University:
California State University, Los Angeles
Course:
CS4780 | Cryptography and Information Security
Academic year:

2023
Views:

265

Pages:

4
Author:

Julie E. J.

146 Properties of congruences 230 a = b(mod n) if in/a-b 2. a = b(mod n) → b = a (mod 3. a = b (modn) b = c (mod n) a = c(mod n) Modular arithmetic operations. 1. [Ca mod n) + (b mo'dn)] modn = (a+b) modn Eg: a=111 b = 15 n=8 Atts [(a modn) +(bmodn) modn >[mod 8 15 mods] mods. mod 8 + 15 mod (3+7) mod8 10 mod 8 Rts: (a+b) modn (11+15) mod 8 = 26 mod 8 = 2 LHSR-HS 2. [(a modn) (bimodn)] modn (a-b) mod n hts [3-7] mod 8 =-4 mode =4 Rts: (a-b) modn =(11-15) mod 8 =-4 mode 4 Lets Ritts 15 26 826 24 २ 3. [(amoan); x (b modn) mod n (axb) modn Mts: (3x7) mod 8 = 21 mod 8 V 5 PHS. (11x15) mod 8 = 165 mods Paver of a Friding performed by repeated as in ordinary number is meetti plicat arithmeti ag: Find 117 mod 13. 111214, (mod 18) =" 114 = x² = 4 = 3 (mod 13) 117 = 11×11×114 = 11×4×3 132 2 (mod 18 Properties of modulas anthmetic for integers in I 1. Co romuta tive laws • (0+2) mod n = (x+w) modn •(wx) modn = (aw) mod n 146 Properties of congruences 230 a = b(mod n) if in/a-b 2. a = b(mod n) → b = a (mod 3. a = b (modn) b = c (mod n) a = c(mod n) Modular arithmetic operations. 1. [Ca mod n) + (b mo'dn)] modn = (a+b) modn Eg: a=111 b = 15 n=8 Atts [(a modn) +(bmodn) modn >[mod 8 15 mods] mods. mod 8 + 15 mod (3+7) mod8 10 mod 8 Rts: (a+b) modn (11+15) mod 8 = 26 mod 8 = 2 LHSR-HS 2. [(a modn) (bimodn)] modn (a-b) mod n hts [3-7] mod 8 =-4 mode =4 Rts: (a-b) modn =(11-15) mod 8 =-4 mode 4 Lets Ritts 15 26 826 24 २ 3. [(amoan); x (b modn) mod n (axb) modn Mts: (3x7) mod 8 = 21 mod 8 V 5 PHS. (11x15) mod 8 = 165 mods Paver of a Friding performed by repeated as in ordinary number is meetti plicat arithmeti ag: Find 117 mod 13. 111214, (mod 18) =" 114 = x² = 4 = 3 (mod 13) 117 = 11×11×114 = 11×4×3 132 2 (mod 18 Properties of modulas anthmetic for integers in I 1. Co romuta tive laws • (0+2) mod n = (x+w) modn •(wx) modn = (aw) mod n