[catacomb] / math / t / mpmont

# Test vectors for Montgomery reduction

mul {
  6277101735386680763835789423207666416083908700390324961279
  2455155546008943817740293915197451784769108058161191238065
  340282366920938463500268095579187314689
  5646741895976341600220572388698743135318229029826089708489;
}

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

  6277101735386680763835789423207666416083908700390324961279
  340282366920938463444927863358058659841
  18446744073709551617
  340282366920938463500268095579187314689;
}

mul {
  43289823545
  234324324
  6456542564
  10807149256;

  4325987397987458979875737589783
  1
  4309747041023999857206910900081
  4309747041023999857206910900081;

  170141183460469231731687303715884105727
  2
  2
  4;

  6277101735386680763835789423207666416083908700390324961279
  2455155546008943817740293915197451784769108058161191238065
  340282366920938463500268095579187314689
  5646741895976341600220572388698743135318229029826089708489;

  51518627314818829164222247085233898246715229794943812733936714788310185005015428803253311691709787911812368198649776769324928993075889524373913555618270874746833913595051625422038974326537979654635530320271853851973343513053953211672797425464186157719021174955241645388345195723368057041032310152242301620397
  7041548659011846562361842096561083537784928869240554198760844555642215260669458833049231069318370838770180094409088437631986867239713464317243824963669990014087444248250948204574690463940534304651099653802302150197753463246181762684347288736386534346725039618007392334267637262008343417972878515511486456037
  21451817224897484023627307128311082613304580637202546848860538836010530320943159719981586919811151828606838777812233053319458755053306547823820900602281867134174742586071226220962576712633552196944784360512851517812225731562588375896089193406088239903885470354101095713609394462435076126493339021945199401247
  48192532305912989641372170084506981675917951543147719789775743631071830656350879578731578070582102149232280305157616093002880139716311910835926678896882798493523792373475521651115163420137602661060123597773253524671874189844988793471524978853764238038494563159505836018994860909028653670132922744758133798212;

  0x1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
  0 1 0;
}

exp {
  4325987397987458979875737589783
  435365332435654643667
  8745435676786567758678547
  2439674515119108242643169132064;

  170141183460469231731687303715884105727
  2
  170141183460469231731687303715884105727
  2;

  # --- 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;

  # --- Negative and zero exponents ---

  0xfffffffdffffffffffffffffffffffff 0xfffffffdfffffffffffffffffffffffe 0 1;
  8939489893434234331 1804289383 -8939035539979879765 6139425926295484741;

  # --- 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;

  # --- Regression ---

  3986624077014487421577005607434178981611827907415414229383186257799185035259267946499319317546248903815958429965343062841026732183070884484415037389112766124480881891335541864933360040451772640848433986354946570483859801429553601029855169093153120649968457991955067742589996787220443833463413655161718521778024152687493646856649224308444934694934177848997119462792993163729623894124424825605063456003809024630116233635811919734143467917391222413748618664640084816819791040047135721631646389562380726980090637225607902904093720467390446340147754975063914238763877962986901317873962501987398883284691263121949707967483
  2169501609694605731113683435915932024263931111070470928071742781553833481227229665038394569450673541955381439893533586899516369125587996614390351130855433932967123352056637148142399218614659226596196082977912512097782590337133839376057748669786776861900003976657975002808400242688631641605350346310303557783077961976578644612942618488786721156576047036803063809499458142391930097492829437793780428298460587910313123127299017105180518995858168981798364124607742910479678852164938149352363613709839015911625193499208078080300810729238501127706236236987807659841302058153641198634312186169690290317377895433013774581020
  51190650099377934681679689372059155651634030541122059023228371179527051284414
  2182336244564627050476203952083643687109210844491929333865487949231032236266424033053219865356293652087346833773990958617081657598928894294027838097457060132084513275728637155311686562443969707442331856969523833049082440569661820589637161378175422424940183890787723213162895088451684485064228413121825045190532424942855250521728705814032313019282814300698512615465322506857392325469773301168485302267577566759375501214494771698910873834970265937979350795050000891405548412798945017578510891723221844676960980502437259841806090144299798005080365645221451715661064400809603224286845878809241930399832108000526121054958;
}

# --- Simultaneous exponentiation ---

mexp-1 {
  4325987397987458979875737589783
  435365332435654643667
  8745435676786567758678547
  2439674515119108242643169132064;
}

mexp-2 {
  0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291
  0x626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802
  0xbf655bd046f0b35ec791b004804afcbb8ef7d69d
  0x19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333
  0x821a926312e97adeabcc8d082b5278978a2df4b0
  0x2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e;

