q1) Write a program (in any language you like) to help an analyst decrypt a simple substitution cipher

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q1) Write a program (in any language you like) to help an analyst decrypt a simple substitution cipher. Your program should take the ciphertext as input, compute letter frequency counts, and display these for the analyst. The program should then allow the analyst to guess a key and display the results of the corresponding "decryption" with the putative key.

Upload your source code. File type does not matter.

a. Given the following ciphertext, use your program to find the key.

GBSXUCGSZQGKGSQPKQKGLSKASPCGBGBKGUKGCEUKUZKGGBSQEICACGKGCEUERWKLKUPKQQGCIICUAEUVSHqKGCEUPCGBCGQOEVSHUNSUGKUZCGQSNLSHEHIEEDCUOGEPKHZGBSNKCUGSUKUASERLSKASCUGBSLKACRCACUZSSZEUSBEXHKRGSHWKLKUSQSKCHQTXKZHEUQBKZAENNSUASZFENFCUOCUEKBXGBSWKLKUSQSKNFKQQKZEHGEGBSXUCGSZQGKGSQKUZBCQAEIISKOXSZSICVSHSZGEGBSQSAHSGKHMERQGKGSKREHNKIHSLIMGEKHSASUGKNSHCAKUNSQQKOSPBCISGBCqHSLIMQGKGSZGBKGCGQSSNSZXQSISQQGEAEUGCUXSGBSSJCqGCUOZCLIENKGCAUSOEGCKGCEUqCGAEUGKCUSZUEGBHSKGEHBCUGERPKHEHKHNSZKGGKAD

Enter all in uppercase. For example, LHFGKTMPZECBQRIYAUSODJWNVX means 'a' in plaintext is substituted to L, b is substituted to H, c is substituted to F etc.

b. Insert a screenshot of the test run of your program when trying to decrypt the message in.

q2.

Write a program (in any language you like) to implement the A5/1 algorithm. Your program should be able to take the values in the registers (X, Y, and Z) after a particular step, and output the following:

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a.

Next n keystream bits;

the contents of registers (X, Y, and Z) after these n bits have been generated.

Suppose that, after a particular step, the values in the registers are
X = 1010101010101010101
Y = 1100110011001100110011
Z = 11100001111000011110000

Use your program to find out:

Next 32 keystream bits:  ;

The contents of registers these 32 bits have been generated:

X = 

Y = 

Z = 

b.

Insert a screenshot of the test run of your program when trying to solve.

q3

For RSA, suppose p and q are given, and of course, e is given. Recall that ????????=1mod????(????)ed=1mod?(n) where ????(????)=(????−1)(????−1)?(n)=(p−1)(q−1), and by definition of "mod", ????????=????????(????)+1ed=k?(n)+1. Since for RSA, gcd(????,????(????))=1gcd(e,?(n))=1, we get ????????+????????(????)=gcd(????,????(????))ed+m?(n)=gcd(e,?(n)) where m = -k.

Therefore, if we know p, q, and e, it's not hard to find d and m using the extended Euclidean algorithm.

So, write a program that takes p, q, and e for RSA as inputs, and output the smallest possible d ( > 0) that can be used as a private key using the extended Euclidean algorithm.

Upload your source code. File type does not matter. If you have multiple files, please zip them.

a.

Use your program to find the smallest possible d ( > 0) given p = 233, q = 331, e = 221.

b.

Insert a screenshot of the test run of your program when trying to find the d for the question above.

q4.

Where are random numbers used in ...

a. symmetric key cryptography?
b. RSA?

c. Diffie-Hellman?