Problem 1: One Time Pad

Recall OTP. Assume that the RNG stopped working in the middle of the key generation and generated k1, a key which length is half the length of message m. Answer the following questions.

(a) If we use k1 two times (i. e. use k1||k1 as the key, where || denotes concatenation) to encrypt m using the OTP scheme, will the resulting ciphertext be secure? Why or why not? Justify your answer.

(b) You generate another key, k2, using the same RNG so that if concatenated with k1, the total key length will be same with m (i. e. len(k1||k2) = len(m)). If you use k1||k2, instead of generating a totally new key k′ where len(k′) = len(m), to encrypt m using the OTP scheme, would it affect the confidentiality of the resulting ciphertext? Why or why not? Justify your answer. (Assume that RNG is working correctly.)

NOTE: Answer to each problem in 3 to 5 lines (including the justification). An answer without a justification will result in an automatic 0.