R. C. Merkle and M. E. Hellman, Hiding information and signatures in trapdoor Knapsacks, IEEE Transactions on Information Theory, Vol. 24, No. 5, pp. 525530, 1978. Home/Search Document Not in Database Summary Related Articles Check |
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Survey of Computational Assumptions Used in Cryptography Broken or.. - Zhu (2001) (Correct)
....expansion factor is about 1.6. For these reasons, the scheme receives little attention in practice. MvOV96] 7.2 Knapsack Assumption The subset sum problem is an NP complete problem [GJ79] Knapsack cryptosystems are based on the subset sum problem. The Merkle Hellman knapsack encryption scheme [MH78] was the first public key encryption scheme invented. Many variations have subsequently been proposed but broken. 7.2.1 Knapsack one way function The knapsack problem is to select objects with given weights and profits in such a way that a specified capacity is not exceeded and a specified ....
....is to transform a superincreasing easy knapsack into a nonsuperincreasing general one, and use this transformation as the trapdoor. The most famous transformation is the modular multiplication used by Merkle and Hellman. 7.2. 2 Merkle Hellman cryptosystem The Merkle Hellman knapsack cryptosystem [MH78] is a public key cryptosystem based on the intractability of the subset sum problem. Like the McEliece system, the Merkle Hellman knapsack system uses an easy special case of the NP hard problem, The conjecture that the subset sum problem is one way is based on the failure of known algorithm to ....
R. Merkle and M. Hellman. Hiding information and signatures in trapdoor knapsacks. IEEE Trans. Inform. Theory, IT-24:525--530, September 1978.
Security and Privacy in Radio-Frequency Identification Devices - Weis (2003) (5 citations) (Correct)
....class of hashes rely on the hardness of the Knapsack Problem. The Knapsack Problem is stated as follows: Given a set of integers S = S 1 ; S k and an integer n, find some subset T S such that P t i 2T t i = n. Merkle and Hellman initially used this problem in public key cryptosystem [65]. Harari [45] Damgard [29] and Zemor [114] later proposed both additive and multiplicative Knapsack based hashes. Damgard s scheme was broken by Camion and Patarin [15] Preneel points out weaknesses in Harari s scheme [74] The heavy computational and storage requirements of Knapsack based ....
Ralph Merkle and Marty Hellman. Hiding Information and Signatures in Trapdoor Knapsacks. IEEE Trans. Information Theory, 24:525--530, September 1978.
The Two Faces of Lattices in Cryptology - Nguyen, Stern (2001) (7 citations) (Correct)
....(also called subset sum) problem, a well known NP hard problem considered by Karp, and a particular case of multivariate linear equation: given a set fa 1 ; a 2 ; an g of positive integers and a sum s = i=1 x i a i , where x i 2 f0; 1g, recover the x i s. In 1978, Merkle and Hellman[96] invented one of the first public key cryptosystems, by converting some easy knapsacks into what they believed were hard knapsacks. It was basically the unique alternative to RSA until 1982, when Shamir [126] proposed a (heuristic) attack against the simplest version of the Merkle Hellman scheme. ....
R. Merkle and M. Hellman. Hiding information and signatures in trapdoor knapsacks. IEEE Trans. Inform. Theory, IT-24:525--530, September 1978.
Lattices and Cryptography: an Overview - Stern (1998) (2 citations) (Correct)
....suggests that it is hopeless to try to extend this inapproximability result to n. The relevance of lattice reduction algorithms to cryptography was immediately understood: in April 1982, Shamir ( Sha82] found a polynomial time algorithm breaking the Merkle Hellman public key cryptosystem ( MH78] based on the knapsack problem, that had been basically the unique alternative to RSA. Shamir used Lenstra s integer programming algorithm but, the same year, Adleman ( Adl83] extended Shamir s work by treating the cryptographic problem as a lattice problem rather than a linear programming ....
R. Merkle and M. Hellman. Hiding information and signatures in trapdoor knapsacks. IEEE Trans. Inform. Theory, IT-24:525--530, September 1978.
