security/nss/lib/freebl/mpi/doc/expt.txt@6474c204b198
security/nss/lib/freebl/mpi/doc/expt.txt
Wed, 31 Dec 2014 06:09:35 +0100
- author
- Michael Schloh von Bennewitz <michael@schloh.com>
- date
- Wed, 31 Dec 2014 06:09:35 +0100
- changeset 0
- 6474c204b198
- permissions
- -rw-r--r--
Cloned upstream origin tor-browser at tor-browser-31.3.0esr-4.5-1-build1
revision ID fc1c9ff7c1b2defdbc039f12214767608f46423f for hacking purpose.
1 Exponentiation
3 For exponentiation, the MPI library uses a simple and fairly standard
4 square-and-multiply method. The algorithm is this:
6 Input: a, b
7 Output: a ** b
9 s = 1
11 while(b != 0)
12 if(b is odd)
13 s = s * a
14 endif
16 b = b / 2
18 x = x * x
19 endwhile
21 return s
23 The modular exponentiation is done the same way, except replacing:
25 s = s * a
27 with
28 s = (s * a) mod m
30 and replacing
32 x = x * x
34 with
36 x = (x * x) mod m
38 Here is a sample exponentiation using the MPI library, as compared to
39 the same problem solved by the Unix 'bc' program on my system:
41 Computation of 2,381,283 ** 235
43 'bc' says:
45 4385CA4A804D199FBEAD95FAD0796FAD0D0B51FC9C16743C45568C789666985DB719\
46 4D90E393522F74C9601262C0514145A49F3B53D00983F95FDFCEA3D0043ECEF6227E\
47 6FB59C924C3EE74447B359B5BF12A555D46CB819809EF423F004B55C587D6F0E8A55\
48 4988036A42ACEF9F71459F97CEF6E574BD7373657111648626B1FF8EE15F663B2C0E\
49 6BBE5082D4CDE8E14F263635AE8F35DB2C280819517BE388B5573B84C5A19C871685\
50 FD408A6471F9D6AFAF5129A7548EAE926B40874B340285F44765BF5468CE20A13267\
51 CD88CE6BC786ACED36EC7EA50F67FF27622575319068A332C3C0CB23E26FB55E26F4\
52 5F732753A52B8E2FB4D4F42D894242613CA912A25486C3DEC9C66E5DB6182F6C1761\
53 CF8CD0D255BE64B93836B27D452AE38F950EB98B517D4CF50D48F0165EF0CCCE1F5C\
54 49BF18219FDBA0EEDD1A7E8B187B70C2BAED5EC5C6821EF27FAFB1CFF70111C52235\
55 5E948B93A015AA1AE152B110BB5658CB14D3E45A48BFE7F082C1182672A455A695CD\
56 A1855E8781E625F25B41B516E77F589FA420C3B058861EA138CF7A2C58DB3C7504FD\
57 D29554D78237834CC5AE710D403CC4F6973D5012B7E117A8976B14A0B5AFA889BD47\
58 92C461F0F96116F00A97AE9E83DC5203680CAF9A18A062566C145650AB86BE4F907F\
59 A9F7AB4A700B29E1E5BACCD6DCBFA513E10832815F710807EED2E279081FEC61D619\
60 AB270BEB3D3A1787B35A9DD41A8766CF21F3B5C693B3BAB1C2FA14A4ED202BC35743\
61 E5CBE2391624D4F8C9BFBBC78D69764E7C6C5B11BF005677BFAD17D9278FFC1F158F\
62 1B3683FF7960FA0608103792C4163DC0AF3E06287BB8624F8FE3A0FFBDF82ACECA2F\
63 CFFF2E1AC93F3CA264A1B
65 MPI says:
67 4385CA4A804D199FBEAD95FAD0796FAD0D0B51FC9C16743C45568C789666985DB719\
68 4D90E393522F74C9601262C0514145A49F3B53D00983F95FDFCEA3D0043ECEF6227E\
69 6FB59C924C3EE74447B359B5BF12A555D46CB819809EF423F004B55C587D6F0E8A55\
70 4988036A42ACEF9F71459F97CEF6E574BD7373657111648626B1FF8EE15F663B2C0E\
71 6BBE5082D4CDE8E14F263635AE8F35DB2C280819517BE388B5573B84C5A19C871685\
72 FD408A6471F9D6AFAF5129A7548EAE926B40874B340285F44765BF5468CE20A13267\
73 CD88CE6BC786ACED36EC7EA50F67FF27622575319068A332C3C0CB23E26FB55E26F4\
74 5F732753A52B8E2FB4D4F42D894242613CA912A25486C3DEC9C66E5DB6182F6C1761\
75 CF8CD0D255BE64B93836B27D452AE38F950EB98B517D4CF50D48F0165EF0CCCE1F5C\
76 49BF18219FDBA0EEDD1A7E8B187B70C2BAED5EC5C6821EF27FAFB1CFF70111C52235\
77 5E948B93A015AA1AE152B110BB5658CB14D3E45A48BFE7F082C1182672A455A695CD\
78 A1855E8781E625F25B41B516E77F589FA420C3B058861EA138CF7A2C58DB3C7504FD\
79 D29554D78237834CC5AE710D403CC4F6973D5012B7E117A8976B14A0B5AFA889BD47\
80 92C461F0F96116F00A97AE9E83DC5203680CAF9A18A062566C145650AB86BE4F907F\
81 A9F7AB4A700B29E1E5BACCD6DCBFA513E10832815F710807EED2E279081FEC61D619\
82 AB270BEB3D3A1787B35A9DD41A8766CF21F3B5C693B3BAB1C2FA14A4ED202BC35743\
83 E5CBE2391624D4F8C9BFBBC78D69764E7C6C5B11BF005677BFAD17D9278FFC1F158F\
84 1B3683FF7960FA0608103792C4163DC0AF3E06287BB8624F8FE3A0FFBDF82ACECA2F\
85 CFFF2E1AC93F3CA264A1B
87 Diff says:
88 % diff bc.txt mp.txt
89 %
91 ------------------------------------------------------------------
92 This Source Code Form is subject to the terms of the Mozilla Public
93 # License, v. 2.0. If a copy of the MPL was not distributed with this
94 # file, You can obtain one at http://mozilla.org/MPL/2.0/.
