bitcoin/src/minisketch/doc/moduli.md

2.8 KiB

These are the irreducible polynomials over GF(2) used to represent field elements:

  • x2 + x + 1
  • x3 + x + 1
  • x4 + x + 1
  • x5 + x2 + 1
  • x6 + x + 1
  • x7 + x + 1
  • x8 + x4 + x3 + x + 1
  • x9 + x + 1
  • x10 + x3 + 1
  • x11 + x2 + 1
  • x12 + x3 + 1
  • x13 + x4 + x3 + x + 1
  • x14 + x5 + 1
  • x15 + x + 1
  • x16 + x5 + x3 + x + 1
  • x17 + x3 + 1
  • x18 + x3 + 1
  • x19 + x5 + x2 + x + 1
  • x20 + x3 + 1
  • x21 + x2 + 1
  • x22 + x + 1
  • x23 + x5 + 1
  • x24 + x4 + x3 + x + 1
  • x25 + x3 + 1
  • x26 + x4 + x3 + x + 1
  • x27 + x5 + x2 + x + 1
  • x28 + x + 1
  • x29 + x2 + 1
  • x30 + x + 1
  • x31 + x3 + 1
  • x32 + x7 + x3 + x2 + 1
  • x33 + x10 + 1
  • x34 + x7 + 1
  • x35 + x2 + 1
  • x36 + x9 + 1
  • x37 + x6 + x4 + x + 1
  • x38 + x6 + x5 + x + 1
  • x39 + x4 + 1
  • x40 + x5 + x4 + x3 + 1
  • x41 + x3 + 1
  • x42 + x7 + 1
  • x43 + x6 + x4 + x3 + 1
  • x44 + x5 + 1
  • x45 + x4 + x3 + x + 1
  • x46 + x + 1
  • x47 + x5 + 1
  • x48 + x5 + x3 + x2 + 1
  • x49 + x9 + 1
  • x50 + x4 + x3 + x2 + 1
  • x51 + x6 + x3 + x + 1
  • x52 + x3 + 1
  • x53 + x6 + x2 + x + 1
  • x54 + x9 + 1
  • x55 + x7 + 1
  • x56 + x7 + x4 + x2 + 1
  • x57 + x4 + 1
  • x58 + x19 + 1
  • x59 + x7 + x4 + x2 + 1
  • x60 + x + 1
  • x61 + x5 + x2 + x + 1
  • x62 + x29 + 1
  • x63 + x + 1
  • x64 + x4 + x3 + x + 1