Schnorr & Adapter Signature flowchart

schnorr_sig_chart.md

  flowchart TD
    classDef root fill:#f96;
    classDef expr fill:#ff0;
    classDef leaf fill:#0f0;
    A:::root
    A2:::root
    A3:::root
    A4:::root
    A5:::root
    A6:::root
    
    P22:::leaf
    A(The secret key 'sk': a 32-byte array) --> B(sk)
    B --> C["Let pk = bytes(int(sk).G"]
    C:::expr --> D(pk)
    D --> E("Let P = lift_x(int(pk))")
    E:::expr --> F(P)
    B --> C2["Let d' = int(sk)"]
    
    A5("tweak 't': a 32-byte array") --> B5(t)
    B5 --> C5["Let T = t.G"]
    C5:::expr --> D5(T)
    C2:::expr --> D2(d')
    
    B2 --> join2
    B2 --> join10
    
    subgraph createAdaptor
    D5 --> join11
    D2 --> E2["Let P = d'.G"]
    E2:::expr --> F2(P)
    
    D2 --> join1
    F2 --> join1
    join1((o)) --> G2["Let d = d' if has_even_y(P), \n otherwise let d = n - d'"]
    G2:::expr --> H2(d)
    H2 --> join9((o))
    join9 --> I2["Let t be the byte-wise xor \n of bytes(d) and hash[BIP340/aux](a)"]
    I2:::expr --> J2(t)
    
    J2 --> join2
    F2 --> join2
    join2((o)) --> Z22["Let rand = hash[BIP0340/nonce] \n (t || bytes(P) || m )"]
    Z22:::expr --> Y22(rand)
    Y22 --> K2["Let k' = int(rand) mod n"]
    K2:::expr --> L2(k')
    L2 --> M2["Let R = k'.G"]
    M2:::expr --> N2(R)
    F2 --> join10
    N2 --> join10((o))
    join10 --> O2["Let e = int(hash[BIP340/challenge]\n(bytes(R) || bytes(P) || m)) mod n"]
    O2:::expr --> R2(e)
    N2 --> P2["Let k = k' if has_even_y(R), \n otherwise let k = n - k'"]
    P2:::expr --> Q2(k)
    N2 --> join11((o))
    join11 --> U2["Let R' = R + T"]
    U2:::expr --> S2(R')
    R2 --> join7((o))
    Q2 --> join7
    join7 --> T2["Let s = bytes((k + e.d) mod n)"]
    T2:::expr --> V2(S)
    V2 --> join12((o))
    join12 --> W2["Let sig' = bytes(R') || s"]
    end
    
    S2 --> join12
    W2:::expr --> X2(sig')
    X2 --> Y2["Let s = int(sig'[32:64])"]
    Y2:::expr --> A22(s)
    X2 --> Z2["Let r' = int(sig'[0:32])"]
    Z2:::expr --> B22(r')
    B5 --> join6
    
    subgraph recoverSignatureFromAdaptor
    B22 --> join6((o))
    join6 --> C22["Let r = r' + t"]
    C22:::expr --> D22(r)
    A22 --> join8((o))
    D22 --> join8
    join8 --> E22["Let sig = r || s"]
    end
    
    E22:::expr --> F22(sig)
    F22 --> H22["Let r = int(sig[0:32])"]
    H22:::expr --> J22(r)
    F22 --> G22["Let s = int(sig[32:64])"]
    G22:::expr --> I22(s)
    
    B2 --> join3
    
    subgraph verifySignature
    F --> join4((o))
    I22 --> join4
    L22 --> join4

    F --> join3
    J22 --> join3((o))
    join3 --> K22["Let e = int(hash[BIP0340/challenge]\n(bytes(r) || bytes(P) || m)) mod n"]
    K22:::expr --> L22(e)
    
    
    join4 --> M22["Let R = s.G - e.P"]
    M22:::expr --> N22(R)
    N22 --> join5((o))
    J22 --> join5
    join5 --> O22["!is_infinite(R) && has_even_y(R) && x(R) == r"]
    
    O22:::expr --> P22(success)
    end
    
    A2(The message 'm': a 32-byte array) --> B2(m)
    
    A3("Auxiliary random data 'a': a 32-byte array.") --> C3(a)
    C3 --> join9
    
    A4("The curve order 'n': 
        0xFFFFFFFF FFFFFFFF \n 
        FFFFFFFF FFFFFFFE \n
        BAAEDCE6 AF48A03B \n
          BFD25E8C D0364141\n") --> B4(n)
          
          
    A6("Base point 'G'") --> B6(G) 

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