  0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291
  0x626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802
  0xbf655bd046f0b35ec791b004804afcbb8ef7d69d
  0x19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333
  -0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adabb090e849367fc31d4c6a97bac0b4be56a79a0de0
  0x2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e;
}
Commit	Line	Data
d3409d5e	1	# Test vectors for Montgomery reduction
d3409d5e	2
444083ae MW	3	mul {
	4	6277101735386680763835789423207666416083908700390324961279
	5	2455155546008943817740293915197451784769108058161191238065
	6	340282366920938463500268095579187314689
	7	5646741895976341600220572388698743135318229029826089708489;
	8	}
	9
d3409d5e	10	create {
	11	340809809850981098423498794792349 # m
	12	266454859 # -m^{-1} mod b
	13	130655606683780235388773757767708 # R mod m
	14	237786678640282040194246459306177; # R^2 mod m
0e70bd46 MW	15
	16	6277101735386680763835789423207666416083908700390324961279
	17	340282366920938463444927863358058659841
	18	18446744073709551617
	19	340282366920938463500268095579187314689;
d3409d5e	20	}
	21
	22	mul {
	23	43289823545
	24	234324324
	25	6456542564
	26	10807149256;
83c017f3	27
3119b3ae MW	28	4325987397987458979875737589783
	29	1
	30	4309747041023999857206910900081
	31	4309747041023999857206910900081;
	32
379829cb MW	33	170141183460469231731687303715884105727
	34	2
	35	2
	36	4;
	37
0e70bd46 MW	38	6277101735386680763835789423207666416083908700390324961279
	39	2455155546008943817740293915197451784769108058161191238065
	40	340282366920938463500268095579187314689
	41	5646741895976341600220572388698743135318229029826089708489;
	42
83c017f3	43	51518627314818829164222247085233898246715229794943812733936714788310185005015428803253311691709787911812368198649776769324928993075889524373913555618270874746833913595051625422038974326537979654635530320271853851973343513053953211672797425464186157719021174955241645388345195723368057041032310152242301620397
	44	7041548659011846562361842096561083537784928869240554198760844555642215260669458833049231069318370838770180094409088437631986867239713464317243824963669990014087444248250948204574690463940534304651099653802302150197753463246181762684347288736386534346725039618007392334267637262008343417972878515511486456037
	45	21451817224897484023627307128311082613304580637202546848860538836010530320943159719981586919811151828606838777812233053319458755053306547823820900602281867134174742586071226220962576712633552196944784360512851517812225731562588375896089193406088239903885470354101095713609394462435076126493339021945199401247
	46	48192532305912989641372170084506981675917951543147719789775743631071830656350879578731578070582102149232280305157616093002880139716311910835926678896882798493523792373475521651115163420137602661060123597773253524671874189844988793471524978853764238038494563159505836018994860909028653670132922744758133798212;
366e9701 MW	47
	48	0x1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
	49	0 1 0;
d3409d5e	50	}
	51
	52	exp {
	53	4325987397987458979875737589783
	54	435365332435654643667
	55	8745435676786567758678547
	56	2439674515119108242643169132064;
	57
379829cb MW	58	170141183460469231731687303715884105727
	59	2
	60	170141183460469231731687303715884105727
	61	2;
	62
890e34fd	63	# --- Bizarre bug ---
	64	#
	65	# This was caused by omission of the test-and-subtract step in the
	66	# Montgomery reduction.
	67
	68	8939489893434234331 1804289383 454353454354565 6139425926295484741;
	69	8939489893434234331 1804289383 8939489893434234330 1;
	70
a69a3efd	71	# --- Negative and zero exponents ---
21bebf11	72
45c0fd36	73	0xfffffffdffffffffffffffffffffffff 0xfffffffdfffffffffffffffffffffffe 0 1;
21bebf11	74	8939489893434234331 1804289383 -8939035539979879765 6139425926295484741;
21bebf11	75
f790765d	76	# --- DSA public key derivation ---
f790765d	77
32ccc3c3	78	0xc9c7feaeaedb16505389c5582df1858d0fdb3eecfe61c230d612661bef8c1bc5
	79	0x5cd41fc97d0db5322bab7d659354db2ed9f88e39d2c6fae9f29acab5a522131e
	80	0x1234
	81	0x51812af9600c89ffe0f73902eb09015c03b4e0fbf6ccf073931c12f9aad1fb47;
f790765d	82
32ccc3c3	83	0xdde5808744e1cd37c88667e7033694b2513a7429f035f11c0bafc4dff2b96a672bd0a3ca16aba2ea526df00c8571106ba4a1d83eb62605fc9274ab70bef0a111cd070cca2d8b10edf042d6c44f863c36fabea8bb0d7340eb8c169da27a4b0ba2713c166152a0244235093391c5f71aee8c03dcaf2335a2e4689ccb27ba365ec7
	84	0x65985e4c2d6027a8afdeb9b44cc619e1c4d46bde873e0d4b45325412a2f8365e51245324f888704295fe8233a6666624d9a4701172dbfcab5c9643e1caab79eb2a0c85284d1b858688b8f16804326321f53a723502a6d6ae08dcbffccf2187a799f6281c2478ef0faed5c5c80adeabc5ee435cff8b9ae0b603e47fb08d73b014
