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Mathematical Foundations
Published in Chintan Patel, Nishant Doshi, Internet of Things Security, 2018
In the above Figure 2.19 computation, even though intruder gets the hash value, he can not use it for the next communication because server computation does not match to stored value. So hash chain is the set of values h0, h1, h2, h3, h4, ……, hn for n ∈ ℤ, such that hi = H(hi−1) for some hash function H, where i ∈ [1, n], x0 is valid input for H. So hash chain n is the total number of times hash operation is performed. Hash chain must be easy to compute. Any value xi can be calculated from any value xj if value of i ≥ j. So computation of hash chain makes it suitable tool for platforms with less memory and less computing. If the synchronous between user and server breaks, then user is sending hj, and system using hk to authenticate, j ≠ k then this can be detected by repeatedly applying hash function to both the values until match is obtained. So if j > k then computes and if j < k, requests later values. So if j = 5 and k = 3 than h5 = H2 (h3).
Secure Routing in Wireless Mesh Networks
Published in Yan Zhang, Jun Zheng, Honglin Hu, Security in Wireless Mesh Networks, 2008
SAODV uses hash chains to authenticate the hop count of RREQ and RREP messages in such a way that allows every node that receives the message (either an intermediate node or the final destination) to verify that the hop count has not been decremented by an attacker. This prevents an attack of type 2. A hash chain is formed by applying a one-way hash function repeatedly to a seed.
A lightweight privacy-preserving data aggregation scheme with provable security for internet-of-things
Published in International Journal of Computers and Applications, 2020
A cryptographic hash function operation on a message which produces multiple random values is referred to as hash chain. Suppose there is a message m and a hash function h, then a hash chain of length j is represented by meaning perform hash of the output of in times. That is, . Based on the random oracle model, the j results obtained are random numbers, where only one value is needed to be stored to recompute the j set values.