# Data Security Homework 2

Homework 2

Rule: Finish all of the following on your own.

1. (Hints: Use Fermat Theorem, Euler Theorem, properties of totient functions, etc, or write program code as assistance)

(1) 123416 mod 17

(2) 5451 mod 17

(3) ø(51)

(4) gcd(33, 121)

(5) 2-1 mod 17 (i.e., multiplicative inverse of 2 mod 17) (6)ind2,5(4)

(7) ø(8000)

(8) ø(98803519)

1. Write a computer program to implement the extended Euclid’s algorithm, use your code to compute the following. Submit your code and results.
2. GCD (10012012,2314213) b. GCD(28176412,29108188) c.GCD(38172,23812188)
1. The multiplicative inverse of 12091 mod24123123.
2. The multiplicative inverse of 28173928 mod129182771.

1. Prove that a=n-1 is always a solution to a2=1 mod n.
2. What are the differences between symmetric and asymmetric keycrypto.
3. Explain the feasibility and security ofRSA.
4. Alice designs a double-RSA cipher. She first generates two secret primes p and q, and compute n=p*q, then choose two public encryption exponents e1 and e2 that are relatively prime to ø(n). So <e1, e2, n> becomes the public key. She tells people to encrypt message M by computing C1=M e1 mod n and then C= C1e2 mod n, finally sending just C
5. Show the decryption process (i.e., how Alice can obtain the plain text M from the final ciphertextC).

1. Is the double-RSA cipher more secure, less secure, or just as secure as the regular RSA cipherwith the same modulus but only one encryption exponent? Why?
2. Charlie got Alice’s instructions confused, and encrypt message M for Alice using e1 and e2 in the reverse order (i.e., Charlie uses C1=M e2 mod n then C= C1e1 mod n). What would happen when Alice, unaware of Charlie’s error, triesto decipher the ciphertext using her usual procedure?

Last Updated on February 21, 2019

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