帮我用Go写一个基于RSA的VRF函数

RSA是一种非对称加密算法，可以用于生成数字签名和验证数字签名。下面是一个使用RSA实现VRF的示例代码：

package main

import (
    "crypto/rand"
    "crypto/rsa"
    "crypto/sha256"
    "crypto/subtle"
    "math/big"
)

// VRF generates a verifiable random number using the provided secret key and message.
func VRF(secretKey *rsa.PrivateKey, message []byte) ([]byte, []byte, error) {
    // Generate a random nonce.
    nonce, err := rand.Int(rand.Reader, secretKey.PublicKey.N)
    if err != nil {
        return nil, nil, err
    }
    nonceBytes := nonce.Bytes()

    // Compute the hash of the message and the nonce.
    h := sha256.New()
    h.Write(message)
    h.Write(nonceBytes)
    hash := h.Sum(nil)

    // Use the secret key to sign the hash.
    sig, err := rsa.SignPKCS1v15(rand.Reader, secretKey, crypto.SHA256, hash)
    if err != nil {
        return nil, nil, err
    }

    // Compute the output by XORing the hash with the signature.
    output := make([]byte, len(hash))
    for i := range hash {
        output[i] = hash[i] ^ sig[i]
    }

    return output, nonceBytes, nil
}

// VerifyVRF verifies the output of a VRF function using the provided public key, message, output, and nonce.
func VerifyVRF(publicKey *rsa.PublicKey, message, output, nonce []byte) bool {
    // Compute the hash of the message and the nonce.
    h := sha256.New()
    h.Write(message)
    h.Write(nonce)
    hash := h.Sum(nil)

    // Compute the signature for the hash using the public key.
    sig, err := rsa.EncryptPKCS1v15(rand.Reader, publicKey, hash)
    if err != nil {
        return false
    }

    // Compute the expected output by XORing the hash with the signature.
    expectedOutput := make([]byte, len(hash))
    for i := range hash {
        expectedOutput[i] = hash[i] ^ sig[i]
    }

    // Compare the expected output with the provided output.
    return subtle.ConstantTimeCompare(output, expectedOutput) == 1
}

func main() {
    // Generate a new RSA key pair.
    privateKey, err := rsa.GenerateKey(rand.Reader, 2048)
    if err != nil {
        panic(err)
    }
    publicKey := &privateKey.PublicKey

    // Generate a message to be signed.
    message := []byte("hello world")

    // Generate a verifiable random number using the VRF function.
    output, nonce, err := VRF(privateKey, message)
    if err != nil {
        panic(err)
    }

    // Verify the output using the VerifyVRF function.
    isValid := VerifyVRF(publicKey, message, output, nonce)
    if isValid {
        println("The output is valid!")
    } else {
        println("The output is not valid!")
    }
}

注意，上述示例中的签名和验证函数使用了RSA PKCS#1 v1.5 填充。在实际应用中，您可能需要使用更安全的填充方案，例如RSA-PSS。