complexity.md

The Degree of Difficulty for Mio.sign

Equation

Explanation

• 16

  • The fidelity argument ranges from (0, 1) at 16 distinct points
    • So really, fidelity = [1, 16] in that sense

• 

  • Get the sum of n=16 up to n=36 for n^256!
  • Mio.sign returns its output using the numerical bases from Base₁₆ (0-9, a-f) to Base₃₆ (0-9, a-z)

• n^256!

  • Get the permutations of n^256!
    • Use 256! since the signature can be any length of (0, 256] (see intervals)
    • The signature's length will only be 0 for an empty string
  • Mio.sign will return a string with a length between (0, 256] (see intervals)

• + 1

  • Include the empty string

Other hashing algorithms and their degrees of difficulty

• MD5

  • 32 characters using Base₁₆
  • 16³²

• SHA-1

  • 40 characters using Base₁₆
  • 16⁴⁰

• SHA-2

  • 56 characters using Base₁₆
  • 16⁵⁶