Need to answer these questions
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1. A and B want to exchange encrypted messages; specically, B wants to send a message M
written in binary format to A, which needs to be encrypted. They agree in using the RSA
Encryption Scheme. Therefore, A sends to B its public key (N; k) = (91; 5).
(a) Why is (N; k) = (91; 5) a valid public key?
(Show that both conditions are satised.)
(b) B's binary message is M = 110.
What decimal number does it represent?
(c) What is the decimal number representing the encrypted message?
(d) What is the binary representation of the encrypted message?
(e) For (N; k) = (91; 5), the decimal number N = 91 has the binary representation 91 =
1 26 + 1 24 + 1 23 + 1 21 + 1 20 = 64 + 16 + 8 + 2 + 1 1011011, i.e. the binary
representation length is n = 7 and the conditions requested in 1(a) can be veried
without the use of a computer/calculator. Nevertheless, by today's state of algorithmic
knowledge, RSA encryption is considered to be safe. Why is this the case?
2. We assume the elementary deterministic model of Turing Machines (L-II: 11 March); in
particular, innite in both directions tape, tape symbols ? and j, two special states Sstart and
Sstop, and a nite program consisting of instructions [S;X] ! [Y;M; S0].
The initial conguration is dened by the TM being in state Sstart and the R/W-Head reading
the symbol in the tape-cell left from the leftmost j-symbol, if there is a j-symbol. If there
is no j-symbol as part of the representation of the input, the R/W-Head can be positioned
anywhere on the tape.
We consider TMs processing natural numbers N 0. The numbers are represented by the
corresponding number of j-symbols, e.g. N = 3 j j j and N = 0 empty, i.e., if N = 0 is
the input, then there are only ?-symbols on the tape.
(a) Write a program for a TM that
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