How to sign with private key(Not secret key) that was created by "RFC-8032"(described below contents) on offline?

Question

Backgrounds

I am working on "ASTAR" parachain scene(TestNet: Shibuya).

I can sign message(unsigned-transaction) on offline environment and then broadcast signed-messaged(signed-transaction). When signing message, I used "signWith" method with keypair(keyring.addFromUri(mnemonic)).

---

Issue

I need to sign message(unsigned-transaction) with private-key created by below attached logic on offline environment.

But, I couldn't find out how to sign with that key.

    import { mnemonicGenerate, cryptoWaitReady, mnemonicToMiniSecret, ed25519PairFromSeed } from '@polkadot/util-crypto';
    import { hexToU8a, u8aToHex } from '@polkadot/util';
    import * as ed from '@noble/ed25519';  // npm install @noble/[email protected] (2.0 doesn't support import via 'require')
    
    const generatePrivateKeys = async () => {
    
        const mnemonic = mnemonicGenerate(); // Creates a valid mnemonic string using using [BIP39]
        console.log(`mnemonic : ${mnemonic}`);
    
        await cryptoWaitReady();
    
        const seed = mnemonicToMiniSecret(mnemonic);
        console.log(`seed : ${seed}`);
    
        const { publicKey, secretKey } = ed25519PairFromSeed(seed);
    
        const seedToImport = hexToU8a(u8aToHex(secretKey).slice(2,66));
        // console.log("initial seed :", u8aToHex(seedToImport));
    
        // Derive the Ed25519 key pair from the seed according to RFC-8032 (Section 5.1.5)
        const hash = await ed.utils.sha512(seedToImport)    
        let left = hash.slice(0,32)
        left[0] &= 248;
        left[31] &= 127;
        left[31] |= 64;
        const privateKeyToImport = modlLE(left);
        const publicKeyToImport = ed.Point.BASE.multiply(privateKeyToImport);
        console.log("private key :", privateKeyToImport.toString(16).padStart(64, '0'))
        console.log("public key  :", Buffer.from(publicKeyToImport.toRawBytes()).toString("hex"))
    }
    
    function mod(a, b) {
        const res = a % b;
        return res >= BigInt(0) ? res : b + res;
    }
    function bytesToNumberLE(uint8a) {
        if (!(uint8a instanceof Uint8Array))
            throw new Error('Expected Uint8Array');
        return BigInt('0x' + bytesToHex(Uint8Array.from(uint8a).reverse()));
    }
    function modlLE(hash) {
        return mod(bytesToNumberLE(hash), ed.CURVE.l);
    }
    const hexes = Array.from({ length: 256 }, (v, i) => i.toString(16).padStart(2, '0'));
    function bytesToHex(uint8a) {
        if (!(uint8a instanceof Uint8Array))
            throw new Error('Uint8Array expected');
        let hex = '';
        for (let i = 0; i < uint8a.length; i++) {
            hex += hexes[uint8a[i]];
        }
        return hex;
    }
    
    generatePrivateKeys().catch(console.error).finally(() => process.exit());

---

Questions

Q1) Is it possible to sign a message with private key?

Q1-1) If so, can I get some reference contents or sample code?

Q1-2) If not, is it need to convert private key or another methods?

Q2) Where can I get some technical-information about cryptography on polkadot? Substate? or Parity?

Thanks~

Answer 1

Where can I get some technical-information about cryptography on polkadot? Substate? or Parity?

You can read the following resources to understand polkadot cryptography: https://wiki.polkadot.network/docs/learn-cryptography

https://research.web3.foundation/crypto