$12.$ Which of these statements are correct

The Kerckhoffs's principle states that cryptosystems should be secure even when only the decryption key is kept secret.

In cryptography using finite sets is not very common.

A group is a set of elements G together with an operation which combines two elements of G$,$ having following properties: the group operation is closed and associative, there is a neutral element in the group and there is an inverse element in the group $($a group is abelian or commutative if for all elements of the group the operation combining two elements does not depend on the order of elements$).$

A stream cipher using a truly random key binary sequence is the unbreakable One$-$Time Pad cipher $($under a condition that each key stream bit is used only once, i$.$e$.$ the key binary sequence is as long as the message binary sequence and is used only once$).$

$13.$ Which of the statements below on classical cryptography fundamentals are correct

A$)$ AES MixColumn Sublayer involves a non$-$linear transformation which can be represented by a $4$x$4$ matrix multiplication.

B$)$ In a shift cipher the letters at the end of the alphabet will be replaced with letters from the beginning of the alphabet upon wrapping around corresponding to modular arithmetic.

C$)$ Possible block ciphers modes of operation include e$.$g$.$ ECB, CBC$,$ OFB, CFG and Counter Mode.

D$)$ Exhaustive key search is not always a brute$-$force attack.

$14.$ Which of the below statements on classical cryptography fundamentals are correct

A$)$ The parameter t of the EEA $($extended Euler algorithm$)$ is r with index $1$ modulo r with index $0.$

B$)$ The Euler's theorem states that if a and m are a divisor equal to $1($are coprime numbers$)$ then a raised to the power of phi function on m $($Euler$\text{'}$s totient function$)$ is congruent to $1$ modulo n$.$

C$)$ A shift cipher cannot be easily broken by a brute$-$force attack $($key search$),$ because the key space is very large, due to modular arithmetic properties corresponding to wrapping around.

D$)$ The maximum period generated by an LSFR $($linear feedback shift register$)$ of degree m is $2$ to the power m minus $1.$

$15.$ Which statements on classical cryptography fundamentals are correct

A$)$ The encryption function in the RSA cipher is simply only an exponentiation $($by the e component of the public key$)$ modulo n$,$ while the decryption function is exponentiation with a different exponent, namely d constituting the private key used for decryption.

B$)$ In asymmetric cryptography the relationship between the public key and private key is asymmetric, so for the encryption it is easy to compute a private key from the public key, while the opposite operation is difficult.

C$)$ In breaking DES cryptosystem differential cryptanalysis is more efficient than linear cryptanalysis.

D$)$ An encryption scheme is deterministic if a particular plaintext is mapped to the same ciphertext when the key used has not been changed.