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NTT

NTT Example​

package main

import (
    "github.com/ingonyama-zk/icicle/v3/wrappers/golang/core"
    "github.com/ingonyama-zk/icicle/v3/wrappers/golang/curves/bn254"
    "github.com/ingonyama-zk/icicle/v3/wrappers/golang/curves/bn254/ntt"
    "github.com/ingonyama-zk/icicle/v3/wrappers/golang/runtime"

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

func init() {
  // Load backend using env path
    runtime.LoadBackendFromEnvOrDefault()
    // Set Cuda device to perform
    device := runtime.CreateDevice("CUDA", 0)
    runtime.SetDevice(&device)

    cfg := core.GetDefaultNTTInitDomainConfig()
    initDomain(18, cfg)
}

func initDomain(largestTestSize int, cfg core.NTTInitDomainConfig) runtime.EIcicleError {
    rouMont, _ := fft.Generator(uint64(1 << largestTestSize))
    rou := rouMont.Bits()
    rouIcicle := bn254.ScalarField{}
    limbs := core.ConvertUint64ArrToUint32Arr(rou[:])

    rouIcicle.FromLimbs(limbs)
    e := ntt.InitDomain(rouIcicle, cfg)
    return e
}

func main() {
    // Obtain the default NTT configuration with a predefined coset generator.
    cfg := ntt.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 := ntt.Ntt(scalars, dir, &cfg, results)
    if err != runtime.Success {
        panic("NTT operation failed")
    }

    ntt.ReleaseDomain()
}

NTT Method​

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

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​

  • EIcicleError: A runtime.EIcicleError value, which will be runtime.Success if the operation was successful, or an error if something went wrong.

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 {
    StreamHandle       runtime.Stream
    CosetGen           T
    BatchSize          int32
    ColumnsBatch       bool
    Ordering           Ordering
    areInputsOnDevice  bool
    areOutputsOnDevice bool
    IsAsync            bool
    Ext                config_extension.ConfigExtensionHandler
}

Fields​

  • StreamHandle: Specifies the stream (queue) to use for async execution.
  • CosetGen: Coset generator. Used to perform coset (i)NTTs.
  • 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.
  • Ordering: Ordering of inputs and outputs (KNN, KNR, KRN, KRR), 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.
  • Ext: Extended configuration for backend.

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 bn254.ScalarField, cfg core.NTTInitDomainConfig) runtime.EIcicleError

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() runtime.EIcicleError

Return Value​

  • EIcicleError: A runtime.EIcicleError value, which will be runtime.Success if the operation was successful, or an error if something went wrong.