Foundations of security for hash chains in ad hoc networks

Nodes in ad hoc networks generally transmit data at regular intervals over long periods of time. Recently, ad hoc network nodes have been built that run on little power and have very limited memory. In ad hoc networks authentication can be a significant challenge, even without considering size and power constraints. Assuming idealized hashing, this paper examines lower bounds for ad hoc broadcast authentication for μ-TESLA-like protocols. In particular this paper focuses on idealized hashing for generating preimages of hash chains. Using variations on these idealized hash functions, this paper gives an idealized time-space product Ω(t² log⁴ n) bit operation¹ lower-bound for optimal preimage hash chain generation. Where n is the total length of the hash chain and the hash elements are t-wise independent. Given our foundations, these results follow as corollaries to a lower bound of Coppersmith and Jakobsson.