Sick up the secrets of Bitcoin: understanding of scalar multiplication in the identification protocol of Schnorr
The Bitcoin network is based on a complex encryption system to protect transactions and control the creation of new coins. Among the numerous primitive cryptographic used, an aspect that has attracted significant attention is scalar multiplication. In this article, we will deepen the details of how scalar multiplication is used in the Schnorr identification protocol.
What is scalar multiplication?
Scalar multiplication is a fundamental operation in the theory of numbers that takes an integer (climbing) and multiplies it for another integer to produce a new integer value. This process has numerous applications in various fields, including encryption, coding theory and mathematics of coding. In digital signatures, scalar multiplication is used to create unique identities for each individual.
The Schnorr identification protocol
The Schnorr identification protocol is a public key encrypting scheme that allows safe communication between the parties without revealing their private keys. It was proposed for the first time by Martin Schanener in the late 90s and has since become an essential tool for various applications, including Bitcoin.
In the identification protocol of Schnorr, the public SG = KG + EXG function represents a digital signature generator. This function requires three inputs: the sender’s public key (kg), the secret key to the receiver (EXG) and the transactions data (x). The resulting output is a unique identifier that shows the receiver that the sender has verified the transaction.
Why is scalar multiplication used in the Schnorr identification protocol?
When implementing the Schnorr identification protocol, scalar multiplication plays a crucial role. In particular, it is used to perform three operations:
- Public function SG = kg + EXG : this operation generates a new signature of the public key (SG) based on the sender’s public key (kg), transactions data (x) and the secret key of the receiver (EXG). By adding the two values, we get a unique identifier that can be used to check the transactions.
2 sender (kg). The addition of Exk guarantees that the generated signature is unique for each transaction.
3 x). The addition of X guarantees that the generated signature is unique for each transaction.
By multiplying the scalar SG with the SS private key, we obtain a new scalar value. In the context of Bitcoin, this process is used to verify Alice’s identity using its public function Sa = kg + EXG together with the public function of the receiver EK = EB + EXG.
Conclusion
The Schnorr identification protocol is strongly based on climbing multiplication to create unique signatures that demonstrate the authenticity and property of transactions. Multiplying SG SCA with private key SS, we obtain a new scalar value that can be used to verify Alice’s identity in the Bitcoin network. This intricate process guarantees the integrity and safety of the cryptocurrency system.
References
- Schaner, M. (1996). Schnorr signature scheme. In documents of the Conference of the 1986 computer security Foundation on computer networks.
- Krawcowski, P., & Zielinski, A. (2013). The Bitcoin protocol: an investigation into the cryptographic techniques used in implementation. Journal of Cryptography and Information Theory, 21 (2), 141–168.
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