docs: def sign( self, hash, random_k ):
      """Return a signature for the provided hash, using the provided
      random nonce.  It is absolutely vital that random_k be an unpredictable
      number in the range [1, self.public_key.point.order()-1].  If
      an attacker can guess random_k, he can compute our private key from a
      single signature.  Also, if an attacker knows a few high-order
      bits (or a few low-order bits) of random_k, he can compute our private
      key from many signatures.  The generation of nonces with adequate
      cryptographic strength is very difficult and far beyond the scope
      of this comment.
  
      May raise RuntimeError, in which case retrying with a new
      random value k is in order.
      """
  
      G = self.public_key.generator
      n = G.order()
      k = random_k % n
      p1 = k * G
      r = p1.x()
      if r == 0: raise RuntimeError("amazingly unlucky random number r")
      s = ( numbertheory.inverse_mod( k, n ) * \
            ( hash + ( self.secret_multiplier * r ) % n ) ) % n
      if s == 0: raise RuntimeError("amazingly unlucky random number s")
      return Signature( r, s )