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NTT

NTT Example​

package main

import (
  "github.com/ingonyama-zk/icicle/v2/wrappers/golang/core"
  cr "github.com/ingonyama-zk/icicle/v2/wrappers/golang/cuda_runtime"
  bn254 "github.com/ingonyama-zk/icicle/v2/wrappers/golang/curves/bn254"

  "github.com/consensys/gnark-crypto/ecc/bn254/fr/fft"
)

func init() {
  cfg := bn254.GetDefaultNttConfig()
  initDomain(18, cfg)
}

func initDomain[T any](largestTestSize int, cfg core.NTTConfig[T]) core.IcicleError {
  rouMont, _ := fft.Generator(uint64(1 << largestTestSize))
  rou := rouMont.Bits()
  rouIcicle := bn254.ScalarField{}

  rouIcicle.FromLimbs(rou[:])
  e := bn254.InitDomain(rouIcicle, cfg.Ctx, false)
  return e
}

func main() {
  // Obtain the default NTT configuration with a predefined coset generator.
  cfg := bn254.GetDefaultNttConfig()

  // Define the size of the input scalars.
  size := 1 << 18

  // Generate scalars for the NTT operation.
  scalars := bn254.GenerateScalars(size)

  // Set the direction of the NTT (forward or inverse).
  dir := core.KForward

  // Allocate memory for the results of the NTT operation.
  results := make(core.HostSlice[bn254.ScalarField], size)

  // Perform the NTT operation.
  err := bn254.Ntt(scalars, dir, &cfg, results)
  if err.CudaErrorCode != cr.CudaSuccess {
    panic("NTT operation failed")
  }
}

NTT Method​

func Ntt[T any](scalars core.HostOrDeviceSlice, dir core.NTTDir, cfg *core.NTTConfig[T], results core.HostOrDeviceSlice) core.IcicleError

Parameters​

  • scalars: A slice containing the input scalars for the transform. It can reside either in host memory or device memory.
  • dir: The direction of the NTT operation (KForward or KInverse).
  • cfg: A pointer to an NTTConfig object, containing configuration options for the NTT operation.
  • results: A slice where the results of the NTT operation will be stored. This slice can be in host or device memory.

Return Value​

  • CudaError: Returns a CUDA error code indicating the success or failure of the NTT operation.

NTT Configuration (NTTConfig)​

The NTTConfig structure holds configuration parameters for the NTT operation, allowing customization of its behavior to optimize performance based on the specifics of your protocol.

type NTTConfig[T any] struct {
    Ctx cr.DeviceContext
    CosetGen T
    BatchSize int32
    ColumnsBatch bool
    Ordering Ordering
    areInputsOnDevice  bool
    areOutputsOnDevice bool
    IsAsync bool
    NttAlgorithm NttAlgorithm
}

Fields​

  • Ctx: Device context containing details like device ID and stream ID.
  • CosetGen: Coset generator used for coset (i)NTTs, defaulting to no coset being used.
  • BatchSize: The number of NTTs to compute in one operation, defaulting to 1.
  • ColumnsBatch: If true the function will compute the NTTs over the columns of the input matrix and not over the rows. Defaults to false.
  • Ordering: Ordering of inputs and outputs (KNN, KNR, KRN, KRR, KMN, KNM), affecting how data is arranged.
  • areInputsOnDevice: Indicates if input scalars are located on the device.
  • areOutputsOnDevice: Indicates if results are stored on the device.
  • IsAsync: Controls whether the NTT operation runs asynchronously.
  • NttAlgorithm: Explicitly select the NTT algorithm. Default value: Auto (the implementation selects radix-2 or mixed-radix algorithm based on heuristics).

Default Configuration​

Use GetDefaultNTTConfig to obtain a default configuration, customizable as needed.

func GetDefaultNTTConfig[T any](cosetGen T) NTTConfig[T]

Initializing the NTT Domain​

Before performing NTT operations, it's necessary to initialize the NTT domain; it only needs to be called once per GPU since the twiddles are cached.

func InitDomain(primitiveRoot ScalarField, ctx cr.DeviceContext, fastTwiddles bool) core.IcicleError

This function initializes the domain with a given primitive root, optionally using fast twiddle factors to optimize the computation.

Releasing the domain​

The ReleaseDomain function is responsible for releasing the resources associated with a specific domain in the CUDA device context.

func ReleaseDomain(ctx cr.DeviceContext) core.IcicleError

Parameters​

  • ctx: a reference to the DeviceContext object, which represents the CUDA device context.

Return Value​

The function returns a core.IcicleError, which represents the result of the operation. If the operation is successful, the function returns core.IcicleErrorCode(0).

Example​

import (
    "github.com/icicle-crypto/icicle-core/cr"
    "github.com/icicle-crypto/icicle-core/core"
)

func example() {
  cfg := GetDefaultNttConfig()
  err := ReleaseDomain(cfg.Ctx)
  if err != nil {
      // Handle the error
  }
}