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.