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Molnar, D. Turner, and D. 58-74, SpringerVerlag, 2006. 7. D. Chaum and H. 212-216, Springer-Verlag, 1989. 8. X. Chen, F. Zhang, and K. 87-98, Springer-Verlag, 2004. 9. T. 469-472, 1985. 10. S. Even, O. Goldreich, and S. 263-277, Springer-Verlag, 1989. 30 X. Chen et al. 11. S. Even, O. Goldreich, and S. 35-67, Springer-Verlag, 1996. 12. A. Fiat and A. Shamir, How to prove yourself: Practical solutions to identification and signature problems, Advances in Cryptology-Crypto 1986, LNCS 263, pp. 186-194, Springer-Verlag, 1986.
Shor. Algorithms for quantum computation: Discrete logarithms and factoring. In Proc. 35th Annual Symposium on Foundations of Computer Science, pages 124–134. IEEE Comput. Soc. Press, 1994. 13. Michael Szydlo. Merkle tree traversal in log space and time (preprint). com/. 14. Michael Szydlo. Merkle tree traversal in log space and time. In Proc. Advances in Cryptology (Eurocrypt’04), volume 3027 of Lecture Notes in Computer Science, pages 541–554. Springer-Verlag, 2004. A Merkle’s Tree Authentication Scheme The tree authentication scheme was proposed by Merkle in [11] for using multiple one-time signature instances with a single “master” public key.
T1,0 T2,1 T2,0 SigT RootT ... T TT ,0 TT ,1 ... l Fig. 1. General construction of GMSS For any given signature s ∈ {0, . . +hT − 1}, there is a unique path p from the Merkle tree on the lowest layer T , which is used to sign the digest, to the single Merkle tree on the top layer 1 (T1,0 ). This path involves one Merkle tree at each layer i = 1, . . , T . A GMSS signature of a message digest d contains the one-time signature Sigd of d and the one-time signatures SigT of the roots of all Merkle trees on path p, except for T1,0 .