Comments about section 2 (from 2nd Expert Review)

[yumi-sakemi]

Comments from Chloe (Expert Reviewer)

• 2.2: 'The optimal Ate pairing is considered to be the most efficient to compute is the one that is most commonly used for practical implementation.' -> 'The optimal Ate pairing is considered to be the most efficient to compute and is the one that is most commonly used for practical implementation.'
• 2.2: Choose G_2 or G2 (probably G_2 is easier since there are many instances also of G_1 and G_T)
• 2.2: 'There also exists cyclic subgroup' -> 'There also exists a cyclic subgroup'
• 2.3: 'b is an element of multiplicative group of order p' -> 'b is a nonzero element of F_p' OR 'b is an element of a multiplicative group (F_p)^* of order p-1' OR 'b is an element of the multiplicative group of F_p'
• 2.3: 'embedded degree' -> 'embeddiing degree'
• 2.4: 'r-torsions' -> 'r-torsion'
• 2.5: (paragraph 2): of degree d' -> of degree d

[yumi-sakemi]

A word G2 is my mistake and G_2 is correct. I replaced G2 with G_2.

[Tsune3110]

OK!

This is a cross-check as a co-author.

[yumi-sakemi]

Thank you for your checking :-) I close this issue!