Which of the following statements are correct

$$ In a shift cipher to account for wrapping around we would need to use mod K$,$ where K is a value of a key, i$.$e$.$ the number for letters shifting in the alphabet.

$$ Rijndael cipher won a competition call by NIST to become the AES cryptosystem in $2000$ in competing against $70$ other algorithm submissions.

$$ For the RSA cryptosystem to be secure the initial large prime numbers selected for the keys computing algorithm should be really large $($i$.$e$.$ at least $512$ bits or even twice or $4$ times as much$).$

$$ Public$-$key cryptography $($asymmetric cryptography$)$ is used solely to solve the problem of the key distribution.

$$

$7.$ Which of the statements below are correct

$$ The public$-$key cryptography has been introduced to be used for encryption, but if the asymmetric relation in terms of the complexity in computing keys is reversed, it can be used for authentication rather than for encryption.

$$ A probabilistic encryption scheme uses randomness to achieve a non$-$deterministic generation of a cyphertext.

$$ Security of block ciphers does not depend on combining multiple times of the confusion and diffusion operations, as these operations do not increase when combined in multiple numbers.

$$ In modular arithmetic mod $2$ addition and subtraction are different operations.

$8.$ 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 $1.$