Exercise 13 Name: 11.5 (Multiplicative ElGamal). Let G be a cyclic group of prime order q generated by g € G. Consider a simple variant of the ElGamal encryption system EMEG = (G. E, D) that is defined over (G. G²). The key generation algorithm G is the same as in EEG, but encryption and decryption work as follows: ⚫ for a given public key pku G and message mЄ G: E(pk, m) := eum, output (v, e) ⚫ for a given secret key sk= a € Zq and a ciphertext (v,e) € G²: D(sk, (v, e)) e/v Show that EMEG has the following property: given a public key pk, and two ciphertexts C1E(pk, m) and c2 E(pk, m2), it is possible to create a new ciphertext e which is an encryption of m₁ m2. This property is called a multiplicative homomorphism.

Q: Problem #1 Given below is a well-known cryptosystem called affine Caesar cipher, as well as some…

A: One of the earliest and most basic encryption techniques is the Caesar Cipher. It is merely a sort…

Q: Exercise 2 (MAC schemes derived from block ciphers ( Let E denote the family of encryption functions…

A: we assume that it is not collision resistant, i.e. we can find a pain of messages x and y where xty…

Q: Exercise: "Let the messages consist of all strings of length 2 over GF(3). Encode the message ab to…

A: In this exercise, we deal with messages consisting of all strings of length 2 over the Galois Field…

Q: The parity function is a very simple hash function producing a one-bit digest, which is 0 if the…

A: Hamming code is a bunch of error detection codes that can be utilized to distinguish and address the…

Q: Suppose we have public key encryption system with E the encryption function and Dµ the decryption…

A: Process for authenticating the message using public key k (E k ) and secret key k (Dk).

Q: RSA cryptosystem = = Let p = 29 and q = 31. Then the RSA modulus n pq 899. We set the length of…

A: One of the most popular and safe public-key encryption techniques is the RSA cryptosystem. The…