Abstract
We introduce a new knapsack type public key cryptosystem. The system is based on a novel application of arithmetic in finite fields, following a construction by Bose and Chowla. Appropriately choosing the parameters, we can control the density of the resulting knapsack. In particular, the density can be made high enough to foil “low density” attacks against our system. At the moment, we do not know of any attacks capable of “breaking” this system in a reasonable amount of time.
Research supported by NSF grant MCS-8006938. Part of this research was done while the first author was visiting Bell Laboratories, Murray Hill, NJ.
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References
Bose, R.C. and S. Chowla, “Theorems in the additive theory of numbers”, Comment. Math. Helvet., vol. 37, pp. 141–147, 1962.
Brickell, E.F., “A new knapsack based cryptosystem”, Presented in Crypto83.
Brickell, E.F., “Are most low density knapsacks solvable in polynomial time?”, Proceedings of the Fourteenth Southeastern Conference on Combinatorics, Graph Theory and Computing, 1983.
Brillhart, J., D.H. Lehmer, J.L. Selfridge, B. Tuckerman and S.S. Wagstaff, Jr., Factorization of b n ± 1, in Contemporary Mathematics, vol. 22, AMS, Providence, 1983.
Coppersmith, D., “Fast Evaluation of Logarithms in Fields of Characteristic Two”, to appear, IEEE Trans. Inform. Theory; extended abstract in Proceedings of the Sixteenth Annual Symposium on Theory of Computing, ACM, pp. 201–207, 1984.
Cover, T.M., “Enumerative Source Encoding”, IEEE Trans. Inform. Theory, vol IT-19, pp. 73–77, 1973.
Diffie, W. and M. Hellman, “New directions in cryptography”, IEEE Trans. Inform. Theory, vol. IT-22, pp. 644–654, 1976.
Goldwasser, S. and S. Micali, “Probabilistic Encryption”, Proceedings of the Fourteenth Annual Symposium on Theory of Computing, ACM, pp. 365–377, 1982.
Halberstram, H. and K.F. Roth, Sequences, Springer-Verlag, New York, 1983.
Kannan, R., “Improved algorithms for integer programming and related lattice problems”, Proceedings of the Fifteenth Annual Symposium on Theory of Computing, ACM, pp. 193–206, 1983.
Lagarias, J.C. and A.M. Odlyzko, “Solving low-density subset sum problems”, Proceedings of the Twenty-Fourth Annual Symposium on Foundations of Computer Science, IEEE, pp. 1–10, 1983.
McEliece, R.J., “A public-key cryptosystem based on algebraic coding theory”, DSN Progress Report 42-44, pp. 114–116, 1978.
Merkle, R.C. and M.E. Hellman, “Hiding information and signatures in trap-door knapsacks”,IEEE Trans. Inform. Theory, vol. IT-24, pp. 525–530, 1978.
Odlyzko, M.O., “Cryptanalytic attacks on the multiplicative knapsack cryptosystem and on Shamir’s fast signature scheme”, preprint, 1983.
Pohlig, R.C. and M. Hellman, “An improved algorithm for computing logarithms over GF(p) and its cryptographic significance”, IEEE Trans. Inform. Theory, vol. IT-24, pp. 106–110, 1978.
Rabin, M.O., “Digitalized signatures and public-key functions as intractable as factorization”, Technical report MIT/LCS/TR-212, MIT, 1979.
Rivest, R.L., A. Shamir and L. Adelman, “On digital signatures and public key cryptosystems”, Commun. ACM, vol. 21, pp. 120–126, 1978.
Shamir, A., “A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem”, Proceedings of the Twenty-Third Annual Symposium on Foundations of Computer Science, IEEE, pp. 145–152, 1982.
Schroeppel, R. and A. Shamir, “A T = O(2n/2), S = O(2n/4) algorithm for certain NP-complete problems”, SIAM J. Comput., vol. 10, No. 3, pp. 456–464, 1981.
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Chor, B., Rivest, R.L. (1985). A Knapsack Type Public Key Cryptosystem Based On Arithmetic in Finite Fields (preliminary draft). In: Blakley, G.R., Chaum, D. (eds) Advances in Cryptology. CRYPTO 1984. Lecture Notes in Computer Science, vol 196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39568-7_6
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DOI: https://doi.org/10.1007/3-540-39568-7_6
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