perf(csp): reduce allocations using in-place scalar operations

[neetance]

Summary

This PR optimizes the CSP (Compressed Sigma Protocol) prover and verifier by reducing allocation overhead in scalar operations.

The changes are based on the mathlib optimizations (fr.Element-based Zr) and introduce in-place arithmetic and scratch reuse across the CSP proof methods.

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Changes

• Replace allocation-heavy operations:

  • ModAddMul -> ModAddMul2InPlace / ModAddMul3InPlace
  • ModMul -> ModMulInPlace

• Introduce scratch variable reuse in verifier:

  • avoid repeated Zr allocations inside loops

• Optimize folding steps in prover:

  • eliminate temporary scalar allocations during vector reduction

• Optimize sVector computation:

  • use in-place updates instead of allocating intermediate values

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Performance Improvement

• Significant reduction in the allocs/op metric (by 13%)
• Lower GC pressure in CSP proof generation and verification
• Execution time remains stable (no regressions observed)

The actual benchmark results given in the mathlib pr

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Testing

• All tests pass:
  go test ./token/core/zkatdlog/nogh/v1/...

• Benchmarks executed successfully

• No functional changes

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Note

I modified the go.mod file to replace the actual mathlib library url with my current mathlib commit, which can be changed back to normal once the mathlib pr is merged

Let me know if this looks good
Thanks 🙏

[adecaro]

why removing the comments on all these fields?

[adecaro]

why removing these comments?

[adecaro]

@neetance , fantastic, thanks. Please, just restore the code comments unless they are not appropriate anymore, but I don't think so. Thanks 🙏

[adecaro]

LGTM

[adecaro]

Hi @neetance , I have merged your PR on mathlib and created the tag v0.1.0. Please, update the go.mod of the token-sdk and we are good to merge this. Thanks a lot for this great effort 🙏

[adecaro]

@neetance , would you like to work on porting token/core/zkatdlog/nogh/v1/crypto/math/math.go#BatchInverse to further improve its efficiency? What do you think?

[neetance]

@adecaro yes sure sounds good to me 😄
Will analyze the code in detail and figure out where we can make some optimizations and open an issue once I come up with a solution