Transitive Signature Schemes
We introduce and provide the first example of a transitive digital signature scheme. Informally, this is a way to digitally sign vertices and edges of a dynamically growing, transitively closed, graph G so as to guarantee the following properties:
Given the signatures of edges (u, v) and (v,w), anyone can easily derive the digital signature of the edge (u,w).
It is computationaly hard for any adversary to forge the digital signature of any new vertex or other edge of G, even if he can request the legitimate signer to digitally sign any number of G’s vertices and edges of his choice in an adaptive fashion (i.e., even if he can choose which vertices and edges the legitimate signer should sign next after he sees the legitimate signatures of the ones requested so far).
Keywordspublic-key cryptography digital signatures graphs transitive closure
Unable to display preview. Download preview PDF.
- 2.Matt Blaze, Gerrit Bleumer, and Martin Strauss. Divertible protocols and atomic proxy cryptography. In Kaisa Nyberg, editor, Proceedings EUROCRYPT’ 98, pages 127–144. Springer, 1998.Google Scholar
- 3.D. Chaum, E. van Heijst, and B. Pfitzmann. Cryptographically strong undeniable signatures, unconditionally secure for the signer. In J. Feigenbaum, editor, Proceedings CRYPTO’ 91, pages 470–484. Springer, 1992. Lecture Notes in Computer Science No. 576.Google Scholar
- 4.David Chaum. Blind signatures for untraceable payments. In R. L. Rivest, A. Sherman, and D. Chaum, editors, Proceedings CRYPTO 82, pages 199–203, New York, 1983. Plenum Press.Google Scholar
- 6.Thomas H. Cormen, Charles E. Leiserson, and Ronald L. Rivest. Introduction to Algorithms. MIT Press/McGraw-Hill, 1990.Google Scholar
- 7.D. Dolev, C. Dwork, and M. Naor. Non-malleable cryptography. In Proc. STOC’ 91, pages 542–552. ACM, 1991.Google Scholar
- 8.Joan Feigenbaum. Encrypting problem instances: Or...can you take advantage of someone without having to trust him? In H. C. Williams, editor, Proceedings CRYPTO 85, pages 477–488. Springer, 1986. Lecture Notes in Computer Science No. 218.Google Scholar
- 12.Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone. Handbook of Applied Cryptography. CRC Press, 1997.Google Scholar
- 13.T.P. Pedersen. Non-interactive and information-theoretic secure verifiable secret sharing. In J. Feigenbaum, editor, Proceedings CRYPTO’ 91, pages 129–140. Springer, 1992. Lecture Notes in Computer Science No. 576.Google Scholar
- 14.Ronald L. Rivest, Leonard Adleman, and Michael L. Dertouzos. On data banks and privacy homomorphisms. In R. DeMillo, D. Dobkin, A. Jones, and R. Lipton, editors, Foundations of Secure Computation, pages 169–180. Academic Press, 1978.Google Scholar
- 15.Tomas Sander, Adam Young, and Moti Yung. Non-interactive cryptocomputing for NC 1. In Proceedings 40th IEEE Symposium on Foundations of Computer Science, pages 554–566, New York, 1999. IEEE.Google Scholar