Which statements on classical cryptography fundamentals are correct

$$ The square and multiple algorithm involves the following steps upon scanning the exponent bits left$-$to$-$right: $1)$ in every iteration one needs to square, $2)$ if current bit is equal to $1,$ then multiple it by inversion of x$.$

$$ The RSA cryptosystem was invented in $1977$ and patented in the USA until $2020.$

$$ Under mod $3$ operation there are $2$ equivalence classes.

$$ The AES irreducible polynomial is x to the power $8$ plus x to the power $4$ plus x to the power $3$ plus x plus $1.$

Which of the following statements on classical cryptography fundamentals are correct

$$ GSM system uses $11$ LSFRs coupled together in implementing a stream cipher in order to assure difficulty in breaking its security.

$$ Cryptanalysis can be divided into social engineering, implementation attacks $($including side$-$channel attacks$)$ and classical cryptanalysis $($further divided into analytical attacks and brute forces attacks$).$

$$ DES protocol uses $16$ subkeys and its effective key length is $56$ because it drops bits number $8,16,24,32,40,48,56$ and $64,$ because these bits serve as parity bits.

$$ In terms of basic algebraic structures fields generalize rings $($fields include division operation and have a multiplicative inverse for every element other than $0),$ while rings generalize groups $($rings include multiplication operation$).$

$10.$ Which of the following statements on classical cryptography fundamentals are correct

$$ The only really nondeterministic true random numbers generators $($TRNG$)$ are quantum random numbers generators $($QRNG$).$

$$ DES protocol was introduced to improve the security of the AES cryptosystem and successfully doing so became a world standard in practical encryption, later on improved by the $3$DES cryptosystem.

$$ The Feistel network iteratively runs multiple times a simple round function, which allows for easier hardware implementation of a block cipher cryptographic system.

$$ Pseudo random numbers generators recursively compute consecutive random numbers from a seed, which is an input random $($either truly or pseudo random$)$ number.

$11.$ Which of these statements are correct

$$ In general cryptographic encryption requires a key to encrypt messages $($encryption key$)$ and a key to decrypt messages $($decryption key$),$ which do not have to be identical, except for the symmetric$-$key cryptography.

$$ A pseudo random numbers generator, a hash function or a message authentication code $($MAC$)$ can be built from the block cipher.

$$ In the RSA cipher for Alice to encrypt the message to Bob, she needs to receive the public key of Bob, which must be sent to her by a reliable, however not necessarily secure$,$ communication channel.

$$ A block cipher can be easily turned into a stream cipher while the opposite is not the case.

$12.$ 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

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

$$ 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.

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

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

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

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

$$ 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$.$

$$ 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.

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