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

2023
Views:

258

Pages:

5
Author:

Julie E. J.

Point addibon weirdest – = J+k (x, y) (ban) S= Yj-yk mod, siis 152-75-xk mod P ye = -yj + (j-xe.) modp Point doubling J= (x, yj) 2.JA = (x, y) full S=(3xj2+0) 11 zyj mod P Al= 82-2xj madp yl = -gj +s Caj-de) modp. Q. consider the group E28, (9,17). This es the group deefined by equation ya mod 23= (x²+ 9x +17) mod 23. what is the discrète logarithro k of (416) to the base P= (16,5) Ans: P= (16,5) 29 =, 2x (16,5 = (xl, yl)-1 2yj mod P 2 3 x16 +a 2x5 moap 768+9 10 mod 23 mod 779 mod 23 27023 10 mod 22 10/28 1-2x0 0-1×2 23-2X1D 3 3/19 0-3x1 1-(-2x2) 10-9 =-3 = (777x7) mod 23 5489 mod 23 23591 5- 2xj mod p 21 = (119-2x16) mod 23 = 121 - 32 mod 23 2124-9 (121 32) mod 23 = 20 yl = yg + 8 (xj-xl mod P =-5+11 (16-20) mod p =-5+11 (-4) mod P -49 mod 23 =(-49+(8x22)) mod 28. 20 mod 23 ep2p + P = 20,20)+(16,5) S= Yj-yk mod p 20-5 mod 23 15 mod 23 20-16 Bmod 2.3 Extended tuckiedican algorithm S (15x6) mod 23 = 90 mod 23. 2 xj mod P 2 - 2x20 mod 23 -401 mod 23 s_xj-ak mod p -(212-20-16) modfa =405 mod 23. = 14 ge = -yits (zj-xl) mod 23 =(-20+21 (20-14) mad 21 -20+21 (6) mod 23 106 mod 23 = 106 1 39- (19,14)