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We present a hybrid approach to bounding exponential sums over kth powers via Vinogradov's mean value theorem, and derive estimates of utility for exponents k of intermediate size.and define the mean value J s,k (P ) = T k |g(α; P )| 2s dα,where T denotes the unit interval [0, 1). Estimates for J s,k (P ) fall under the general appellation of Vinogradov's mean value theorem, and take the form J s,k (P ) ≪ P 2s− 1 2 k(k+1)+∆ s,k , (1.1)

This paper introduces a lightweight and secure framework enabling the refreshing of private keys in identitybased public key infrastructures. The framework is applied to enable secure inter-operation between entities with different trusted authorities in dynamic coalition environments. The approach is particularly well-suited to coalition forming in computation and bandwidth-limited MANETs.

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