Cyptography and network security unit 3-1
- 2. The principles of a public key cryptographic system are as follows: • Public and Private Keys: As the name suggests, there are two keys in this system. The public key is freely available to anyone and is used for encryption. The private key is kept secret by the owner and is used for decryption. • Encryption: The sender uses the recipient's public key to encrypt the message. Once encrypted, the message cannot be decrypted with the public key; only the corresponding private key can decrypt it. • Decryption: The recipient, who possesses the corresponding private key, uses it to decrypt the message. Since only the private key can decrypt the message encrypted with the public key, the secrecy of the communication is maintained.
- 3. • Digital Signatures: Public key cryptography also enables the creation of digital signatures. A digital signature is generated using the sender's private key and can be verified using the sender's public key. This ensures the authenticity and integrity of the message. • Key Exchange: Public key cryptography can also be used for secure key exchange. For example, in protocols like Diffie-Hellman key exchange, two parties can agree upon a shared secret key over an insecure channel without directly exchanging the secret key. • Security: The security of public key cryptography relies on the computational difficulty of certain mathematical problems, such as factoring large prime numbers or computing discrete logarithms. For example, in RSA encryption, the security is based on the difficulty of factoring large composite numbers into their prime factors. • Trust: Users need to trust that the public keys they receive actually belong to the intended recipients. This trust is often established through digital certificates issued by trusted third parties known as certificate authorities (CAs). • Revocation: In cases where a private key is compromised or no longer valid, mechanisms for revoking and replacing keys are essential to maintaining the security of the system.
- 4. • public key cryptography provides a powerful framework for secure communication, digital signatures, and key exchange in various applications, including secure email, online transactions, and digital identity management.
- 5. RSA • RSA (Rivest-Shamir-Adleman) is one of the most widely used public- key cryptography algorithms. It is named after its inventors Ron Rivest, Adi Shamir, and Leonard Adleman, who introduced it in 1977. The RSA algorithm is based on the computational difficulty of factoring large integers, which forms the basis of its security.
- 6. • Key Generation: • Choose two large prime numbers, p and q. • Compute their product, n=p×q. This forms the modulus for the public and private keys. • Compute Euler's totient function, ϕ(n)=(p−1)×(q−1). This function is important for ensuring the security of RSA. • Choose an integer e such that 1<e<ϕ(n) and e is coprime with ϕ(n). Typically, e is chosen as a small prime, • Compute the modular multiplicative inverse d×e≡1 modϕ(n). This will be the private exponent.
- 7. • Public and Private Keys: • The public key is (e,n). • The private key is (d,n). • The public key is made available to everyone, while the private key is kept secret. • Encryption: • To encrypt a message M, the sender uses the recipient's public key (e,n). • The sender computes mod C≡Memodn. • The ciphertext C is then sent to the recipient.
- 8. • Decryption: • The recipient uses their private key (d,n) to decrypt the ciphertext C. • The recipient computes M≡Cdmodn. • The decrypted message M is then obtained.
- 9. • Security: • The security of RSA relies on the difficulty of factoring the large composite number n into its prime factors p and q. As long as factoring large numbers remains computationally infeasible, RSA encryption remains secure. • Digital Signatures: • RSA can also be used for digital signatures. To create a signature, the sender encrypts a hash of the message using their private key. The recipient can then decrypt the signature using the sender's public key and verify the authenticity of the message.
- 10. • RSA is widely used in various applications such as secure communication (SSL/TLS), digital signatures, and secure email. However, it's worth noting that RSA's security relies on the proper selection of key sizes. As computing power increases, longer key sizes may be necessary to maintain security.
- 11. Rsa algorithm example • Key Generation: • Choose two prime numbers: p=5 and q=7. • Compute n= p × q = 5 ×7 = 35. • Compute ϕ(n)=(p−1)×(q−1)=4×6=24. • Choose e=5 (relatively prime to ϕ(n)). • Compute the modular multiplicative inverse of e modulo ϕ(n). Here,d=5 since (5×5)mod 24=1(5×5)mod24=1. • So, the public key is (e,n)=(5,35) and the private key is (d,n)=(5,35).
- 12. • Encryption: • Let's encrypt the message M=10. • To encrypt, we use the public key (e,n). • Compute C≡ 10 ^5 mod35=10. • So, the ciphertext C is 10. • Decryption: • To decrypt, we use the private key (d,n). • Compute M ≡ 10^ 5mod 35. • The result is M=10, which is the original message. • So, we successfully decrypted the ciphertext back to the original message M=10.
- 13. Symmetric key distribution using symmetric encryption • For symmetric encryption to work, the two parties to an exchange must share the same key, and that key must be protected from access by others. • For two parties A and B, key distribution can be achieved in a number of ways, as fllows: • A can select a key and physically deliver it to B • A third party can select the key and physically deliver it to A and B • If A and B have previously and recently used a key, one party can transmit the new key to the other, encrypted using the old key • If A and b each has an encrypted connection to a third party C, C can deliver a key on the encrypted links to A and B
- 15. Key management • Key Generation: • Asymmetric key pairs consist of a public key and a corresponding private key. These keys are generated using algorithms like RSA, DSA, or ECC. • The generation process must use secure random number generators to ensure that the keys are sufficiently unpredictable. • Key Storage: • Private keys must be securely stored to prevent unauthorized access. They are typically stored in key stores or hardware security modules (HSMs) that provide strong physical and logical protection. • Public keys are generally distributed widely and are not considered sensitive information. • Key Distribution: • Public keys are distributed to entities with whom secure communication is desired. This distribution can be done through various means, such as public key directories, digital certificates, or direct exchange. • Public keys should be authenticated to ensure that they belong to the intended owner. This can be achieved through digital signatures or certificates issued by trusted certificate authorities (CAs).
- 16. • Key Rotation and Expiration: • Asymmetric keys may have a limited lifespan due to security reasons or regulatory requirements. Key rotation involves replacing old keys with new ones periodically. • Key expiration policies ensure that keys are not used beyond their validity period, reducing the risk associated with compromised keys. • Revocation and Key Recovery: • In case of compromise or loss of a private key, mechanisms for revocation and recovery should be in place. This typically involves publishing revocation information through certificate revocation lists (CRLs) or using online certificate status protocol (OCSP). • Key recovery mechanisms may also be implemented to recover encrypted data in the event of key loss, though these should be carefully controlled to prevent unauthorized access to private keys. • Secure Key Destruction: • When asymmetric keys are no longer needed or have reached the end of their lifecycle, they should be securely destroyed to prevent unauthorized use. This may involve cryptographic erasure techniques or physical destruction of storage media.
- 17. • Key Usage: • Public keys are used for encryption and verification of digital signatures. • Private keys are used for decryption of encrypted messages and generation of digital signatures. • Private keys should never be shared and should only be used by the intended owner.
- 18. Distribution of public keys • Several techniques have been proposed for the distribution of public keys. Virtually all these proposals can be grouped into the following general schemas. • Public announcement • Publicly available directory • Public-key authority • Public-key certificates
- 21. • Public-Key Authority • Stronger security for public-key distribution can be achieved by providing tighter control over the distribution of public keys from the directory. As before, the scenario assumes that a central authority maintains a dynamic directory of public keys of all participants. In a addition, each participant reliably knows a public key for authority, with only the authority knowing the corresponding private key.