[u/mdw/catacomb] / tests / mpmont

# Test vectors for Montgomery reduction
#
# $Id: mpmont,v 1.5 2000/06/17 12:11:18 mdw Exp $

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

mul {
  43289823545
  234324324
  6456542564
  10807149256;

  51518627314818829164222247085233898246715229794943812733936714788310185005015428803253311691709787911812368198649776769324928993075889524373913555618270874746833913595051625422038974326537979654635530320271853851973343513053953211672797425464186157719021174955241645388345195723368057041032310152242301620397
  7041548659011846562361842096561083537784928869240554198760844555642215260669458833049231069318370838770180094409088437631986867239713464317243824963669990014087444248250948204574690463940534304651099653802302150197753463246181762684347288736386534346725039618007392334267637262008343417972878515511486456037
  21451817224897484023627307128311082613304580637202546848860538836010530320943159719981586919811151828606838777812233053319458755053306547823820900602281867134174742586071226220962576712633552196944784360512851517812225731562588375896089193406088239903885470354101095713609394462435076126493339021945199401247
  48192532305912989641372170084506981675917951543147719789775743631071830656350879578731578070582102149232280305157616093002880139716311910835926678896882798493523792373475521651115163420137602661060123597773253524671874189844988793471524978853764238038494563159505836018994860909028653670132922744758133798212;
}

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;

  # --- DSA public key derivation ---

  0xc9c7feaeaedb16505389c5582df1858d0fdb3eecfe61c230d612661bef8c1bc5
  0x5cd41fc97d0db5322bab7d659354db2ed9f88e39d2c6fae9f29acab5a522131e
  0x1234
  0x51812af9600c89ffe0f73902eb09015c03b4e0fbf6ccf073931c12f9aad1fb47;

  0xdde5808744e1cd37c88667e7033694b2513a7429f035f11c0bafc4dff2b96a672bd0a3ca16aba2ea526df00c8571106ba4a1d83eb62605fc9274ab70bef0a111cd070cca2d8b10edf042d6c44f863c36fabea8bb0d7340eb8c169da27a4b0ba2713c166152a0244235093391c5f71aee8c03dcaf2335a2e4689ccb27ba365ec7
  0x65985e4c2d6027a8afdeb9b44cc619e1c4d46bde873e0d4b45325412a2f8365e51245324f888704295fe8233a6666624d9a4701172dbfcab5c9643e1caab79eb2a0c85284d1b858688b8f16804326321f53a723502a6d6ae08dcbffccf2187a799f6281c2478ef0faed5c5c80adeabc5ee435cff8b9ae0b603e47fb08d73b014
  0x23a252f60bae4907a8ed5b6203e2b1da32848cd9
  0x9720498d8ec1208585635faaf952c1204c37119acccc64ed7942867be24770e33db39ffcfa1194549ead8495a7918a20e15144e68125860ef4f8c1a3d771bad690938bdb2c8817e2b89a8fc615d067084a7a2f2f9280e15fb9ccebfe713584260d5ed30545b69745d7b22977bfd44d60d7c5e657aab1c79dc5cb33ff29ee9074;  

