Mladen Markov mladenmarkov

## secp256k1-endomorphism.md

      
        
          
            
              
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                paulmillr
                / secp256k1-endomorphism.md
            
            
              Last active
              September 28, 2023 14:53
            
              
                Speed-up secp256k1 by using endomorphism https://paulmillr.com/posts/noble-secp256k1-fast-ecc/
              
          
        
      
        
  
      
    Hal Finney's explanation of secp256k1 "efficiently computable endomorphism" parameters used secp256k1 libraries, archived from source.
The same optimization could be applied to any Koblitz curve (e.g. Short Weistrass curve with a=0).

I implemented an optimized ECDSA verify for the secp256k1 curve, based on pages 125-129 of the Guide to Elliptic Curve Cryptography, by Hankerson, Menezes and Vanstone. I own the book but I also found a PDF on a Russian site which is more convenient.
secp256k1 uses the following prime for its x and y coordinates: