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

2023
Views:

284

Pages:

7
Author:

Julie E. J.

RSA Algorithm Rivest Ahamber Adelman. n1024 bits • It is a public key easyption Algonth most popular and Proven assymmels Key cxcyption algorithm - Developed by Ron Rivest, Adi shames, hen Adehuan at MIT Labs in 1977. IT Here o thang th and CT intequu are miteau -A typical size of in is 1024 bits. Algorithm to Select & prime Such that Panda 2. Calculate n= Pq 3. Calculate (n) = (P-1) (9-1) 1. beleet an integer ged (Φ(n), e) =10 "e Buch that =10 where ike<中(e). 5. Calculate od where de'(mad d Public Key pufe,ny Puvate key PR={din? Encryption Plaintext: Man apher lext: cm² modn Decryphon Ciphertext: C plaintext:M = camodn g 1. Select 2 prime nois 20 Calculate in = 19 = say p. 17 and q=11. 17 x 11 = 187 17 17 7 17 3. calculate (n) = (P-1) (q-1) (17-1) (1-1) =(16) (10) = 160 = 4. Select an get e is integer ce such that Latively Priime to $(n) and less than 4(n). Bay e = 7 5. Calculate d rouch that d = 1 mod (n) and d<160 So, d = 23 because 23x7=1mod 160 can be fonded out by entended Euclididantinlily algorithm The resulting keys are Pu = {ein]={7,187] PR = Ediny = {x8, 1877 let, M=88 C = Me modn 887 mod 187 Bst mod 167 88 882 mod 187 - 7744 mod 187 =7711 1884 mog 187 = 54, 96, 132 88 mod 187 = 11 Decryphon, M= ed mod'n 23 11 mod 187 1193 mod 187 = [it mod 187 X x117 mod 187 ximal 8 I mod 17 X 118 mod 187 = 88 Il mod 187 117 mod 187 11 mod 187 11- 121 114 mod 187 = $5 118 mod 18733 [" x33 1 x 121 x 55 x 33 x8 -(79720245) mod 17 88 79720167 2034 982 Frncryption PT88 mod 187 = 11 Pecryphon 23 11 mod 187-88 PT 88 Pu=7, 1871 49: P=3, 9=11 P=3, 9-11 ۱۰ PR=23,187 n = Pq 3 ×11=33 = (2) (10) = 20 3. Calculate $(n)= (p-1) (2-1) 4. seclect è such that e is relatively Prinie to $(n) and less than $(n). e=7 5 Calculate od such that d = i mod d(n) and d < 20 so, 7 xd mod 20 7d mod 20-1 7xd mod 20-1 d=3 Shom 37s med 20-1 1-2XG 0-2x1 26-2X7 =7 =-2 =-1 0-1×1 1-1x2 3 d=3 Keys are Pus {en] = {7, 7,53 Pk. {din} = {3,33] let M=2 Memodn CM = 2 7 mod 33 22 mod 33 28=4 4 mod 33 24 = 4 = $6 mod 83 272x22x24 =2×4×16 126 mod 33 = 29 Decryption, M= ed modn = 29 mod 33 29 mod 33 = [ 29 mod 83 x 29mod 33]mod 33 24 mod 33 = 29 29 mod 380 (29) = 841, mod 33 ⇒ (29 x16) mod 33 16 14 964 mod 33 33 464 462 Q. using data P=3, 9 = 11; n = Pxq, dat d=7 En RSA algorithm find the CT of the given PT BUBARU SUZANNE a. BUTA b. SUZANNE XYZ ABCD d. HBCDXYz C+3) mod 18+37 mod 26 91 Mold 26 19.33. d(n) = 20, e-B Pu = {n}={3,833 let M=19 C. Me modn - 19 mod 33 28 B A. ButAEEZ 33/65 648