By Asim Kumar Pal, Debabrata Nath and Sumit Chakraborty
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Extra resources for A Discriminatory Rewarding Mechanism for Sybil detection with application to TOR
We compute all p2i p1 and pn . The missing ⌊n 2⌋ − 1 prefixes p2i+1 = p2i ◦ x2i+1 can be computed in parallel. By C(k n) and D(k n) we denote the size and depth resp. of Ak (n) . Furthermore D∗ (k n) is the depth of pn using Ak (n) . 38) We have used the fact that Ak(n) computes pn before the last step. 38) easily follows from induction. 4 : 0 ≤ k ≤ ⌈log n⌉ The prefix problem is solved by Ak(n) . 40) How can we use the prefix problem for the addition of binary numbers ? We use the subcircuits S1 and S5 of Krapchenko’s adder with size 2n and n − 1 resp.
In depth 2 . The number of blocks of size 2l may be estimated by 2m−l . 13) S4 is rather simple too. In S3 we have computed all ck 2τ −1 . The other carry bits are computed in τ steps where we compute all ck 2τ −l −1 in step l . For even k these carry bits have already been computed. 14) G(2j+1) 2τ −l −1 (2j) 2τ −l ∨ V(2j+1) 2τ −l −1 (2j) 2τ −l c(2j) 2τ −l −1 The terms on the right-hand side are computed in S2 , S3 or in earlier steps of S4 . The depth of step l is 2 while the size is 2 for each new 2m−τ +l −1 − 1} .
Ones which are neighbors correspond to implicants of length 3 . The ones in the first column correspond to a b c and the first two ones in the second column correspond to a b c . The 1-colored subcube for a b c can be enlarged to the 1-colored subcube of the ones in the first and last column corresponding to the implicant b c . Since the 1-colored subcube for a b c cannot be enlarged, a b c is a prime implicant. We easily detect prime implicants in Karnaugh diagrams. Furthermore, we see that the one in the first row is contained only in one maximal 1-colored subcube, namely for a b c , which therefore 31 has to be contained in a minimal polynomial.
A Discriminatory Rewarding Mechanism for Sybil detection with application to TOR by Asim Kumar Pal, Debabrata Nath and Sumit Chakraborty