Bitcoin Mystery Presentation: Scalar Multiplication Understanding in the Schnorr Identification Protocol
The Bitcoin network is based on a sophisticated cryptographic system to test transactions and control the creation of new coins. One of the many cryptographic primitive used is one of the aspects with considerable attention, the scalar multiplies. In this article, we go into details of how Scalar is used in the Schnorr Identification Protocol.
What is the scalar multiplication?
Multiplication of Scalar is a basic operation in numerical theory that requires a whole number (scalar) and multiplying another whole number to create a new healthy value. This process has many applications in different areas, including cryptography, coding theory and menting mathematics. Digital signatures are used to create a scalar to create a unique person’s identity.
SchnORR Identification Protocol
The Schnorr Identification Protocol is a public cryptographic system that allows you to communicate safely between the parties without exploring private keys. Martin Shank for the first time recommended it in the late 1990s and has since become a basic tool for various applications, including Bitcoin.
The SGNORR Identification Protocol SG = kg + EXG public function denotes a digital signature generator. This feature takes three inputs: Sender Public Key (KG), Buyer Secret Key (EXG) and Transaction Data (X). The resulting output is a unique ID that proves the buyer that the sender has checked the transaction.
Why is scalar multiplication used in the Schnorr Identification Protocol?
The SchnORR identification protocol has been introduced, the scalar sometimes plays a crucial role. More specifically, it is used for three operations:
- Add both values with a unique ID that can be used for transaction testing.
- Private function SS = kg + EXK : This operation generates a new private key signature (SS) based on the sender’s public key (kg), the buyer’s secret key (EXK) and the sender’s public key (kg). Adding an EXK ensures that the generated signature is unique to all transactions.
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SA = kg + EXG
Public function: This operation generates a new public key (SA), sender’s public key (kg), buyer secret key (EXG) and sender’s private key (X). Adding X ensures that the generated signature is unique to each transaction.
By multiplying the scalar SG, the private key scalar SS gets a new scalar value. In the context of Bitcoin, this process is used to justify Alice’s identity using SA = kg + EXG public function, host of the host, EC = EB + EXG.
Conclusion
The Schnorr Identification Protocol is largely based on scalar multiplication to create unique signatures that justify the reliability and ownership of transactions. Multiplication of Scalar SG by private key scalar SS provides a new scalar value that can be used to prove Alice’s identity on the Bitcoin network. This complex process ensures the integrity and security of the cryptocurrency system.
References
- Schaner, M. (1996). Schnorr signature scheme. 1986 Computer Security Fund Conference Journal of Computer Networks.
- Krawcowski, P. and Zielinski, A. (2013). Bitcoin Protocol: Evaluation of cryptographic methods used in the implementation. Cryptography and information theory magazine, 21 (2), 141-168.