Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 31.7, Problem 1E
Program Plan Intro
To determine value of
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suppose p=5 and q=11. what is the private key of an RSA cryptosystem with public key (n,e)= (55,9)?
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?
For practical encryption that involves secret message transmission from Alice to Bob, why is the message encrypted with the shared symmetric key rather than Bob's public key?
What is the significance of using Bob's public key to encrypt the shared symmetric key?
Chapter 31 Solutions
Introduction to Algorithms
Ch. 31.1 - Prob. 1ECh. 31.1 - Prob. 2ECh. 31.1 - Prob. 3ECh. 31.1 - Prob. 4ECh. 31.1 - Prob. 5ECh. 31.1 - Prob. 6ECh. 31.1 - Prob. 7ECh. 31.1 - Prob. 8ECh. 31.1 - Prob. 9ECh. 31.1 - Prob. 10E
Ch. 31.1 - Prob. 11ECh. 31.1 - Prob. 12ECh. 31.1 - Prob. 13ECh. 31.2 - Prob. 1ECh. 31.2 - Prob. 2ECh. 31.2 - Prob. 3ECh. 31.2 - Prob. 4ECh. 31.2 - Prob. 5ECh. 31.2 - Prob. 6ECh. 31.2 - Prob. 7ECh. 31.2 - Prob. 8ECh. 31.2 - Prob. 9ECh. 31.3 - Prob. 1ECh. 31.3 - Prob. 2ECh. 31.3 - Prob. 3ECh. 31.3 - Prob. 4ECh. 31.3 - Prob. 5ECh. 31.4 - Prob. 1ECh. 31.4 - Prob. 2ECh. 31.4 - Prob. 3ECh. 31.4 - Prob. 4ECh. 31.5 - Prob. 1ECh. 31.5 - Prob. 2ECh. 31.5 - Prob. 3ECh. 31.5 - Prob. 4ECh. 31.6 - Prob. 1ECh. 31.6 - Prob. 2ECh. 31.6 - Prob. 3ECh. 31.7 - Prob. 1ECh. 31.7 - Prob. 2ECh. 31.7 - Prob. 3ECh. 31.8 - Prob. 1ECh. 31.8 - Prob. 2ECh. 31.8 - Prob. 3ECh. 31.9 - Prob. 1ECh. 31.9 - Prob. 2ECh. 31.9 - Prob. 3ECh. 31.9 - Prob. 4ECh. 31 - Prob. 1PCh. 31 - Prob. 2PCh. 31 - Prob. 3PCh. 31 - Prob. 4P
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- Let's say you generated RSA keys and you chose p=59, q=43, and the smallest encryption exponent that qualifies for this p and q. (You will have to follow the key generation algorithm to fill in the details.) If someone gives you 99 as the ciphertext they created using your public key, what is the plaintext you get when you use your private key to decrypt? What is e?____ What is d?____ What is the decrypted value?____arrow_forwardIn the context of cryptography, what are the differences between a cipher that uses symmetric keys and a cipher that uses asymmetric keys? The industry standard for the size of the RSA public key is much bigger than the size of a symmetric key? Why? Are ciphers based on symmetric keys not s secure as RSA?arrow_forwardWhat is the absolute bare minimal number of keys that have to be used when putting into practice cryptography that is dependent on public keys?arrow_forward
- Consider the RSA cryptosystem. If we take P=13 and Q=19 then: 1. What could be the possible value of e , if we take e < 15 ? Calculate a suitable d for the e you have selected above.arrow_forwardFor the given scenario where Alice is trying to send encrypted data to Bob, and Bob is trying to decrypt it, using Elgamal encryption scheme, fill the values in the tablearrow_forwardSo, what exactly is the difference between a secret key and a public key when it comes to cryptography?arrow_forward
- Public key cryptography faced the challenge of distributing keys in the beginning. To easily show how key distribution may be carried out, why not use an example?arrow_forwardWhat is the absolute bare minimal number of keys required to utilize public key cryptography?arrow_forwardA government department decides it needs to use encryption to protect communication between itself and its international counterparts. At a meeting with its counterparts, it is decided to develop a proprietary cryptographic algorithm for this purpose. Is this decision justifiable? What risks are being taken?arrow_forward
- Is it possible that two different plaintexts can give the same ciphertexts using Hill Cipher? Support your answer with an example.arrow_forwardSuppose 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 Abovearrow_forwardWhat is the minimal number of keys needed for public-key cryptography?arrow_forward
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