Faster RP commits with multi-exponentiation

[dvdplm]

Use the MultiExponentiationBoundedExp trait to speed up commitment creation, which is common operation in some of our ZK Proofs.

This optimization had better results for the proofs in CGGMP'21. In the '24 version the impact is less pronounced and we should seriously consider whether the (small) gains are actually worth it.

group                                      master                          mine
-----                                      ------                          ----
AffG proof/prove                           1.27     88.3±0.10ms            1.00     69.5±1.17ms        
AffG proof/verify                          1.09     65.9±7.31ms            1.00     60.2±5.24ms        
AffG* proof/prove                          1.00      11.8±0.03s            1.00      11.8±0.03s        
AffG* proof/verify                         1.00      10.6±0.02s            1.00      10.6±0.02s        
Dec proof/prove                            1.00       7.7±0.01s            1.00       7.7±0.02s        
Dec proof/verify                           1.01       5.8±0.07s            1.00       5.7±0.01s        
Elog proof/prove                           1.00    140.5±0.78µs            1.00    140.7±0.93µs        
Elog proof/verify                          1.00    220.6±0.37µs            1.00    221.3±0.79µs        
EncElg proof/prove                         1.33     34.3±1.05ms            1.00     25.7±0.05ms        
EncElg proof/verify                        1.12     23.2±1.88ms            1.00     20.6±0.06ms        
Fac proof/prove                            1.65     58.1±0.86ms            1.00     35.3±0.09ms        
Fac proof/verify                           1.27     39.2±3.45ms            1.00     30.9±2.70ms        
Paillier-Blum modulus proof/prove          1.01   1088.7±5.12ms            1.00   1083.3±1.84ms        
Paillier-Blum modulus proof/verify         1.00    860.2±5.90ms            1.00    857.9±1.54ms        
Pedersen Ring params (prm) proof/prove     1.01    370.9±2.24ms            1.00    367.7±0.86ms        
Pedersen Ring params (prm) proof/verify    1.01    370.0±0.33ms            1.00    367.5±0.52ms        
Schnorr (sch) proof/prove                  1.00      9.4±0.02µs            1.00      9.4±0.03µs        
Schnorr (sch) proof/verify                 1.00     63.8±0.14µs            1.00     63.7±0.10µs        

Performance is essentially unchanged, except for EncElg and Fac.

The price we pay is a "powerset" proliferation of normal/wide and secret/public methods. Worth it?

[codecov]

Codecov Report

❌ Patch coverage is 99.00000% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 89.32%. Comparing base (48fb491) to head (93dd378).
⚠️ Report is 72 commits behind head on master.

Files with missing lines	Patch %	Lines
synedrion/src/cggmp21/sigma/aff_g.rs	85.71%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #184   +/-   ##
=======================================
  Coverage   89.31%   89.32%           
=======================================
  Files          40       40           
  Lines       10999    11016   +17     
=======================================
+ Hits         9824     9840   +16     
- Misses       1175     1176    +1     

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[dvdplm]

@fjarri I left these in, but they are not particularly useful long-term I think. I wrote them to check on progress as I was changing code, but I think we should remove them now.

[dvdplm]

Putting this back as draft because:

• it could have some merit to leverage the optimized multi-exp impl in different places in the code
• or, by way of a larger refactor of the way setup comittments, find a way to use multi-exp for RP commits

EIther way it's non-urgent and the gains likely minor.