R6. Suppose N people want to communicate with each of N-1 other people using symmetric key encryption. All communication between any two people, i and j, is visible to all other people in this group of N, and no other person in this group should be able to decode their communication. How many keys are required in the system as a whole? Now suppose that public key encryption is used. How many keys are required in this case?

R6. Suppose N people want to communicate with each of N-1 other people using symmetric key encryption. All communication between any two people, i and j, is visible to all other people in this group of N, and no other person in this group should be able to decode their communication. How many keys are required in the system as a whole? Now suppose that public key encryption is used. How many keys are required in this case?

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Consider the case of Alice sending a message, m, to Bob. Both Alice and Bob use public key cryptography and each has a public and private key as described in the text. The figure attached below shows the operations that Alice must perform to provide confidentiality, authentication, and integrity when sending a message to Bob over the network. We can use either symmetric key or public key cryptography to encrypt a message. For our purposes, either technique will encrypt the message, and applying both doesn't make it "more secure". Also, we can assume that the session key would remain a secret so the fact that it is discarded does not make it "more secure". Why do we use a session key, Ks, instead of relying only on public key Cryptography? In other words, why do we use both public key and symmetric key cryptography?
Let Π = (Gen,Enc,Dec) be a private-key encryption scheme that has indistinguishable en- cryptions in the presence of an eavesdropper. Which of the following encryption schemes are also necessarily secure against an eavesdropper? If you think a scheme is secure, sketch a proof, if not, provide a counterexample. Here, for a bit string s, parity(s) is 1 if the number of 1’s in s is odd, and 0 otherwise. The || symbol stands for concatenation. So, for strings if x = 00 and y = 11, x||y = 0011. (a) Enc1k(m) = 0||Enck(m)(b) Enc2k(m) = Enck(m)||parity(m) (c) Enc3k(m) = Enck(m)||Enck(m)(d) Enc4k(m) = Enck(m)||Enck(m + 1). Here think of m as an integer. Please type answer note write by hend.
Consider a large institution that has 16891 employees. How many keys are necessary to allow any pair of employees to securely communicate using a symmetric cipher? Suppose that we instead use an asymmetric cryptographic scheme. How many keys are required in this case?
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?
We have the following encryption scheme for message space . Gen will uniformly choose the key k from the key space . Enc(k, m) returns and Dec(k, c) returns . Is EAV secure (computationally indistinguishable)?
Problem #1Given below is a well-known cryptosystem called affine Caesar cipher, as well as someciphertext generated using the affine Caesar cipher.P = C = Z 26 = {0, 1, 2, ..., 25};K = {(a, b) Z26 Z26 | gcd(a, 26) = 1}y = E([a,b], x) = (ax + b) mod 26,x = D([a,b], y) = a-1 (y – b) mod 26,where x P, y C. Ciphertext sample:VPWOMFUWOFMYMHUNWBBWGCRVVPSFVPUTHUJWMCOMFUOVSVWOVWGSRSFSREOWOQMHKOBMHVPWOUFGHETVWMFOEOVUYVMMZCVGSFEMCCOUEMCHKFMQRUNIUMBRWFUSHSRIUZHSVMBWFNVPUOUGHUVKUEVMMVPUFEMCQWRRPSJUVHCREGHSGKUNVPUOEOVUY For this problem, please do the following:(a) provide an analysis detailing its strength/weakness;(b) attempt to uncover the plaintext associated with the ciphertext;(c) attempt to determine the secret key (a, b) used.
Suppose your RSA public key is PK: {n, e} = {13861, 37}. Your friend sends you a ciphertext C = 9908. But unfortunately you have forgotten your private key, now you have to crack it yourself.a) Write down a possible condition of factors p and q.p= q=b) What is your private key SK: {d}?d=c) What is the plaintext of your friend’s message?The plaintext M =d) Suppose the plaintext M is a 12-digit number consisting of a prefix “19” and 1234567890. What is the corresponding ciphertext? Since M is greater than n, you only need to encrypt four digits at a time. Ignore redundant zeros. e.g., 0001 = 1. The result should contain three integers.The ciphertext C0 =
An affine cipher has the form c = (am+b) mod n. Suppose m is an integer between 0 and 25, eachinteger representing a letter.(a) Let n = 26, a = 3, and b = 123. What is the ciphertext corresponding to the phrase THIS IS A CIPHERMESSAGE.(b) A requirement for a cipher is that every plaintext letter correspond to a different ciphertext letter. If either aand b is not relatively prime to n, does the affine cipher meet this property? Either prove it does or presenta counterexample.
We consider ElGamal cryptosystem with public prime p = 53 and generator g = 2. Let h = 16 be Bob’s public-key (his private key x is unknown, h = g^x ). Alice encrypted message m with Bob’s public key and sent the corresponding ciphertext to Bob: (C1 ,C2 ) = (15, 50). You intercepted this ciphertext. Can you break the encryption and recover the original message m? Hint: Both g and h are very small numbers, can you deduce private key x?
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?
Suppose p=5 and q=11. Which of the following is the private key of an RSA cryptosystem with public key (n,e)=(55,7)? a. (55, 23) b. (55, 15) c. (55, 39) d. None of the Above
1. (a) Suppose you are given an ElGamal encryption of an unknown plaintext M ∈G. Show how to construct a different ciphertext that also decrypts to the same M. (b) Suppose you are given two ElGamal encryptions, of unknown plaintexts M1,M2 ∈G. Show how to construct a ciphertext that decrypts to their product M1 ·M2