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R. C. Merkle and M. E. Hellman, Hiding information and signatures in trapdoor Knapsacks, IEEE Transactions on Information Theory, Vol. 24, No. 5, pp. 525530, 1978.
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R. Merkle and M. Hellman, Hiding Information and Signatures in Trapdoor Knapsacks, IEEE Trans. on Information Theory, Vol. 24, pp. 525--530, 1978.
Public-Key Cryptosystems Based on Composite - Degree Residuosity Classes (Correct)
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R. Merkle and M. Hellman, Hiding Information and Signatures in Trapdoor Knapsacks, IEEE Trans. on Information Theory, Vol. 24, pp. 525--530, 1978.
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R. Merkle and M. Hellman. Hiding information and signatures in trapdoor knapsacks. IEEE Transactions on Information Theory, 24(5):525-530, Sept. 1978.
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R. Merkle and M. Hellman. Hiding information and signatures in trapdoor knapsacks. IEEE Trans. Inform. Theory, IT-24:525--530, September 1978.
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R. C. Merkle and M. Hellman, "Hiding information and signatures in trapdoor knapsacks", in IEEE Transactions on Information Theory,vol. 24, no. 5, pp. 525-530, 1978.
Public-Key Cryptosystems Based on Composite Degree Residuosity.. - Paillier (1999) (144 citations) (Correct)
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R. Merkle and M. Hellman, Hiding Information and Signatures in Trapdoor Knapsacks, IEEE Trans. on Information Theory, Vol. 24, pp. 525--530, 1978.
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R. C. Merkle and M. Hellman, "Hiding information and signatures in trapdoor knapsacks", in IEEE Transactions on Information Theory, vol. 24, no. 5, pp. 525-530, 1978.
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R. Merkle & M. Hellman, Hiding information and signatures in trapdoor knapsacks, IEEE Transactions on Information Theory, vol. it 24 n 5, pp. 525--530, 1978.
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R. C. Merkle and M. Hellman, "Hiding information and signatures in trapdoor knapsacks", IEEE Transactions on Information Theory, vol. 24, no. 5, pp. 525-530, 1978.
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A New Public-Key Cryptosystem - Naccache, Stern (1997) (14 citations) (Correct)
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R. Merkle & M. Hellman, Hiding information and signatures in trapdoor knapsacks, IEEE Transactions on Information Theory, vol. it 24 n 5, pp. 525--530, 1978.
Public-Key Cryptosystems Based on Composite Degree Residuosity.. - Paillier (1999) (144 citations) (Correct)
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R. Merkle and M. Hellman, Hiding Information and Signatures in Trapdoor Knapsacks, IEEE Trans. on Information Theory, Vol. 24, pp. 525--530, 1978.
Unknown - (Correct)
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Merkle, R., and M. Hellman, "Hiding Information and Signatures in Trapdoor Knapsacks," IEEE Transactions of Information Theory, IT-24,5, September 1978.
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Merkle R.C. and Hellman M.E., Hiding information and signatures in trapdoor knapsacks, IEEE Trans. Inf. Theory, 24, 525--530, (1978).
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R. Merkle and M. Hellman, Hiding Information and Signatures in Trapdoor Knapsacks, IEEE Trans. on Information Theory, Vol. 24, pp. 525--530, 1978.
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R. Merkle & M. Hellman, Hiding information and signatures in trapdoor knapsacks, IEEE Transactions on Information Theory, vol. it 24 n 5, pp. 525--530, 1978.
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R.C. Merkle and M.E. Hellman. Hiding information and signatures in trapdoor knapsacks. IEEE Transactions on Information Theory, IT-24:525--530, 1978.
Survey of Computational Assumptions Used in Cryptography Broken or.. - Zhu (2001) (Correct)
No context found.
R. Merkle and M. Hellman. Hiding information and signatures in trapdoor knapsacks. IEEE Trans. Inform. Theory, IT-24:525-530, September 1978.
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Merkle, R. C., and Hellman, M. E. Hiding information and signatures in trapdoor knapsacks. In IEEE Trans. Inform. Theory (1978), vol. IT-24, pp. 525--530.
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