Acceleration of Inner-Pairing Product Operation for Secure Biometric Verification

. 2021 Apr 19;21(8):2859. doi: 10.3390/s21082859

Algorithm 4 Fixed-Q pairing.

Input:

s = 6 t + 2

m =

the bit length of

s, P \in G_{1}

Q^{'} = (G_{D B L}, G_{A D D}, π_{Q}, {π^{2}}_{Q})

(the precomputation tuple for Q, where

Q \in G_{2}

)
Output:

e (P, Q)

1:
Write s in signed binary form, $s = \sum_{i = 0}^{m - 1} s [i] 2^{i}$ with $s [i] \in {- 1, 0, 1}$
2:
$f \leftarrow 1, c n t \leftarrow 1$
3:
for $i \leftarrow m - 2$ down to 0 do
4:
$λ, c \leftarrow G_{D B L} [i]$
5:
Compute $g \leftarrow (y_{P} + λ x_{P} + c)$
6:
$f \leftarrow f^{2} \cdot g$
7:
if $s [i] \neq 0$ then
8:
$λ, c \leftarrow G_{A D D} [c n t]$
9:
Compute $g \leftarrow (y_{P} + λ x_{P} + c)$
10:
$c n t \leftarrow c n t + 1$
11:
$f \leftarrow f \cdot g$
12:
end if
13:
end for
14:
$λ, c \leftarrow π_{Q}$
15:
Compute $g \leftarrow (y_{P} + λ x_{P} + c)$
16:
$f \leftarrow f \cdot g$
17:
$λ, c \leftarrow {π^{2}}_{Q}$
18:
Compute $g \leftarrow (y_{P} + λ x_{P} + c)$
19:
$f \leftarrow f \cdot g$
20:
$f \leftarrow f^{(p^{12} - 1) / r}$
21:
returnf