Question

5.6 Exercise. Describe an RSA Public Key Code System based on the primes and 17. Encode and decode several messages Of coursc, the fun of being a spy is to break codes. So get on your trench coal, pull out your magnifying glass, and begin to spy. The next exercise asks you to break an RSA code and save the world 5.7 Excrcise. You are a secret agent. An evil spy with shallow mumber thery skills uses the RSA Public Key Coding System in which the public modulus is n 1537, and the encoding exponent is E-47. You intercept one of the encoded secret messages heing sent to the evil spy, namely the number 570. Using your superior mumber theory skills, decode this mes- sage, thereby saving countless people from the fienlish plat of the evil spy The ncxt exercise asks you to explain in general how you can break RSA codes if you are able to factor n. 5.8 Exercise. Suppase an RSA Public Key Coding System publishes n (which is equal to the product of two undisclosed primes p and q) and E, with E relatively prime to (p- 1)( 1). Suppose someone wants to send a secret message and so encodes the message number w (less than n) by finding the mumber m less than n such that m WE (mod n). Suppose ou intercept this number m and you are able to factor n. How can you figure out the original message W

Answer 1

ANSWER Encoding exporent 153 Pultie meduhs is The encekel eeret wetsage = 570 is E 47 -(29 Neres n 533 k(n) Pvate Ke where, d ad kare 11 Autegers) Kx(153) k x (29x53) + 47 K (29) 4(s3) + 47 X 1456 k t K K28 K 52t1 47 47 31 47

number meinge of 540 d Desded (570) med n) (5t0) (d153) 13 13 (m) a) 3(e) 1Ca) The mersage ふe, acal ma 5.8 Enercise Publie wedlus Enponentz E txg Message no W 4 ()(--) Enesded mesage nnmber mod n Prvte Key d We shall calenlate the K P(n) t K san K(t-e-) we usill find integer k al use t to fird l am doy trial 2,3,- en,-2,-3, eた Anteger ehoice of K will be NS an After tding a, sebtained by ewr deeoded mexsage nnber d (m) (mod n) W