Which statements are correct

$$ A block cipher according to Shannon should comprise two atomic operations, i$.$e$.$ confusion $($obscuring relationship between plaintext and ciphertext$)$ and diffusion $($single bits of ciphertext influenced by many bits of plaintext$).$

$$ B$)$ In cryptography key space refers to possible keys used by a certain cryptographic protocol.

$$ C$)$ In modular arithmetic under a mod $5$ operation the numbers $7$ and $12$ are equivalent.

$$ D$)$ Substitution cipher is an example of a historical cypher in which every plaintext letter is replaced by another fixed letter, hence it is an example of an asymmetric cipher.

Which statements on classical cryptography fundamentals are correct

$$ The DES protocol is a block cipher using $56$ bits long keys which is considered not secure due to increases of computing power.

$$ Encryption and decryption functions need to be kept secret for the cryptographic protocol to remain secure$.$

$$ A field F is a set of elements with following properties: all elements of F form an additive group with the group operation $+$ and the neutral element $0,$ all elements of F except $0$ form a multiplicative group with the group operation x and the neutral element $1,$ when the two group operations are mixed the distributivity law holds.

$$ Fermat's little theorem $($stating that if p is a prime number, then for any integer a$,$ the number a to the power of p minus a is an integer multiple of p$)$ is very important for private$-$key cryptography.

Which statements are correct

$$ Electronic code book mode $($ECB$)$ allows for a simple block cipher encryption of large input plaintext by breaking the plaintext into subsequent blocks.

$$ Insecure communication channels may include Internet, GSM$,$ wireless networks $($Wi$-$Fi$).$

$$ Letter frequency analysis attack is considered effective against substitution cipher because identical plaintexts map to identical ciphertexts.

$$ Double encryption using DES may seem secure but is prone to the meet$-$in$-$the$-$middle attack.

Which of the statements below are correct

$$ A condition for the affinity cipher to work with a key $($a$,$b$)$ is that for having a greatest common divisor for a and m $($number of letters in alphabet$)$ equal to $1,$ which will mean that the cipher's encryption function is injective.

$$ In cryptography unencrypted message is referred to as the plaintext, while the encrypted message is referred to as the ciphertext.

$$ An exhaustive key search attack $($brute$-$force type of attack$)$ is considered effective against substitution cipher.

$$ Unconditional security of a cipher can be referred to as information$-$theoretic security $($meaning it cannot be broken even with infinite computing resources$)$ and is only true for the OTP cipher, however under a condition that the truly random key $($of length such as of the plaintext message$)$ can be distributed between the parties, which can only be done unconditionally securely using the quantum key distribution.

Which of these statements are correct

$$ Cryptography can be generally divided into symmetric $($public$-$key$)$ and asymmetric $($private$-$key$)$ cryptography.

$$ A linear feedback shift register $($LSFR$)$ has an input bit being a linear function of its previous state and can be easily implemented from flip$-$flops, however due to security issues it was not used in any practical cryptographic scenario.

$$ Permutation is an example of diffusion in a block cipher.

$$ Stream ciphers encrypt individual bits using public keys.

$.$ 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.

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.