Question

Discrete Math

1. Use the primes P₁ = 3 and P₂ = 17 and the value E = 3 with the RSA algorithm to compute the values below needed to get the keys:

1. What is the value of N?
2. What is the value of Z?
3. What is the value of D?

(ABET 5) Using the values from the problem 9) above, show how to encrypt the message, M = 44. Do NOT simplify, just show the computation needed to encrypt it.

2. (ABET 5) Using the values from the problem 9) above, show how you would decrypt the cipher message, C = 25. Do NOT simplify, just show the computation needed to decrypt it.

3. (ABET 5) Suppose that Jerry Jones, the owner of the Dallas Cowboys, wants to send a message, M, to all the players. But he wants to digitally sign his message so that the players know it was from him.

4. Assume that Jerry Jones has the public key N and E, and the private key, D. Show what Jerry would compute, C, to digitally sign his message, M.

Answer 1

Solutions page . . Given that use the poines P1=3 and and o the value E=3 with RSA algorithm In ouder to solve any RSA algoouths problems we have to know sam thm to know some basics stopy. (i) (ii) consider two longe perime number calculate N > N= P, & P2 (multiply two large - ocime numbeuty) (ii) calculate zou oon) = (P-1)*(24) (iv) (ul. Assume E' such that ged (E, 2] =) Assume o - D - E mod z =) x t = 1 hod z -) Die modz = 1 mod z. » DE mod z = 1 public key = LE,N} porivate teey : Lon} cui) Encertyphicon MCN then came mod in Cuir) see you on top mod N

Page prime numbers are Given that two and E= 3 P123, P2 = 17 The value of N Ni Pi* P2 1. = 3 * 17 N: 51 value of z z = (1,-1) * (P2-1) = (3-1) +(141) :(2) *016) = 32 © value of D value of D we know that D&E mod z = 1 =) * 3 mod 32 = 1 . 1 . Assume 0ll will be = 11*3 mod 32:1 :>> 33 mod 327, e) les Therefore D is = 11 using above values i encaypt the message Malune foi enceryption .. * obtain the recipient publickey public key =LENY -631513

* Represent the alarn text message as Seo пі% 12мг N possitive integen r with * compute the cipher text = S c HE modn Therefore c: us Mod 5 1 144 ) 3 Muy N:51 2 using the above , decerupt the message (=25 • *> use the private lery . private they = L DIN? -L11,513 Exteract the plaintext from the мекче стерлеfеntіvе 'н' foom Decoryption we tenow that Ma comoda - 25" med 5! 100 C25 319 . N:51) I have provided the formula for the - ③ Computation of c. , OLMLM ME ZACZ Enougatich: Griven a message use public keyce,n) Compute ca Hemod n Ceza-bog

. let Public - page ② us assume that jenay jones has the key Ni and E. and the private key резонот - Criven n a a cipheatent ciphea tent c, use private key complute cd mod.in =(MEnod nga modna med mod nam // Hence puroved above solutions // vion please upvote ......