Bench marking Chaum-Pedersen Signature in the G1 vs in another sister group

[drskalman]

This is to see if we get a significant speed up using another (smaller) curve to compute Chaum-Pedersen Signatures instead of doing it in G1.

[drskalman]

I'm getting this result from benchmarking, these are for 100 operation in each benchmark:

test bench::test_add_in_signature_group_no_glv_no_mul_by_a        ... bench:      52,390.58 ns/iter (+/- 7,576.31)
test bench::test_add_in_weirestarss_sister_group                  ... bench:      31,420.78 ns/iter (+/- 1,886.16)
test bench::test_base_field_mul_in_signature_group                ... bench:       3,314.71 ns/iter (+/- 189.57)
test bench::test_base_field_mul_in_weirestarss_sister_group       ... bench:       1,756.46 ns/iter (+/- 152.71)
test bench::test_double_in_signature_group_no_glv_no_mul_by_a     ... bench:      41,997.51 ns/iter (+/- 4,560.46)
test bench::test_double_in_weirestarss_sister_group               ... bench:      31,403.28 ns/iter (+/- 4,360.36)
test bench::test_scalar_mul_in_signature_group                    ... bench:   9,855,113.30 ns/iter (+/- 1,388,543.03)
test bench::test_scalar_mul_in_signature_group_no_glv_no_mul_by_a ... bench:  15,120,891.70 ns/iter (+/- 2,198,052.41)
test bench::test_scalar_mul_in_weirestarss_sister_group           ... bench:   9,961,467.90 ns/iter (+/- 1,480,594.64)

while field multiplication is (/ 3314.71 1756.46) 88% faster, Curve addition and doubling are only (/ 52390.58 31420.78) = 66% (/ 41997.51 31403.28) = 33% faster respectively. So I don't find it a surprise that scalar multiplication is only (/ 15120891.70 9961467.90) = 51% faster. And that advantage is erased by use of GLV which is (/ 15120891.70 9855113.30) = 53% faster than naive scalar multiplication.