Abstract Algebra: Theory and Applications

Use the euler_phi()function in Sage to compute $\varphi (893456123)\text{.}$

Use the power_mod()function in Sage to compute $7^{324}(\mathrm{mod}895)\text{.}$

Explain the mathematical basis for saying: encrypting a message using an RSA public key is very simple computationally, while decrypting a communication without the private key is very hard computationally.

Explain how in RSA message encoding differs from message verification.

Explain how one could be justified in saying that Diffie and Hellman’s proposal in 1976 was “revolutionary.”