Topic
Knapsack cryptosystems
About: Knapsack cryptosystems is a research topic. Over the lifetime, 47 publications have been published within this topic receiving 2706 citations.
Papers
TL;DR: Specific instances of the knapsack problem that appear very difficult to solve unless one possesses "trapdoor information" used in the design of the problem are demonstrated.
Abstract: The knapsack problem is an NP-complete combinatorial problem that is strongly believed to be computationally difficult to solve in general. Specific instances of this problem that appear very difficult to solve unless one possesses "trapdoor information" used in the design of the problem are demonstrated. Because only the designer can easily solve problems, others can send him information hidden in the solution to the problems without fear that an eavesdropper will be able to extract the information. This approach differs from usual cryptographic systems in that a secret key is not needed. Conversely, only the designer can generate signatures for messages, but anyone can easily check their authenticity.
923 citations
TL;DR: This method gives a polynomial time attack on knapsack public key cryptosystems that can be expected to break them if they transmit information at rates below dc (n), as n → ∞.
Abstract: The subset sum problem is to decide whether or not the 0-l integer programming problem Sni=l aixi = M, ∀I, xI = 0 or 1, has a solution, where the ai and M are given positive integers. This problem is NP-complete, and the difficulty of solving it is the basis of public-key cryptosystems of knapsack type. An algorithm is proposed that searches for a solution when given an instance of the subset sum problem. This algorithm always halts in polynomial time but does not always find a solution when one exists. It converts the problem to one of finding a particular short vector v in a lattice, and then uses a lattice basis reduction algorithm due to A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovasz to attempt to find v. The performance of the proposed algorithm is analyzed. Let the density d of a subset sum problem be defined by d = n/log2(maxiai). Then for “almost all” problems of density d
491 citations
TL;DR: This paper shows that the basic variant of the Merkle-Hellman cryptosystem, in which the elements of the public key are modular multiples of a superincreasing sequence, is breakable in polynomial time.
Abstract: The Merkle-Hellman cryptosystem is one of the two major public-key cryptosystems proposed so far. It is shown that the basic variant of this cryptosystem, in which the elements of the public key are modular multiples of a superincreasing sequence, is breakable in polynomial time.
381 citations
3 Nov 1982
TL;DR: This paper shows that the basic variant of the Merkle-Hellman cryptosystem, in which the elements of the public key are modular multiples of a superincreasing sequence, is breakable in polynomial time.
Abstract: The cryptographic security of the Merkle-Hellman cryptosystem has been a major open problem since 1976. In this paper we show that the basic variant of this cryptosystem, in which the elements of the public key are modular multiples of a superincreasing sequence, is breakable in polynomial time.
200 citations
1 May 1988
TL;DR: Attacks on the knapsack cryptosystems, congruential generators, and a variety of two key secrecy and signature schemes are discussed, and some of the basic tools available to the cryptanalyst are explained.
Abstract: Cryptosystems are tested by subjecting them to cryptanalytic attacks by experts. Most of the cryptosystems that have been publicly proposed in the last decade have been broken. Some of the attacks that have been used are outlined, and some of the basic tools available to the cryptanalyst are explained. Attacks on the knapsack cryptosystems, congruential generators, and a variety of two key secrecy and signature schemes are discussed. There is also a brief discussion of the status of the security of cryptosystems for which there is no known feasible attack, such as the RSA, discrete exponentiation, and DES cryptosystems. >
154 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2018 | 1 |
| 2017 | 1 |
| 2016 | 2 |
| 2013 | 2 |
| 2012 | 5 |