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   1 # Test vectors for Montgomery reduction
   2 #
   3 # $Id: mpmont,v 1.2 1999/11/19 13:18:39 mdw Exp $
   4
   5 create {
   6   340809809850981098423498794792349     # m
   7   266454859                             # -m^{-1} mod b
   8   130655606683780235388773757767708     # R mod m
   9   237786678640282040194246459306177;    # R^2 mod m
  10 }
  11
  12 mul {
  13   43289823545
  14   234324324
  15   6456542564
  16   10807149256;
  17 }
  18
  19 exp {
  20   4325987397987458979875737589783
  21   435365332435654643667
  22   8745435676786567758678547
  23   2439674515119108242643169132064;
  24
  25   # --- Bizarre bug ---
  26   #
  27   # This was caused by omission of the test-and-subtract step in the
  28   # Montgomery reduction.
  29
  30   8939489893434234331 1804289383 454353454354565 6139425926295484741;
  31   8939489893434234331 1804289383 8939489893434234330 1;
  32
  33   # --- Quick RSA test ---
  34
  35   905609324890967090294090970600361             # This is p
  36   3
  37   905609324890967090294090970600360             # This is (p - 1)
  38   1;                                            # Fermat test: p is prime
  39
  40   734589569806680985408670989082927             # This is q
  41   5
  42   734589569806680985408670989082926             # And this is (q - 1)
  43   1;                                            # Fermat again: q is prime
  44
  45   # --- Encrypt a message ---
  46   #
  47   # The public and private exponents are from the GCD test.  The message
  48   # is just obvious.  The modulus is the product of the two primes above.
  49
  50   665251164384574309450646977867045404520085938543622535546005136647
  51   123456789012345678901234567890123456789012345678901234567890
  52   5945908509680983480596809586040589085680968709809890671
  53   25906467774034212974484417859588980567136610347807401817990462701;
  54
  55   # --- And decrypt it again ---
  56
  57   665251164384574309450646977867045404520085938543622535546005136647
  58   25906467774034212974484417859588980567136610347807401817990462701
  59   514778499400157641662814932021958856708417966520837469125919104431
  60   123456789012345678901234567890123456789012345678901234567890;
  61 }
  62
  63 # --- Simultaneous exponentiation ---
  64
  65 mexp-1 {
  66   4325987397987458979875737589783
  67   435365332435654643667
  68   8745435676786567758678547
  69   2439674515119108242643169132064;
  70 }
  71
  72 mexp-2 {
  73   16_8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291
  74   16_626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802
  75   16_bf655bd046f0b35ec791b004804afcbb8ef7d69d
  76   16_19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333
  77   16_821a926312e97adeabcc8d082b5278978a2df4b0
  78   16_2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e;
  79 }