Suppose that you are computing an RSA key pair. (Marks 6) What are ? and ?...
- Suppose that you are computing an RSA key pair. (Marks 6) What are ? and ? and ?(?) for an ? = 51?
Find a legal RSA public key pair for this ? and ?.
How many possible values for ?? are there?
In a RSA cryptosystem, a person Renee uses two prime numbers p = 13 and q = 17 to generate her public and private keys. If the public key of Renee is 35, then the private key of Renee is _______.
Homework Answers
- Given the prime numbers p and q, and the public key e = 35, The private key can be obtained by finding the multiplicative inverse of e mod ((p-1)*(q-1)).
- The multiplicate inverse is a number d, such that d<(p-1)(q-1) and ed mod (p-1)(q-1) = 1 mod (p-1)(q-1).
- here e = 35, p = 13 , q = 17.
- 35*d mod (12*16) = 35*d mod*192 = 1 mod 192.
- The value of d has to be checked one by one from 1 to 191. This long computation process is exactly why RSA is efficient.
- For d = 11 we get 35*11 mod 192 = 385 mod 192 = 1 = 1 mod n
- 11, is the multiplcative inverse of 35 mod 192 and it is the private key for the given system
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Suppose that you are computing an RSA key pair.
(Marks
6) What are ?
and ?...
In a RSA cryptosystem, a participant A uses two prime numbers p = 13 and q...
In a RSA cryptosystem, a participant A uses two prime numbers p = 13 and q = 17 to generate her public and private keys. If the public key of A is 35, then the private key of A is 11. Alice wants to encrypt a message to Bob by using the RSA algorithm and using keys in (A) The plaintext = “HI”. Answer: _______________
Question 1 (1.5 marks): Asymmetric Security (The RSA algorithm) Consider the last two pairs of tw...
Question 1 (1.5 marks): Asymmetric Security (The RSA algorithm) Consider the last two pairs of two digits of your student ID. Select two prime numbers that are http://en.wikipedia.org/wiki/List of prime numbers#The first 500 prime numbers For example: Student ID 9001346 -1346 The closest prime number to 13 is itself 13 and the closest prime number to 46 is 47. a. Assuming that these two prime numbers are the variables P and Q, determine the private and public keys used by...
just need help with part c key and public key cryptography methods 2. (a) Explain the...
just need help with part c
key and public key cryptography methods 2. (a) Explain the difference between the symmetric (b) In the famou s RSA algorithm for public key cryptography, very large prime numbers are used so as to make ult for the attackers to find from their product the prime factors. However, for an illustration of the ideas behind the RSA algorithm, you could chooses two small prime numbers 7 and 11, and a public key e 13...
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p=3, q=7
Suppose that Bob wants to create an example of an RSA public-key cryptosystem by using the two primes p ??? and q ???. He chooses public encryption key e He was further supposed to compute the private decryption key d such that ed 1 mod A(pq)). However, he confuses A and and computes instead d' such that ed' =1 (mod P(pq)). (i) Prove that d' works as a decryption key, even though it is not necessarily the same...
Use C++ forehand e receiver creates a public key and a secret key as follows. Generate...
Use C++
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Using RSA algorithm, if p=3 and q=11, k=3, then the public key is equal to (You...
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Consider the RSA algorithm. Let the two prime numbers, p=11 and q=41. You need to derive appropriate public key (e,n) and private key (d,n). Can we pick e=5? If yes, what will be the corresponding (d...
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Problem 3 In RSA, we will consider what happens when Alice makes the mistake of choosing...
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O-8. (15 points) Bob's simple toy RSA eryptosystem has public key kyub(n, e) (65,5), where n =p,-...
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Write code for RSA encryption package rsa; import java.util.ArrayList; import java.util.Random; import java.util.Scanner; public class RSA...
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Question 1 (1.5 marks): Asymmetric Security (The RSA algorithm) Consider the last two pairs of two digits of your student ID. Select two prime numbers that are http://en.wikipedia.org/wiki/List of prime numbers#The first 500 prime numbers For example: Student ID 9001346 -1346 The closest prime number to 13 is itself 13 and the closest prime number to 46 is 47. a. Assuming that these two prime numbers are the variables P and Q, determine the private and public keys used by...
just need help with part c
key and public key cryptography methods 2. (a) Explain the difference between the symmetric (b) In the famou s RSA algorithm for public key cryptography, very large prime numbers are used so as to make ult for the attackers to find from their product the prime factors. However, for an illustration of the ideas behind the RSA algorithm, you could chooses two small prime numbers 7 and 11, and a public key e 13...
p=3, q=7
Suppose that Bob wants to create an example of an RSA public-key cryptosystem by using the two primes p ??? and q ???. He chooses public encryption key e He was further supposed to compute the private decryption key d such that ed 1 mod A(pq)). However, he confuses A and and computes instead d' such that ed' =1 (mod P(pq)). (i) Prove that d' works as a decryption key, even though it is not necessarily the same...
Use C++
forehand e receiver creates a public key and a secret key as follows. Generate two distinct primes, p andq. Since they can be used to generate the secret key, they must be kept hidden. Let n-pg, phi(n) ((p-1)*(q-1) Select an integer e such that gcd(e, (p-100g-1))-1. The public key is the pair (e,n). This should be distributed widely. Compute d such that d-l(mod (p-1)(q-1). This can be done using the pulverizer. The secret key is the pair (d.n)....
Using RSA algorithm, if p=3 and q=11, k=3, then the public key is equal to (You may use the formulas below): Select two large prime numbers P, 9 Compute n = pxq v = (p-1) (q-1) • Select small odd integer k relatively prime to v gcd(k, v) = 1 Compute d such that (d k)%v = (k d)%v = 1 Public key is (k, n) Private key is (d, n) . . . Select one: a. (3,11) b. (33,3)...
o-8. (15 points) Bob's simple toy RSA eryptosystem has public key kyub(n, e) (65,5), where n =p,-5x13-65 and e-5. I. Describe the key pair generation procedure for Bob to generate his private key kor- d. With the above given parameters, use EEA to calculate d 2. Describe RSA encryption procedure that Alice uses to encrypt her plaintext message x to its above given parameters, what will be y? ciphertext y before sending the message to Bob. Suppose Alice's message x-...
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