How can I derive the correct public key and signature from a prehashed private key using the Go package golang.org/x/crypto/ed25519?

Ed25519 Public Key Discrepancy

Problem Description:

Using the Go package golang.org/x/crypto/ed25519, attempts to derive the public key from a given private key produce a different result compared to the expected public key as defined in a given test case.

Root Cause:

The discrepancy arises from the use of different ed25519 private key formats.

Private Key Format Difference:

• The Go package expects a private key format that consists of the 32-byte seed concatenated with the 32-byte public key.
• The test case uses a private key format that is the 64-byte result of a hash applied to the seed (or possibly 64 random bytes used as a substitute).

Solution:

Since reversing the hash used to generate the test case private keys is not feasible, conversion to a format compatible with the Go package is not possible.

Proposed Solution:

To obtain the correct public key for the test case, a modified version of the Go package can be created that utilizes the following custom functions:

getPublicKey:

<code class="go">// GetPublicKey generates the public key from the prehashed private key.
func getPublicKey(privateKey []byte) []byte {
    var A edwards25519.ExtendedGroupElement
    var hBytes [32]byte
    copy(hBytes[:], privateKey)
    edwards25519.GeScalarMultBase(&A, &hBytes)
    var publicKeyBytes [32]byte
    A.ToBytes(&publicKeyBytes)
    return publicKeyBytes[:]
}</code>

sign:

<code class="go">// Sign generates a signature from the prehashed private key, public key, and message.
func sign(privateKey, publicKey, message []byte) []byte {
    var privateKeyA [32]byte
    copy(privateKeyA[:], privateKey)
    var messageDigest, hramDigest [64]byte
    h := sha512.New()
    h.Write(privateKey[32:])
    h.Write(message)
    h.Sum(messageDigest[:0])
    var messageDigestReduced [32]byte
    edwards25519.ScReduce(&messageDigestReduced, &messageDigest)
    var R edwards25519.ExtendedGroupElement
    edwards25519.GeScalarMultBase(&R, &messageDigestReduced)
    var encodedR [32]byte
    R.ToBytes(&encodedR)
    h.Reset()
    h.Write(encodedR[:])
    h.Write(publicKey)
    h.Write(message)
    h.Sum(hramDigest[:0])
    var hramDigestReduced [32]byte
    edwards25519.ScReduce(&hramDigestReduced, &hramDigest)
    var s [32]byte
    edwards25519.ScMulAdd(&s, &hramDigestReduced, &privateKeyA, &messageDigestReduced)
    signature := make([]byte, 64)
    copy(signature[:], encodedR[:])
    copy(signature[32:], s[:])
    return signature
}</code>

Usage Example:

<code class="go">privateKeyHex := "e06d3183d14159228433ed599221b80bd0a5ce8352e4bdf0262f76786ef1c74db7e7a9fea2c0eb269d61e3b38e450a22e754941ac78479d6c54e1faf6037881d"
privateKey, _ := hex.DecodeString(privateKeyHex)
expectedPublicKey := "77ff84905a91936367c01360803104f92432fcd904a43511876df5cdf3e7e548"
expectedSig := "6834284b6b24c3204eb2fea824d82f88883a3d95e8b4a21b8c0ded553d17d17ddf9a8a7104b1258f30bed3787e6cb896fca78c58f8e03b5f18f14951a87d9a08"
publicKey := getPublicKey(privateKey)
fmt.Printf("Calculated Public Key: %x\n", publicKey)
fmt.Printf("Expected Public Key:   %s\n", expectedPublicKey)
calculatedSig := sign(privateKey, publicKey, []byte("Hello, World!"))
fmt.Printf("Calculated Signature: %x\n", calculatedSig)
fmt.Printf("Expected Signature:   %s\n", expectedSig)</code>

This approach allows for the calculation of the correct public key and signature using the modified Go package, as specified in the test case.

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