Tangem Wallet Pack of 2 - Secure Crypto Wallet - Trusted Cold Storage for Bitcoin, Ethereum, NFT's &

Tangem Wallet Pack of 2 - Secure Crypto Wallet - Trusted Cold Storage for Bitcoin, Ethereum, NFT's &
Key item features Ultimate Security: Generates a private key that remains on the card, safeguarding crypto and NFTs from hackers with EAL6+ certification and audited firmware. Versatile Compatibility: Manages over 13,000 tokens across 70+ blockchains, supporting DeFi, NFTs, and DeEx without wires, Bluetooth, or USB. Effortless Operation: Utilizes NFC for secure transactions via a mobile device and the Tangem app, enabling buying and selling crypto with various payment methods. Smart Backup: Features a second Tangem Wallet as a backup, eliminating the need for paper, pictures, or seed phrases for recovery. Durable Design: Boasts IP68 protection against environmental conditions, ensuring longevity and robust physical security. Comprehensive Support: Compatible with Bitcoin, Ethereum, Solana, XRP, USDT, and over 6,000 cryptocurrencies, integrating with dApps and WalletConnect.

LBANK

LBANK

Why do we need additional secret value (k) in ECDSA?

Formula for calculating an ECDSA signature (r, s) is:

s = k-1(z + qr)

k - private key for a random point R
z - hash of a message
q - original private key
r - x(R)

I am interested in why do we need two secret values (k and q) in a formula for calculating ECDSA signature? In other words, why we need one additional secret value k (and its public key - point on a curve) in additional to already existing one secret value q (and its public key)? Couldn't it be realized with only one unknown value (q)?

I found some answer here.

The reason nonce is used is because you need to create two unknowns so that people cannot reverse engineer the private key from the public key.

It seems to me that this is so that we have one equation with two unknowns (which is unsolvable). If only the original private key q is present in the equation, i.e. if it is the only unknown (without the additional secret k), we would have one equation with one unknown, which is solvable. However, I'm not sure. Is that the reason or something else/additional?

Also, why is it used as k-1 in equation and not just k? Some special security reason or just a "design detail" of the algorithm creators?



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