Which of the following statements are correct

$$ Merkle$-$Damg$$rd construction is one possible, but very rarely used hash function.

$$ Complexity of finding a collision in a hash function is equal to $2$ to the power of n$+1,$ where n is a binary length of the output.

$$ Reuse of the secret exponent i is a basis of one of the attacks on the Elliptic Curve Cryptography $($ECC$).$

$$ The Diffie$-$Hellman protocol alone cannot be used for encryption.

Which statements on cryptography are correct

$$ RSA cryptosystem can be used as a digital signature scheme.

$$ The man$-$in$-$the$-$middle attack cannot be launched against the Diffie Hellman protocol.

$$ The set consisting of all integers from $0$ to n$-1$ which are coprime with n forms an abelian group.

$$ A group containing an element with maximum order equal to the order of the group is cyclic $($and elements with maximum order are called generators$).$

Which statements on cryptography are true

$$ Elgamal encryption scheme can be used for key exchange.

$$ Secure message authentication codes should accept arbitrary lengths of inputs, produce fixed output lengths, assure message authentication, assure message integrity and non$-$repudiation.

$$ One of the classes of attacks on cyclic groups based cryptosystems are square root attacks which are characterized by square root of n steps, where n is the cardinality of the cyclic group.

$$ In the RSA based digital signature the signing algorithm $($square and multiple$)$ is faster by a factor of an order of $1000$ compared to symmetric cryptographic protocols $($e$.$g$.$ AES$).$

Which of the statements below are true

$$ Groups of most practical applications in cryptography are multiplicative groups of prime fields and groups of points on curves $($elliptic curve cryptography$).$

$$ Baby$-$step giant$-$step algorithm and Pollard's$-$rho method, known as square root attacks are best known attacks on elliptic curve cryptosystems.

$$ Making collisions easy to find is a way to secure hash functions.

$$ RSA, Discrete Logarithm, Elliptic Curves cryptography are examples of asymmetric cryptography.