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Choose p = 3 and q = 11
Compute n = p * q = 3 * 11 = 33
Compute φ(n) = (p - 1) * (q - 1) = 2 * 10 = 20
Choose e such that 1 < e < φ(n) and e and n are prime. Let e = 7
Compute a value for d such that (d * e) % φ(n) = 1. One solution is d = 3
[(3 * 7) % 20 = 1]
Public key is (e, n) => (7, 33)
Private key is (d, n) => (3, 33)](https://image.slidesharecdn.com/computersecurity-lecture7-170503153649/75/Computer-Security-Lecture-7-RSA-8-2048.jpg)
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Computer Security Lecture 7: RSA
RSA is a widely used asymmetric encryption algorithm, named after its inventors Ron Rivest, Adi Shamir, and Leonard Adleman. It involves a key generation process using two prime numbers to create public and private keys for secure communication. It provides methods for encryption and decryption, along with potential security challenges such as brute force attacks and mathematical vulnerabilities.
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Computer Security Lecture 7: RSA
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- 3. RSA RSA RSA Key generation RSAEncryption RSA Decryption A Real World Example RSA Security
- 4. RSA RSA is oneof the first practical public-key cryptosystems and is widely used for secure data transmission. RSA is made of the initial letters of the surnames of Ron Rivest, Adi Shamir, and Leonard Adleman, who first publicly described the algorithm in 1977.
- 5. RSA RSA isAsymmetric Encryption Encryption Key Decryption Key Encrypt Decrypt $1000 $1000%3f7&4 Two separate keys which are not shared
- 6. RSA RSA RSA Key generation RSAEncryption RSA Decryption A Real World Example RSA Security
- 7. RSA 1) Choose twodistinct prime numbers 𝒑 and 𝒒 2) Compute 𝒏 = 𝑝 ∗ 𝑞 3) Compute φ(n) = (p - 1) * (q - 1) 4) Choose e such that 1 < e < φ(n) and e and n are prime. 5) Compute a value for d such that (d * e) % φ(n) = 1 Public key is (e, n) Private key is (d, n)
- 8. RSA Choose p= 3 and q = 11 Compute n = p * q = 3 * 11 = 33 Compute φ(n) = (p - 1) * (q - 1) = 2 * 10 = 20 Choose e such that 1 < e < φ(n) and e and n are prime. Let e = 7 Compute a value for d such that (d * e) % φ(n) = 1. One solution is d = 3 [(3 * 7) % 20 = 1] Public key is (e, n) => (7, 33) Private key is (d, n) => (3, 33)
- 9. RSA RSA RSA Key generation RSAEncryption RSA Decryption A Real World Example RSA Security
- 10. RSA m =plaintext Public key is (e, n) C= Ciphertext 𝐶 = 𝑚 𝑒 % 𝑛
- 11. RSA m =2 Public key is (e, n) => (7, 33) C = 2 7 % 33 = 29
- 12. RSA RSA RSA Key generation RSAEncryption RSA Decryption A Real World Example RSA Security
- 13. RSA C= Ciphertext m = plaintext Private key is (d, n) 𝑚 = 𝐶 𝑑 % 𝑛
- 14. RSA C= 29 Private key is (d, n) => (3, 33) 𝑚 = 𝐶3 % 33 = 2
- 15. RSA Select twoprime numbers, p = 17 and q = 11. Calculate n = pq = 17 * 11 = 187. Calculate φ (n) = (p - 1)(q - 1) = 16 * 10 = 160. Select e such that e is relatively prime to φ(n) = 160 and less than φ(n); we choose e = 7. Determine d such that d.e = 1 (mod 160) and d < 160. The correct value is d = 23, because 23 * 7 = 161 = (1 * 160) + 1 Public Key= {7, 187} and Private Key = {23, 187}
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- 17. RSA RSA RSA Key generation RSAEncryption RSA Decryption A Real World Example RSA Security
- 18. RSA lets encrypt themessage "attack at dawn“ Convert the message into a numeric format. Each letter is represented by an ASCII character. "attack at dawn" becomes 1976620216402300889624482718775150
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- 22. RSA Encryption: C=1976620216402300889624482718775150 ^e % n C= 35052111338673026690212423937053328511880760811579981 62064280234668581062310985023594304908097338624111378 40407947041939782153784997654130836464387847409523069 32534945195080183861574225226218879827232453912820596 88644037753608246568175007441745915148540744586251102 3472235560823053497791518928820272257787786
- 23. RSA Decryption: P= 35052111338673026690212423937053328511880760811579981620642 80234668581062310985023594304908097338624111378404079470419 39782153784997654130836464387847409523069325349451950801838 61574225226218879827232453912820596886440377536082465681750 07441745915148540744586251102347223556082305349779151892882 0272257787786^d % n P= 1976620216402300889624482718775150 (which is our plaintext "attack at dawn")
- 24. RSA RSA RSA Key generation RSAEncryption RSA Decryption A Real World Example RSA Security
- 25. RSA Two approachesto attacking RSA: brute force key search (infeasible given size of numbers) mathematical attacks (based on difficulty of computing ø(N), by factoring modulus N)
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- 27. RSA www.YourCompany.com © 2020 CompanynamePowerPoint Business Theme. All Rights Reserved. THANKS FOR YOUR TIME