Problem $1.$ Questions from all over.

a$.$ Error correcting codes are used to correct random transmission errors. When combining

encryption and an error correcting code would you encrypt and then apply the error correcting

code or vice versa? Encryption here refers to authenticated encryption, such as encrypt then

MAC. Briefly justify your answer. Note that error correction is not a security mechanism so

that the composed system need not provide ciphertext integrity.

b$.$ Suppose an attacker steals the long$-$term secret TLS $1\mathrm{.}3$ key of a banking web site.

i$.$ Can the attacker act as a passive eavesdropper on future HTTPS connections to that

banking web site?

ii$.$ Can the attacker impersonate the banking web sites to bank customers?

c$.$ In class we showed how to instantiate the ElGamal public key system with one of two groups:

$(1)$ the group $Z_{p_1}^{**}$ for some prime $p_1,$ and $(2)$ the group of points of an elliptic curve $E(F_{p_2})$

for some prime $p_2.$ Why is it that $p_1$ must be at least $2048$ bits, but $p_2$ need only be $256$ bits,

to obtain comparable levels of security?