Modular arithmetic operation

[hecmas]

We introduce the modular arithmetic operation, i.e., the check that:

A*B + C = op (mod D)

as a new instruction on the arithmetic state machine. Note that the E register is not necessary and it is considered to be "free" when checking this instruction.

• proverjs: PR 251.
• zkasmcom: PR 87.
• ROM:
  • ecrecover: PR 348.
  • ecAdd, ecMul and ecPairing: Commit 3178efe057.
  • point-evaluation: Commit 6c8b408136

Numbers

• For ecrecover, we have gone from:

  ; RESOURCES:
  ;   PATH without root:                   [steps: 4601, bin: 8,  arith: 1010]
  ;   PATH with root:                      [steps: 6383, bin: 17, arith: 527, keccak: 1]
  ;   PATH with result of dbl is infinity: [steps: 6368, bin: 16, arith: 527]
  ; --------------------------------------------------------------------------------------
  ;  worst case:                           [steps: 6383, bin: 17, arith: 1010]
  

  to

  ; RESOURCES:
  ;   PATH without root:                   [steps: 3073, bin: 8, arith: 505]
  ;   PATH with root:                      [steps: 6343, bin: 13, arith: 520, keccak: 1]
  ;   PATH with result of dbl is infinity: [steps: 6332, bin: 12, arith: 520]
  ; --------------------------------------------------------------------------------------
  ;  worst case:                           [steps: 6343, bin: 13, arith: 520, keccak: 1]
  

• For polEvalFrBLS12381 we have gone from:

   {
    cntArith: 409948n,
    cntBinary: 205010n,
    cntSteps: 2796040
  }
  

  to

  {
    cntArith: 164004n,
    cntBinary: 124544n,
    cntSteps: 1692140
  }