By Zoque E.

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Olej´ ar and M. Stanek. ” Journal of Universal Computer Science, vol. 8, pp. 705-717, 1998. 50. E. Pasalic and S. Maitra. A Maiorana-McFarland type construction for resilient Boolean functions on n variables (n even) with nonlinearity > 2n−1 −2n/2 +2n/2−2 . Proceedings of the Workshop on Coding and Cryptography 2003, pp. 365-374, 2003. 51. Olsen, J. , Scholtz, R. A. and L. R. Welch. Bent function sequences, IEEE Trans. on Inf. Theory , vol IT- 28, n◦ 6, 1982. 52. E. Pasalic. Degree optimized resilient Boolean functions from Maiorana-McFarland class.

Simpson, E. Dawson, J. Golic and W. Millan. LILI Keystream generator, P roceedings of SAC’2000, Lecture Notes in Computer Science 1807, Springer, pp. 248-261, 2001; cf. au/lili/. 60. Y. V. Tarannikov. On resilient Boolean functions with maximum possible nonlinearity. Proceedings of INDOCRYPT 2000, Lecture Notes in Computer Science 1977, pp. 19-30, 2000. 61. Xiao Guo-Zhen and Massey, J. L. A Spectral Characterization of CorrelationImmune Combining Functions. IEEE Trans. Inf. Theory, Vol IT 34, n◦ 3, pp.

The methodology of using bilinear maps will be applied to more wide areas of secure cryptosystems and protocols. For example, it is applied to more protocol-oriented primitives like group signatures [1, 15], blind signatures [32], threshold PKE [10] and veriﬁable random functions [23]. Acknowledgements The author would like to thank Goichiro Hanaoka for his valuable comments on the preliminary manuscript. 48 T. Okamoto References 1. , de Medeiros, B. org/2005/385 (2005) 2. html. 3. , Pointcheval, D.