Cryptosystems based on an analog of heat flow
It is commonplace to base computer security and information security on hard problems. Recent cryptosystems have been based on the knapsack problem [DE83, pp. 118-126; BRS5] and the problem of factoring an integer [DE83, pp. 104-1091. The former problem is N P complete [GA79, p. 2471. The place of the latter problem in complexity theory is not well understood, but it has been around in number theory for a long time.
KeywordsMaximum Principle Heat Equation Linear Case Finite Difference Scheme Finiteness Assumption
- BL85.G. R. Blakley, Information theory without the finiteness assumption, I: Cryptosystems as group-theoretic objects. in G. R. Blakley and D. Chaum (editors), Advances in Cryptology, Proceedings of Crypto’ 84, Springer-Verlag, Berlin (1985), 314–338.Google Scholar
- BL86.G. R. Blaldey, Information theory without the finiteness assumption, II: Unfolding the DES. in H. Williams (editor), Advances in Cryptology, Proceedings of Crypto’ 85, Springer-Verlag, Berlin (1986), to appear.Google Scholar
- BL87.G. R. Blakley and C Meadows, Information theory without the finiteness assumption, III: Data compression and codes whose rates exceed unity. Proceedings of the 1986 Cirencester Conference on Cryptography and Coding, IMA, (1987) to appear.Google Scholar
- BR85.E. Brickell, Breaking iterated knapsacks, in G. R. Blakley and D. Chaum (editors), Advances in Cryptology, Proceedings of Crypto’ 84, Springer-Verlag, Berlin (1985), 342–358.Google Scholar
- DA86.G. I. Davida, C. Gilbertson and G. Walter, Analog cryptosystems, in Proceedings of Eurocrypt’ 85, Springer-Verlag, Berlin (1986), to appear, also Technical Report TRCS-84-1. Department of Electrical Engineering and Computer Science, University of Wisconsin, Milwaukee, (1984).Google Scholar
- DE83.D. E. R. Denning, Cryptography and Data Security, Addison-Wesley, Reading, Massachusetts (1983).Google Scholar
- FR64.Partial Differential Equations of Parabolic type. Prentice Hall, Englewood Cliffs, New Jersey, (1964).Google Scholar
- HA23.J. Hadamard, Lectures on the Cauchy Problem in Linear Partial Differential Equations, Yale Univ. Press. New Haven, 1923.Google Scholar
- PA74.L. E. Payne, Improperly Posed Problems in Partial Differential Equations, Springer Lecture Notes, (1974).Google Scholar
- PE 86.
- PR67.M. H. Protter and H. Weinberger, Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, New Jersey (1967).Google Scholar
- PU 74.