E. F. Brickell, "The cryptanalysis of knapsack cryptosystems", in Applications of Discrete Mathematics, SIAM, 1988, pp. 3-23  Home/Search   Document Not in Database   Summary   Related Articles   Check

....exists, then a 1 cannot be in the subset which sums to s, and we know that e 1 = 0. We can then recurse and determine e 2 ; e 3 ; e n in sequence. Many public key cryptosystems have been proposed with the difficulty of solving subset sum problems as the basis for their security. See [7, 8, 13, 31] for surveys of this field. Almost all of these cryptosystems have been shown to be insecure; the Chor Rivest one [11] is perhaps the most widely known system which has not yet been broken. The majority of the attacks on knapsack based cryptosystems have involved discovering the secret ....

E. F. Brickell, The cryptanalysis of knapsack cryptosystems. Applications of Discrete Mathematics, R. D. Ringeisen and F. S. Roberts, eds., SIAM (1988), 3-23.

....a i = s: 1) This problem is known to be NP complete [9] in its feasibility recognition form) and so is thought to be very hard in general. This has led to the invention of several public key cryptosystems based on the knapsack problem. Almost all of these have been broken by now, however. See [2, 3, 5, 15] for surveys of this field. Most of the attacks exploited specific constructions of the relevant cryptosystems. In addition, two algorithms have been proposed, one by Brickell [1] and the other by Lagarias and Odlyzko [11] which show that almost all low density subset sum problems can be solved ....

E. F. Brickell, The cryptanalysis of knapsack cryptosystems. Applications of Discrete Mathematics, R. D. Ringeisen and F. S. Roberts, eds., SIAM (1988), 3-23.

.... are many alternative knapsack type public key cryptosystems, a review of which is given in [19] The basic Merkle Hellman cryptosystem was cracked by Shamir [71] and all proposed variants except [12] which is based on arithmetic in a finite field, have been cracked using techniques described in [9]. 73 3.6.2 RSA Named after its inventors, Rivest, Shamir and Adleman [64] it is the most popular public key system. The basis of RSA is the difficulty in factoring very large numbers. A public key, n; e) is generated by firstly finding the product of two large (over 100 digits) prime ....

E. F. Brickell. The cryptanalysis of knapsack cryptosystems. In R. D. Ringeisen and F. S. Roberts, editors, Applications of Discrete Mathematics. SIAM, 1988.

....LLL algorithm comes into play: it looks for short vectors by shortening the basis vectors. The LLL based approach is the most famous and well known approach to solving the Subset Sum problem. In fact it was one of the reasons for the fall of Subset Sum based public key cryptosystems. See [9] and [1] for surveys in this field) Almost all of these cryptosystems have been shown to be insecure. The majority of the attacks exploited specific constructions of the relevant cryptosystems. In addition, two independent algorithms have been proposed, one by Brickell [2] and the other by Lagarias and ....

E. F. Brickell, "The cryptanalysis of knapsack cryptosystems", in Applications of Discrete Mathematics, SIAM, 1988, pp. 3-23

....problem is known to be NP complete [10] in its feasibility recognition form) and so is thought to be very hard in general. This has led to the invention of several public key cryptosystems based on the knapsack problem. 2 Coster et al. Almost all of these have been broken by now, however. See [2, 3, 6, 17] for surveys of this field. Most of the attacks exploited specific constructions of the relevant cryptosystems. In addition, two algorithms have been proposed, one by Brickell [1] and the other by Lagarias and Odlyzko [13] which show that almost all low density subset sum problems can be solved ....

E. F. Brickell, The cryptanalysis of knapsack cryptosystems, in Applications of Discrete Mathematics, R. D. Ringeisen and F. S. Roberts, eds., SIAM, 1988, 3-23.

....i = s: 1.1) This problem is known to be NP complete [10] in its feasibility recognition form) and so is thought to be very hard in general. This has led to the invention of several public key cryptosystems based on the knapsack problem. Almost all of these have been broken by now, however. See [2, 3, 6, 17] for surveys of this field. Most of the attacks exploited specific constructions of the relevant cryptosystems. In addition, two algorithms have been proposed, one by Brickell [1] and the other by Lagarias and Odlyzko [13] which show that 2 Coster et al. almost all low density subset sum ....

E. F. Brickell, The cryptanalysis of knapsack cryptosystems, in Applications of Discrete Mathematics, R. D. Ringeisen and F. S. Roberts, eds., SIAM, 1988, 3-23.

....with the use of tools from the area of diophantine approximation. The paper [6] contains a survey of many of the systems that have been broken as well as descriptions of some of the attacks. For full details, the reader is advised to consult [6] and many of the references contained there, such as [3,4,5,8,11,16,17,18,22,26]. The remainder of this paper is devoted to a description of one each of the two kinds of basic attacks that have been used. Section 2 describes the attack on the singly iterated Merkle Hellman cryptosystem. This attack allows the cryptanalyst to read encrypted messages just about as fast as ....

E. F. Brickell, "The Cryptanalysis of Knapsack Cryptosystems," Applications of Discrete Mathematics, R. D. Ringeisen and F. S. Roberts, eds., SIAM, 1988, pp. 3-23.

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E. F. Brickell, "The cryptanalysis of knapsack cryptosystems", in Applications of Discrete Mathematics, SIAM, 1988, pp. 3-23

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E. F. Brickell, "The cryptanalysis of knapsack cryptosystems", in Applications of Discrete Mathematics, SIAM, 1988, pp. 3-23 4

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Ernest F. Brickell, The cryptanalysis of knapsack cryptosystems, in Applications of Discrete Mathematics (R. D. Ringeisen and F. Roberts, eds.), SIAM, Philadelphia, 1988, 3--23. Another paper which showed that many cryptosystems based on the knapsack problem could be broken. See also [36, 38].

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