Q4.

(a). Solve the congruence 6 2= 5 mod 79) You need to provide all the working which leads to the solution. (b). An RSA cryptosystem with the public key (n, e) = (7042249, 49695) is given. An Eavesdropper managed to derive the private key d = 73771 and found that the prime factorisation of die-1 is 27.511.911 - 1931. Find the prime factors of n. In this question you must not use the calculator's factorisation features. All the intermediate steps of the solution need to be provided. (). The baby-step/giant-step algorithm is used to find a solution of the congruence 6* = 21 ( mod 113) Some of the data produced by the algorithm is as follows: 6-11 101 ( mod 113); 0 1 2 3 4 5 k 101*.21 mod 113) 21 87 86 98 100 By restoring the missing data or otherwise find a solution x of the congruence. (a). Solve the congruence 6 2= 5 mod 79) You need to provide all the working which leads to the solution. (b). An RSA cryptosystem with the public key (n, e) = (7042249, 49695) is given. An Eavesdropper managed to derive the private key d = 73771 and found that the prime factorisation of die-1 is 27.511.911 - 1931. Find the prime factors of n. In this question you must not use the calculator's factorisation features. All the intermediate steps of the solution need to be provided. (). The baby-step/giant-step algorithm is used to find a solution of the congruence 6* = 21 ( mod 113) Some of the data produced by the algorithm is as follows: 6-11 101 ( mod 113); 0 1 2 3 4 5 k 101*.21 mod 113) 21 87 86 98 100 By restoring the missing data or otherwise find a solution x of the congruence