# Test vectors for Montgomery reduction
#
# $Id: mpmont,v 1.2 1999/11/19 13:18:39 mdw Exp $

create {
  340809809850981098423498794792349	# m
  266454859				# -m^{-1} mod b
  130655606683780235388773757767708	# R mod m
  237786678640282040194246459306177;	# R^2 mod m
}

mul {
  43289823545
  234324324
  6456542564
  10807149256;
}

exp {
  4325987397987458979875737589783
  435365332435654643667
  8745435676786567758678547
  2439674515119108242643169132064;

  # --- Bizarre bug ---
  #
  # This was caused by omission of the test-and-subtract step in the
  # Montgomery reduction.

  8939489893434234331 1804289383 454353454354565 6139425926295484741;
  8939489893434234331 1804289383 8939489893434234330 1;

  # --- Quick RSA test ---

  905609324890967090294090970600361		# This is p
  3
  905609324890967090294090970600360		# This is (p - 1)
  1;						# Fermat test: p is prime

  734589569806680985408670989082927		# This is q
  5
  734589569806680985408670989082926		# And this is (q - 1)
  1;						# Fermat again: q is prime

  # --- Encrypt a message ---
  #
  # The public and private exponents are from the GCD test.  The message
  # is just obvious.  The modulus is the product of the two primes above.

  665251164384574309450646977867045404520085938543622535546005136647
  123456789012345678901234567890123456789012345678901234567890
  5945908509680983480596809586040589085680968709809890671
  25906467774034212974484417859588980567136610347807401817990462701;

  # --- And decrypt it again --- 

  665251164384574309450646977867045404520085938543622535546005136647
  25906467774034212974484417859588980567136610347807401817990462701
  514778499400157641662814932021958856708417966520837469125919104431
  123456789012345678901234567890123456789012345678901234567890;
}

# --- Simultaneous exponentiation ---

mexp-1 {
  4325987397987458979875737589783
  435365332435654643667
  8745435676786567758678547
  2439674515119108242643169132064;
}

mexp-2 {
  16_8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291
  16_626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802
  16_bf655bd046f0b35ec791b004804afcbb8ef7d69d
  16_19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333
  16_821a926312e97adeabcc8d082b5278978a2df4b0
  16_2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e;
}