Transaction with "SystemProgram.createAccount" results in "Error: Signature verification failed at Transaction.serialize" - solana

Question

What I'm tryding to achieve is a webpage on which the user connects its phantom wallet and then by a simple press of a button creates a token.
In order to achieve that, I created a simple transaction for now which creates an account for the future token (based on https://www.programcreek.com/typescript/?api=#solana/spl-token.createInitializeMintInstruction)
this is the function which is called when the user press the button:
const onClickCreate = useCallback( async () => {
const lamports = await getMinimumBalanceForRentExemptMint(connection)
const mint = Keypair.generate()
console.log(mint.publicKey.toBase58())
const transaction = new Transaction({feePayer: publicKey})
transaction.add(
SystemProgram.createAccount({
fromPubkey: publicKey,
newAccountPubkey: mint.publicKey,
space: MINT_SIZE,
lamports,
programId: TOKEN_PROGRAM_ID
}),
)
const signature = await sendTransaction(transaction, connection);
await connection.confirmTransaction(signature, 'processed');
}, [publicKey, signTransaction, sendTransaction, connection]);
Executing the code results in the error saying that the signature failed.
I use wallet-adapter to connect the user's wallet (which gives me access to the variable publicKey)
If I replace the createAccount function by SystemProgram.transfer everything works ok :
const transaction = new Transaction().add(
SystemProgram.transfer({
fromPubkey: publicKey,
toPubkey: Keypair.generate().publicKey,
lamports: lamportsI,
})
);
Thank you for your time

Answer 1

Ok so I checked a little bit more and found someone on the solana forums in Feb 2022 who had kind of the same problem I have : https://forums.solana.com/t/signature-error-when-create-a-new-account/5348/2
the answer by #zicklag worked out for me.
for short, you simply have to make the mint keypair sign the transaction (which seems logic after you think about it)
final code (inside the function called by pressing the button):
if (!publicKey) throw new WalletNotConnectedError();
const lamports = await getMinimumBalanceForRentExemptMint(connection)
const mint = Keypair.generate()
const transaction = new Transaction({ feePayer: publicKey, recentBlockhash: (await connection.getLatestBlockhash()).blockhash });
transaction.add(
SystemProgram.createAccount({
fromPubkey: publicKey,
newAccountPubkey: mint.publicKey,
space: MINT_SIZE,
lamports,
programId: TOKEN_PROGRAM_ID
})
)
transaction.sign(mint)
const txID = await sendTransaction(transaction, connection)