move opening to g1

[zhenfeizhang]

No description provided.

[zhenfeizhang]

compared with group switched feature:

• improves committing time
• improve proof size

Before the change, without group switch

KZG commit for 4 variables: 320179 ns
KZG open for 4 variables: 3412926 ns
KZG verify for 4 variables: 3752451 ns
====================================
KZG commit for 5 variables: 397799 ns
KZG open for 5 variables: 4398150 ns
KZG verify for 5 variables: 4002194 ns
====================================
KZG commit for 6 variables: 530965 ns
KZG open for 6 variables: 5730684 ns
KZG verify for 6 variables: 4108040 ns
====================================
KZG commit for 7 variables: 672950 ns
KZG open for 7 variables: 7446902 ns
KZG verify for 7 variables: 4480586 ns
====================================
KZG commit for 8 variables: 1077177 ns
KZG open for 8 variables: 10234624 ns
KZG verify for 8 variables: 4674875 ns
====================================
KZG commit for 9 variables: 1833370 ns
KZG open for 9 variables: 16216657 ns
KZG verify for 9 variables: 4706470 ns
====================================
KZG commit for 10 variables: 2770738 ns
KZG open for 10 variables: 25197178 ns
KZG verify for 10 variables: 4844978 ns
====================================
KZG commit for 11 variables: 5211457 ns
KZG open for 11 variables: 41506955 ns
KZG verify for 11 variables: 5532057 ns
====================================
KZG commit for 12 variables: 8699348 ns
KZG open for 12 variables: 71344089 ns
KZG verify for 12 variables: 5552975 ns
====================================

Before the change, with group switch

KZG commit for 4 variables: 1051915 ns
KZG open for 4 variables: 1161886 ns
KZG verify for 4 variables: 4896675 ns
====================================
KZG commit for 5 variables: 1162792 ns
KZG open for 5 variables: 1554766 ns
KZG verify for 5 variables: 5152696 ns
====================================
KZG commit for 6 variables: 1678406 ns
KZG open for 6 variables: 2091010 ns
KZG verify for 6 variables: 5341615 ns
====================================
KZG commit for 7 variables: 2129416 ns
KZG open for 7 variables: 2941526 ns
KZG verify for 7 variables: 5772759 ns
====================================
KZG commit for 8 variables: 3449067 ns
KZG open for 8 variables: 3892729 ns
KZG verify for 8 variables: 5926604 ns
====================================
KZG commit for 9 variables: 6093248 ns
KZG open for 9 variables: 5731613 ns
KZG verify for 9 variables: 6182187 ns
====================================
KZG commit for 10 variables: 9091568 ns
KZG open for 10 variables: 8584621 ns
KZG verify for 10 variables: 6043149 ns
====================================
KZG commit for 11 variables: 16751166 ns
KZG open for 11 variables: 13702945 ns
KZG verify for 11 variables: 6403623 ns
====================================
KZG commit for 12 variables: 29262912 ns
KZG open for 12 variables: 23269407 ns
KZG verify for 12 variables: 7064318 ns
====================================

After the change

KZG commit for 4 variables: 389357 ns
KZG open for 4 variables: 1330633 ns
KZG verify for 4 variables: 4385702 ns
====================================
KZG commit for 5 variables: 430138 ns
KZG open for 5 variables: 1602065 ns
KZG verify for 5 variables: 4753737 ns
====================================
KZG commit for 6 variables: 604067 ns
KZG open for 6 variables: 2271389 ns
KZG verify for 6 variables: 4949438 ns
====================================
KZG commit for 7 variables: 742126 ns
KZG open for 7 variables: 2853529 ns
KZG verify for 7 variables: 4909454 ns
====================================
KZG commit for 8 variables: 1235471 ns
KZG open for 8 variables: 3917065 ns
KZG verify for 8 variables: 5437127 ns
====================================
KZG commit for 9 variables: 1906835 ns
KZG open for 9 variables: 5908130 ns
KZG verify for 9 variables: 5743415 ns
====================================
KZG commit for 10 variables: 2854581 ns
KZG open for 10 variables: 9411021 ns
KZG verify for 10 variables: 5563053 ns
====================================
KZG commit for 11 variables: 5275810 ns
KZG open for 11 variables: 13650352 ns
KZG verify for 11 variables: 6012449 ns
====================================
KZG commit for 12 variables: 9393401 ns
KZG open for 12 variables: 23776718 ns
KZG verify for 12 variables: 6163272 ns

[chancharles92]

LGTM