The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Hiding information and signatures in trapdoor knapsacks
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.
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Citations
Cites
New directions in cryptography
Diffie, W., & Hellman, M. (1976) · IEEE Transactions on Information Theory · doi:10.1109/tit.1976.1055638 · Cited by 14,713
Self-citationA method for obtaining digital signatures and public-key cryptosystems
Rivest, R. L., Shamir, A., & Adleman, L. (1978) · Communications of the ACM · doi:10.1145/359340.359342 · Cited by 13,462
A method for obtaining digital signatures and public-key cryptosystems
Rivest, R. L., Shamir, A., & Adleman, L. (1983) · Communications of the ACM · doi:10.1145/357980.358017 · Cited by 13,012
Reducibility among Combinatorial Problems
Karp, R. M. (1972) · Complexity of Computer Computations · doi:10.1007/978-1-4684-2001-2_9 · Cited by 11,511
The Design and Analysis of Computer Algorithms
Aho, A. V., & Hopcroft, J. E. (1974) · CERN Document Server (European Organization for Nuclear Research) · Cited by 9,403
Reducibility Among Combinatorial Problems
Karp, R. M. (2010) · 50 Years of Integer Programming 1958-2008 · doi:10.1007/978-3-540-68279-0_8 · Cited by 2,490
Pohlig, S., & Hellman, M. (1978) · IEEE Transactions on Information Theory · doi:10.1109/tit.1978.1055817 · Cited by 1,199
Self-citationFast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Ibarra, O. H., & Kim, C. E. (1975) · Journal of the ACM · doi:10.1145/321906.321909 · Cited by 959
Secure communications over insecure channels
Merkle, R. C. (1978) · Communications of the ACM · doi:10.1145/359460.359473 · Cited by 757
Self-citationComputing Partitions with Applications to the Knapsack Problem
Horowitz, E., & Sahni, S. K. (1974) · Journal of the ACM · doi:10.1145/321812.321823 · Cited by 605
Cited by
Handbook of applied cryptography
(1997) · Choice Reviews Online · doi:10.5860/choice.34-4512 · Cited by 10,357
Public-Key Cryptosystems Based on Composite Degree Residuosity Classes
Paillier, P. (2007) · Lecture Notes in Computer Science · doi:10.1007/3-540-48910-x_16 · Cited by 7,250
Guide to Elliptic Curve Cryptography
(2004) · Springer Professional Computing · doi:10.1007/b97644 · Cited by 3,054
Protocols for Public Key Cryptosystems
Merkle, R. C. (1980) · 1980 IEEE Symposium on Security and Privacy · doi:10.1109/sp.1980.10006 · Cited by 1,418
Self-citationUniversal one-way hash functions and their cryptographic applications
Naor, M., & Yung, M. (1989) · Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89 · doi:10.1145/73007.73011 · Cited by 959
Metadata
- Authors
- Merkle, R., & Hellman, M.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1978-09
- Volume
- 24
- Issue
- 5
- Pages
- 525-530
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2106287110
- Cited by
- 827
- References
- 13
- FWCI
- 18.19
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
