

confidence: 99%

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Quadratic compact knapsack public-key cryptosystem

Wang

2010

Computers & Mathematics with Applications

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a b s t r a c tKnapsack-type cryptosystems were among the first public-key cryptographic schemes to be invented. Their NP-completeness nature and the high speed in encryption/decryption made them very attractive. However, these cryptosystems were shown to be vulnerable to the low-density subset-sum attacks or some key-recovery attacks. 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. The system uses the Chinese remainder theorem to disguise the easy knapsack sequence. The encryption function of the system is nonlinear about the message vector. Under the relinearization attack model, the system enjoys a high density. 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. It is shown that the proposed cryptosystem is also secure against some brute-force attacks and some known key-recovery attacks including the simultaneous Diophantine approximation attack and the orthogonal lattice attack.

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“…Therefore, when dealing with such lattices, we can consider the known practical lattice reduction algorithms as a lattice oracle for solving the shortest nonzero vector problem. It is the fact that makes most of the knapsack cryptographic algorithms broken [14]. Second, the basis v 1 ,v 2 ,...,v 8 of the underlying lattice of our cryptographic algorithm contains a shortest nonzero vector v 6 ÎL.…”

Section: Lattice Reduction Attackmentioning

confidence: 99%

Fast public-key encryption scheme based on Chinese remainder theorem

Wang

Wei

2009

Front. Electr. Electron. Eng. China

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Traditional public-key cryptosystems suffer from a relatively low encryption/decryption speed, which hampers their applications in resource-constrained environments. A fast public-key cryptosystem is proposed to remedy this drawback. The new algorithm uses Chinese remainder theorem to hide the trapdoor information. The encryption of the system only carries out several modular multiplication operations, and the decryption only needs a modular multiplication and a low-dimensional matrixvector multiplication, which makes the speed of the encryption and the decryption of the scheme very high. The security of the system is based on two difficult number-theoretic problems. The attacker has to solve the integer factorization problem and the simultaneous Diophantine approximation problem simultaneously to recover the secret key from the public key. The proposed cryptosystem is also shown to be secure against lattice attack. The analysis shows that the encryption algorithm is a secure, fast and efficient public-key cryptosystem.

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A knapsack-based probabilistic encryption scheme

Cited by 42 publications

References 30 publications

A novel parallel hash function based on 3D chaotic map

A novel parallel hash function based on 3D chaotic map

Quadratic compact knapsack public-key cryptosystem

Fast public-key encryption scheme based on Chinese remainder theorem

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