	85	0x23a252f60bae4907a8ed5b6203e2b1da32848cd9
45c0fd36	86	0x9720498d8ec1208585635faaf952c1204c37119acccc64ed7942867be24770e33db39ffcfa1194549ead8495a7918a20e15144e68125860ef4f8c1a3d771bad690938bdb2c8817e2b89a8fc615d067084a7a2f2f9280e15fb9ccebfe713584260d5ed30545b69745d7b22977bfd44d60d7c5e657aab1c79dc5cb33ff29ee9074;
f790765d	87
d3409d5e	88	# --- Quick RSA test ---
	89
	90	905609324890967090294090970600361 # This is p
	91	3
	92	905609324890967090294090970600360 # This is (p - 1)
	93	1; # Fermat test: p is prime
	94
	95	734589569806680985408670989082927 # This is q
	96	5
	97	734589569806680985408670989082926 # And this is (q - 1)
	98	1; # Fermat again: q is prime
	99
	100	# --- Encrypt a message ---
	101	#
	102	# The public and private exponents are from the GCD test. The message
	103	# is just obvious. The modulus is the product of the two primes above.
	104
	105	665251164384574309450646977867045404520085938543622535546005136647
	106	123456789012345678901234567890123456789012345678901234567890
	107	5945908509680983480596809586040589085680968709809890671
	108	25906467774034212974484417859588980567136610347807401817990462701;
	109
45c0fd36	110	# --- And decrypt it again ---
d3409d5e	111
	112	665251164384574309450646977867045404520085938543622535546005136647
	113	25906467774034212974484417859588980567136610347807401817990462701
	114	514778499400157641662814932021958856708417966520837469125919104431
	115	123456789012345678901234567890123456789012345678901234567890;
c5f2543f	116
	117	# --- Regression ---
	118
	119	3986624077014487421577005607434178981611827907415414229383186257799185035259267946499319317546248903815958429965343062841026732183070884484415037389112766124480881891335541864933360040451772640848433986354946570483859801429553601029855169093153120649968457991955067742589996787220443833463413655161718521778024152687493646856649224308444934694934177848997119462792993163729623894124424825605063456003809024630116233635811919734143467917391222413748618664640084816819791040047135721631646389562380726980090637225607902904093720467390446340147754975063914238763877962986901317873962501987398883284691263121949707967483
	120	2169501609694605731113683435915932024263931111070470928071742781553833481227229665038394569450673541955381439893533586899516369125587996614390351130855433932967123352056637148142399218614659226596196082977912512097782590337133839376057748669786776861900003976657975002808400242688631641605350346310303557783077961976578644612942618488786721156576047036803063809499458142391930097492829437793780428298460587910313123127299017105180518995858168981798364124607742910479678852164938149352363613709839015911625193499208078080300810729238501127706236236987807659841302058153641198634312186169690290317377895433013774581020
	121	51190650099377934681679689372059155651634030541122059023228371179527051284414
	122	2182336244564627050476203952083643687109210844491929333865487949231032236266424033053219865356293652087346833773990958617081657598928894294027838097457060132084513275728637155311686562443969707442331856969523833049082440569661820589637161378175422424940183890787723213162895088451684485064228413121825045190532424942855250521728705814032313019282814300698512615465322506857392325469773301168485302267577566759375501214494771698910873834970265937979350795050000891405548412798945017578510891723221844676960980502437259841806090144299798005080365645221451715661064400809603224286845878809241930399832108000526121054958;
d3409d5e	123	}
890e34fd	124
	125	# --- Simultaneous exponentiation ---
	126
	127	mexp-1 {
	128	4325987397987458979875737589783
	129	435365332435654643667
	130	8745435676786567758678547
	131	2439674515119108242643169132064;
	132	}
	133
	134	mexp-2 {
32ccc3c3	135	0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291
	136	0x626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802
	137	0xbf655bd046f0b35ec791b004804afcbb8ef7d69d
	138	0x19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333
	139	0x821a926312e97adeabcc8d082b5278978a2df4b0
	140	0x2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e;
21bebf11	141
	142	0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291
	143	0x626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802
	144	0xbf655bd046f0b35ec791b004804afcbb8ef7d69d
	145	0x19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333
	146	-0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adabb090e849367fc31d4c6a97bac0b4be56a79a0de0
	147	0x2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e;
890e34fd	148	}