### Symmetric and public-key encryption

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Assignment: Symmetric and Public-Key Encryption

One of the most widely used public-key encryption algorithms is RSA. RSA was developed at the Massachusetts Institute of Technology (MIT) in 1977 by Ron Rivest, Adi Shamir, and Len Adleman.

In the RSA algorithm, two prime numbers (a & b) are selected and multiplied together. The resulting product is used as a modulus for both the public and private keys. Euler's totient function is performed upon the primes: c = (a - 1)*(b - 1). A number d is chosen where 1 < d < c, and c and d are co-prime (their greatest common divisor is 1). The number dis then released as the public-key exponent. The number e, the private-key exponent, is calculated, taking the multiplicative inverse of d(mod c), i.e., d-1(mod c).

A simple example would be as follows:

Use the numbers 61 and 53 for the primes. Multiply them to get 3,233. The totient of 3,233 = 60 x 52 = 3,120. Use 17 for the public key exponent, since 1 < 17 < 3,120. 17 - 1(mod 3,120) = 2,753, the private-key exponent. To encrypt the number 65, for example, compute 6,517(mod 3,233). This yields 2,790. To decrypt 2,790, compute 2,7902,753(mod 3,233). The result of the calculation is 65, the original number.

1. Explain how RSA can help in creating digital signatures. How does a digital signature work in an e-mail system? Can a digital signature in an e-mail avoid packet sniffing?

2. What is the basic difference between symmetric and public-key cryptography?

*Remember to properly cite your sources according to APA guidelines.

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