  # --- 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 {
  0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291
  0x626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802
  0xbf655bd046f0b35ec791b004804afcbb8ef7d69d
  0x19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333
  0x821a926312e97adeabcc8d082b5278978a2df4b0
  0x2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e;
}
Commit	Line	Data
d3409d5e	1	# Test vectors for Montgomery reduction
d3409d5e	2	#
83c017f3	3	# $Id: mpmont,v 1.5 2000/06/17 12:11:18 mdw Exp $
d3409d5e	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;
83c017f3	17
	18	51518627314818829164222247085233898246715229794943812733936714788310185005015428803253311691709787911812368198649776769324928993075889524373913555618270874746833913595051625422038974326537979654635530320271853851973343513053953211672797425464186157719021174955241645388345195723368057041032310152242301620397
	19	7041548659011846562361842096561083537784928869240554198760844555642215260669458833049231069318370838770180094409088437631986867239713464317243824963669990014087444248250948204574690463940534304651099653802302150197753463246181762684347288736386534346725039618007392334267637262008343417972878515511486456037
	20	21451817224897484023627307128311082613304580637202546848860538836010530320943159719981586919811151828606838777812233053319458755053306547823820900602281867134174742586071226220962576712633552196944784360512851517812225731562588375896089193406088239903885470354101095713609394462435076126493339021945199401247
	21	48192532305912989641372170084506981675917951543147719789775743631071830656350879578731578070582102149232280305157616093002880139716311910835926678896882798493523792373475521651115163420137602661060123597773253524671874189844988793471524978853764238038494563159505836018994860909028653670132922744758133798212;
d3409d5e	22	}
	23
	24	exp {
	25	4325987397987458979875737589783
	26	435365332435654643667
	27	8745435676786567758678547
	28	2439674515119108242643169132064;
	29
890e34fd	30	# --- Bizarre bug ---
	31	#
	32	# This was caused by omission of the test-and-subtract step in the
	33	# Montgomery reduction.
	34
	35	8939489893434234331 1804289383 454353454354565 6139425926295484741;
	36	8939489893434234331 1804289383 8939489893434234330 1;
	37
f790765d	38	# --- DSA public key derivation ---
f790765d	39
32ccc3c3	40	0xc9c7feaeaedb16505389c5582df1858d0fdb3eecfe61c230d612661bef8c1bc5
	41	0x5cd41fc97d0db5322bab7d659354db2ed9f88e39d2c6fae9f29acab5a522131e
	42	0x1234
	43	0x51812af9600c89ffe0f73902eb09015c03b4e0fbf6ccf073931c12f9aad1fb47;
f790765d	44
32ccc3c3	45	0xdde5808744e1cd37c88667e7033694b2513a7429f035f11c0bafc4dff2b96a672bd0a3ca16aba2ea526df00c8571106ba4a1d83eb62605fc9274ab70bef0a111cd070cca2d8b10edf042d6c44f863c36fabea8bb0d7340eb8c169da27a4b0ba2713c166152a0244235093391c5f71aee8c03dcaf2335a2e4689ccb27ba365ec7
	46	0x65985e4c2d6027a8afdeb9b44cc619e1c4d46bde873e0d4b45325412a2f8365e51245324f888704295fe8233a6666624d9a4701172dbfcab5c9643e1caab79eb2a0c85284d1b858688b8f16804326321f53a723502a6d6ae08dcbffccf2187a799f6281c2478ef0faed5c5c80adeabc5ee435cff8b9ae0b603e47fb08d73b014
	47	0x23a252f60bae4907a8ed5b6203e2b1da32848cd9
	48	0x9720498d8ec1208585635faaf952c1204c37119acccc64ed7942867be24770e33db39ffcfa1194549ead8495a7918a20e15144e68125860ef4f8c1a3d771bad690938bdb2c8817e2b89a8fc615d067084a7a2f2f9280e15fb9ccebfe713584260d5ed30545b69745d7b22977bfd44d60d7c5e657aab1c79dc5cb33ff29ee9074;
f790765d	49
d3409d5e	50	# --- Quick RSA test ---
	51
	52	905609324890967090294090970600361 # This is p
	53	3
	54	905609324890967090294090970600360 # This is (p - 1)
	55	1; # Fermat test: p is prime
	56
	57	734589569806680985408670989082927 # This is q
	58	5
	59	734589569806680985408670989082926 # And this is (q - 1)
	60	1; # Fermat again: q is prime
	61
	62	# --- Encrypt a message ---
	63	#
	64	# The public and private exponents are from the GCD test. The message
	65	# is just obvious. The modulus is the product of the two primes above.
	66
	67	665251164384574309450646977867045404520085938543622535546005136647
	68	123456789012345678901234567890123456789012345678901234567890
	69	5945908509680983480596809586040589085680968709809890671
	70	25906467774034212974484417859588980567136610347807401817990462701;
	71
	72	# --- And decrypt it again ---
	73
	74	665251164384574309450646977867045404520085938543622535546005136647
	75	25906467774034212974484417859588980567136610347807401817990462701
	76	514778499400157641662814932021958856708417966520837469125919104431
	77	123456789012345678901234567890123456789012345678901234567890;
	78	}
890e34fd	79
	80	# --- Simultaneous exponentiation ---
	81
	82	mexp-1 {
	83	4325987397987458979875737589783
	84	435365332435654643667
	85	8745435676786567758678547
	86	2439674515119108242643169132064;
	87	}
	88
	89	mexp-2 {
32ccc3c3	90	0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291
	91	0x626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802
	92	0xbf655bd046f0b35ec791b004804afcbb8ef7d69d
	93	0x19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333
	94	0x821a926312e97adeabcc8d082b5278978a2df4b0
	95	0x2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e;
890e34fd	96	}