Decode the number using the given private key. Decode the number M = 15 using the private key d = 53 and n = 77. Assume you are decoding the number using the RSA cryptosystem. Note: You can use the Modular Exponentiation calculator to help with the calculation. a 63 (mod 77), decoded number = 63 O b 64 (mod 77), decoded number = 64 65 (mod 77), decoded number = 65 Od 66 (mod 77), decoded number = 66

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In java pls! Thank you!   In many cryptographic applications the Modular Inverse is a key operation. This programming problem involves finding the modular inverse of a number. Given 0 < x < m, where x and m are integers, the modular inverse of x is the unique integer n, 0 < n < m, such that the remainder upon dividing x × n by m is 1. That is, x × n mod m  = 1. Modular inverse is a concept that extends the arithmetic inverse. For example, the inverse of 2 is ½ because 2 x ½ = 1 with decimal operation. Here the inverse number can be a fraction.  In modular inverse, we only allow integers, no fraction. So not all integer has an inverse. For example, m = 26, x = 3, the modular inverse of 3 is 9 because  3 x 9 mod 26 = 1.  However, m = 26, x = 2, the modular inverse of 2 does not exist because you cannot find a number y so that 2 x y mod 26 = 1. Here is another example, m = 17, 4 x 13 = 52 = 17 x 3 + 1, so the remainder when 52 is divided by 17 is 1, and thus 13 is the inverse…

Encode the number using the given public key. Encode the number M = 14 using the public key n = 77 and e = 13. Assume you are encoding the number using the RSA cryptosystem. Note: You can use the Modular Exponentiation calculator to help with the calculation. a 46 (mod 77), encoded number = 46 47 (mod 77), encoded number = 47 48 (mod 77), encoded number = 48 d. 49 (mod 77), encoded number = 49