# Schnorr/EdDSA Signing

The two-party protocol for Schnorr/EdDSA signing is designed for enhanced security in elliptic-curve cryptography. Here's how it functions:

* **Schnorr Signing Algorithm**:
  1. A random $$k$$ is chosen, and $$R=k⋅G$$ is computed.
  2. The hash $$e=H(m∥R)$$ is calculated.
  3. The signature component $$s=k+e⋅xmodq$$ is computed.
  4. The signature is output as a pair $$(e,s)$$.
* **Two-Party Computation of Schnorr**:
  * **Key Generation**: As in ECDSA, parties hold random $$1x1$$ and $$2x2$$, with the public key $$Q=(x1+x2)⋅G$$.
  * **Signature Process**: Each party selects random $$2k1,k2$$ and exchanges $$R1=k1⋅G$$ and $$R2=k2⋅G$$. They then define $$R=R1+R2$$ and locally compute $$e=H(m∥R)$$.
  * **Final Signature Calculation**:
    * $$1P1$$ calculates $$s1=k1+e⋅x1$$.
    * $$2P2$$ calculates $$s2=k2+e⋅x2$$.
    * The final signature $$s$$ is $$2s1+s2$$, satisfying the Schnorr equation.
* **EdDSA Key Generation Challenges**:
  * In EdDSA, the key $$x$$ is derived by hashing it with SHA-512, and the result is split into two parts: one for the secret key and the other for a Pseudorandom Function (PRF).
  * For compatibility with EdDSA keys, a secure computation protocol for SHA-512 can be used.
  * However, for simplicity and security, $$x$$ is currently generated directly in MPC.

**Considerations and Security Implications**

* **Security in Two-Party Computation**: The protocol ensures that neither party knows the full private key or the nonce $$k$$, maintaining robust security.
* **Implementation Subtleties**: While the core ideas are straightforward, careful implementation is required to ensure security and compatibility.


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