Quantum Aware Distributed Ledger Technology …

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Table 2 Mathematical symbols and their description

4.2

Signature Creation

Every method of development of signatures starts with a hash of the signed message

(i.e. hm = H(msg)). In its hexadecimal representation, we process message-hash.

Since we use SHA384, hm is comprised of 96 hexadecimal symbols (Eq.4.2). The

symbols are indexed as one to ninety-six. Then we group the records according to

their symbols, as follows: The index set containing symbol 0; the index set containing

symbol 1; up to the index set containing symbol F (Algorithm 1 steps 1–3). Then, in

each of the 16 sets, we calculate a total of 16 integer values (steps 4–5). We utilize

module operators to ensure all 17 values range from 1 to w (step 6). We calculate a

check-sum for the above sixteen values in the next level: we extract each of the 17 w

values and summarize all those differences (steps 7–8). Subsequently, we produce

message signatures by computing post-images with the initial value “l-1”, numbers

of terms the identical integer value (step 9). However, the ultimate sign component

is created by calculating the post-image number of times the check-sum of the lth

sk-element (step 10). Figure3 illustrates the process of creating signatures with an

example.

hm =

96



i=1

mi= {m1, m2, ......, m96}