b. Now consider we want to reduce this number by generating a smaller pool of prime numbers and making combinations of two of these primes (for each user we pick up a new pair). How is security of RSA cryptosystem affected?

b. Now consider we want to reduce this number by generating a smaller pool of prime numbers and making combinations of two of these primes (for each user we pick up a new pair). How is security of RSA cryptosystem affected?

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 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?
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.
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.
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.
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
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?
In a public-key system using RSA, you intercept the ciphertext C=10, sent to a user whose public key is e=5, n=35. What is the plaintext M? In an RSA system, the public key of a given user is e=31, n=3599. What is the private key of this user? Hint: First use trial-and-error to determine p and q; then use the extended Euclidian algorithm to find the multiplicative inverse of 31 module φ(n).
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?
In the Diffie-Hellman Protocol, each participant selects a secret number x and sends the other participant αx mod q for some public number α. What would happen if the participants sent each other αx for some public number αinstead? Give at least one method Alice and Bob could use for agreeing on a key. Can Eve break your system without finding the secret numbers? Can Eve find the secret numbers? In TLS, why is there a separate Change Cipher Spec Protocol, rather than including a change_cipher_spec message in the Handshake Protocol?
By using 3 prime numbers, we can also define RSA cryptostem where N = pqr. Again we must have gcd(e, ϕ(N)) = 1 and d is the multiplicative inverse of e in modulo ϕ(N). (a) Give an example RSA encryption with prime numbers 41, 43, 47. Choose an encryption key, determine its corresponding decryption key. Send me a message. (b) Why this 3-prime RSA is not preferred? Kindly give an explanation. Thank you
1. Suppose that we use a substitution cipher to encrypt an English word, from which we obtain the ciphertext is “AUXXME”. Which of the following words is possibly the plaintext? (Hint: In a substitution cipher, we replace each letter of the plaintext with another letter) A. greedy B. funny C. secret D. cheese 2. Which of the following statements are incorrect? A. Cryptographic systems tend to involve both an algorithm and a secret value. B. To secure systems, it is more efficient to update algorithms than updating keys. C. Often a scheme can be made more secure by making the key longer. D. We can always change the key length to better secure systems, no matter using which cryptographic algorithms. E. In a secret-key cryptosystem, secret keys can be used for both encryption and decryption. 3. Which of the following statements are incorrect about a cryptographical hash function? A. The input size can be arbitrary and the output size is fixed B. Given the input, the output should…
How would you solve part a and b? This is an applied cryptography type question. a. Suppose ' = 2, so r can be from the set {0,1,2,3}. Assume you, the eavesdropper, gets the sequence: 145471,25245,14596,143468,153125 encrypted via the padded RSA scheme using (N,e) = (157439,5). Without decrypting, find the sequence of votes. b. Suppose now that ' = 100, so r can be from the set {0,1}100. What is the time complexity of your attack from part (a)? Is it feasible? If you were an employee, would you recommend this scheme to the CEO?