7.8. Suppose F is a secure PRP with blocklength n + λ. Below is the encryption algorithm for a scheme that supports plaintext space M = {0, 1}": Enc(k, m): r← {0,1}^ return F(k, m||r) (a) Describe the corresponding decryption algorithm. (b) Prove that the scheme satisfies CPA$ security.

Strings of undefined length are used as keys to access a hash table. Report the C implementation of a proper hash function. Specify and explain (in plain English) how to select the algorithm and how to avoid overflows during the computation of the hash function. Motivate all choices.

Consider Cuckoo hashing with a hash table H[0... 10] and the two hash functions: h₁(x) = (x +2) mod 11 h₂(x) = (4x + 1) mod 11. (When inserting, try h₁ first.) Consider the following sequence of operations: Insert(11) Insert(13) Insert(33) Which position is 33 placed in? 0 1 2 3 4 5 6 O O ос 7 8 9 10

Consider the encryption function for a symmetric cryptosystem E(k, m) described below, where K = M = {0, 1, 2, 3}, C = {0, 1, 2, 3}: E(k, m) = (2 ∗ k + m) mod 4 (a) Give the corresponding decryption function(b) Is this cryptosystem information-theoretically secure(or perfectly secure)? Why or why not?

Question 1. Let H: {0,1}* → {0, 1}" be a hash function that achieves the one-way and collision resistance security properties. (b). Show that the new function H' achieves collision resistance. Suppose that we want to use H for the deployment of a password-based user authentication mechanism that is a variant of the standard password hashing mechanism as follows: when loading a new password P selected by the user with ID U, instead of choosing a random salt, the password P is hashed. Then, the n-bit digest H(P) and password P serve as inputs to produce a fixed-length hash code. Namely, the information that is stored in the password file is the triple (U, H(P), H(H(P)||P)). During password verification for user ID U, the system receives a password P* and (i) computes H(P*), (ii) computes H(H(P*)||P*), and (iii) checks if H(H(P*)||P*) matches the value H(H(P)||P) that is stored for U. 1 Does the aforementioned mechanism provide protection against offline dictionary attacks? Justify your…

If an encryption function er is identical to the decryption function dg, then the key K is said to be an involutory key. (a) Let K = (a, b) be a key in an affine cipher over Z/nZ. Show that K is an involutory key if and only if a- = a (mod n) and b(a+1) = 0 (mod n).

2.(a) Consider the use of OTP. Let m be an arbitrary message to be encrypted and c be a given ciphertext in the ciphertext space. How many possible keys with which m can be mapped to c, i.e., f(m,k)=c? None 1 2 The size of the key space Depends on m (b)  3^(-n) is negligible. True or false? (c) n^(-100) is negligible. True or false?

Question 1. Let H : {0, 1}* →→ {0,1}" be a hash function that achieves the one-way and collision resistance security properties. (a). Let LSB(x) denote the least significant bit of string x and || denote the concatenation of two strings. We define the following function H': {0, 1}* {0,1}+¹ as H'(x) = H (x)||LSB(x). Show that the new function H' achieves collision resistance.

Use a coding matrix A of your choice. Use a graphing utility to find the multiplicative inverse of your coding matrix. Write a cryptogram for each message. C perform all necessary matrix multiplications. DGE OU T AHEAD BR 2 18 4 75 0 15 21 20 0 1 8 5 1 4 .... 1 1 -12 32 -15 Using the coding matrix the coded message is.····☐☐☐☐☐☐☐☐☐☐ 2 2 1 5 4 4 4 7 (Simplify your answers.) 61