As we learnt from the CPS&S course, the confidential and authentication services are critical security services required by the CPS. As a public-key encryption system, the RSA algorithm can achieve both services. Assuming that the RSA algorithm is adopted to provide both services in a CPS, given the public key of a user is e = 31, n = 3599 and M =9:
(1) Calculate the private key d to be used for decryption? (Hint: First use trial and error to determine p and q; then use the extended Euclidean algorithm to find the multiplicative inverse of 31 modulo ø(n).) (40 points)
(2) Show encryption process to calculate C. (30 points)
(3) Using the value of private key d calculated in (1), perform decryption process to get M=9. (30 points)
Sample Solution
