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Diffstat (limited to 'security/nss/lib/freebl/mpi/doc/expt.txt')
| -rw-r--r-- | security/nss/lib/freebl/mpi/doc/expt.txt | 132 |
1 files changed, 0 insertions, 132 deletions
diff --git a/security/nss/lib/freebl/mpi/doc/expt.txt b/security/nss/lib/freebl/mpi/doc/expt.txt deleted file mode 100644 index cea9dcc58..000000000 --- a/security/nss/lib/freebl/mpi/doc/expt.txt +++ /dev/null @@ -1,132 +0,0 @@ -Exponentiation - -For exponentiation, the MPI library uses a simple and fairly standard -square-and-multiply method. The algorithm is this: - -Input: a, b -Output: a ** b - - s = 1 - - while(b != 0) - if(b is odd) - s = s * a - endif - - b = b / 2 - - x = x * x - endwhile - - return s - -The modular exponentiation is done the same way, except replacing: - - s = s * a - -with - s = (s * a) mod m - -and replacing - - x = x * x - -with - - x = (x * x) mod m - -Here is a sample exponentiation using the MPI library, as compared to -the same problem solved by the Unix 'bc' program on my system: - -Computation of 2,381,283 ** 235 - -'bc' says: - -4385CA4A804D199FBEAD95FAD0796FAD0D0B51FC9C16743C45568C789666985DB719\ -4D90E393522F74C9601262C0514145A49F3B53D00983F95FDFCEA3D0043ECEF6227E\ -6FB59C924C3EE74447B359B5BF12A555D46CB819809EF423F004B55C587D6F0E8A55\ -4988036A42ACEF9F71459F97CEF6E574BD7373657111648626B1FF8EE15F663B2C0E\ -6BBE5082D4CDE8E14F263635AE8F35DB2C280819517BE388B5573B84C5A19C871685\ -FD408A6471F9D6AFAF5129A7548EAE926B40874B340285F44765BF5468CE20A13267\ -CD88CE6BC786ACED36EC7EA50F67FF27622575319068A332C3C0CB23E26FB55E26F4\ -5F732753A52B8E2FB4D4F42D894242613CA912A25486C3DEC9C66E5DB6182F6C1761\ -CF8CD0D255BE64B93836B27D452AE38F950EB98B517D4CF50D48F0165EF0CCCE1F5C\ -49BF18219FDBA0EEDD1A7E8B187B70C2BAED5EC5C6821EF27FAFB1CFF70111C52235\ -5E948B93A015AA1AE152B110BB5658CB14D3E45A48BFE7F082C1182672A455A695CD\ -A1855E8781E625F25B41B516E77F589FA420C3B058861EA138CF7A2C58DB3C7504FD\ -D29554D78237834CC5AE710D403CC4F6973D5012B7E117A8976B14A0B5AFA889BD47\ -92C461F0F96116F00A97AE9E83DC5203680CAF9A18A062566C145650AB86BE4F907F\ -A9F7AB4A700B29E1E5BACCD6DCBFA513E10832815F710807EED2E279081FEC61D619\ -AB270BEB3D3A1787B35A9DD41A8766CF21F3B5C693B3BAB1C2FA14A4ED202BC35743\ -E5CBE2391624D4F8C9BFBBC78D69764E7C6C5B11BF005677BFAD17D9278FFC1F158F\ -1B3683FF7960FA0608103792C4163DC0AF3E06287BB8624F8FE3A0FFBDF82ACECA2F\ -CFFF2E1AC93F3CA264A1B - -MPI says: - -4385CA4A804D199FBEAD95FAD0796FAD0D0B51FC9C16743C45568C789666985DB719\ -4D90E393522F74C9601262C0514145A49F3B53D00983F95FDFCEA3D0043ECEF6227E\ -6FB59C924C3EE74447B359B5BF12A555D46CB819809EF423F004B55C587D6F0E8A55\ -4988036A42ACEF9F71459F97CEF6E574BD7373657111648626B1FF8EE15F663B2C0E\ -6BBE5082D4CDE8E14F263635AE8F35DB2C280819517BE388B5573B84C5A19C871685\ -FD408A6471F9D6AFAF5129A7548EAE926B40874B340285F44765BF5468CE20A13267\ -CD88CE6BC786ACED36EC7EA50F67FF27622575319068A332C3C0CB23E26FB55E26F4\ -5F732753A52B8E2FB4D4F42D894242613CA912A25486C3DEC9C66E5DB6182F6C1761\ -CF8CD0D255BE64B93836B27D452AE38F950EB98B517D4CF50D48F0165EF0CCCE1F5C\ -49BF18219FDBA0EEDD1A7E8B187B70C2BAED5EC5C6821EF27FAFB1CFF70111C52235\ -5E948B93A015AA1AE152B110BB5658CB14D3E45A48BFE7F082C1182672A455A695CD\ -A1855E8781E625F25B41B516E77F589FA420C3B058861EA138CF7A2C58DB3C7504FD\ -D29554D78237834CC5AE710D403CC4F6973D5012B7E117A8976B14A0B5AFA889BD47\ -92C461F0F96116F00A97AE9E83DC5203680CAF9A18A062566C145650AB86BE4F907F\ -A9F7AB4A700B29E1E5BACCD6DCBFA513E10832815F710807EED2E279081FEC61D619\ -AB270BEB3D3A1787B35A9DD41A8766CF21F3B5C693B3BAB1C2FA14A4ED202BC35743\ -E5CBE2391624D4F8C9BFBBC78D69764E7C6C5B11BF005677BFAD17D9278FFC1F158F\ -1B3683FF7960FA0608103792C4163DC0AF3E06287BB8624F8FE3A0FFBDF82ACECA2F\ -CFFF2E1AC93F3CA264A1B - -Diff says: -% diff bc.txt mp.txt -% - ------------------------------------------------------------------- -***** BEGIN LICENSE BLOCK ***** -Version: MPL 1.1/GPL 2.0/LGPL 2.1 - -The contents of this file are subject to the Mozilla Public License Version -1.1 (the "License"); you may not use this file except in compliance with -the License. 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