RSA By: Abhishek Naik Viswanath Chennuru CPSC 624

C ONTENTS What is Encryption ? What is RSA ? Key Generation Encryption and Decryption Applications Attacks on RSA Conclusion

W HAT IS ENCRYPTION ? Transforming Plaintext using a Cipher such that only person with the key can read the information. Two types of Encryption are: Symmetric and Public key

W HY PUBLIC KEY ENCRYPTION ? Two different keys for encryption and decryption(public and private) No secret key exchange is necessary Anyone can encrypt using receivers public key but only he can decrypt

W HAT IS PUBLIC KEY ENCRYPTION ?

W HAT IS RSA? Named after Ron Rivest, Adi Shamir and Leonard Adleman, the inventors. Is a Public Key Algorithm first described in 1978 Based on the presumed difficulty of factoring large integers Used for Encryption and Authentication

S TEPS IN RSA Key generation Encryption Transmitting Decryption

K EY GENERATION IN RSA Two distinct prime numbers are chosen, p and q Compute n = pq. n is used as modulus for both private and public key Compute φ(n) = (p – 1)(q – 1), where φ is Euler's totient function.

K EY GENERATION IN RSA

E NCRYPTION AND DECRYPTION Encryption: To encrypt the plain text M using the public key (e, n), represent the message as an integer value between 0 and n – 1. This can be done by breaking the message into blocks and assigning values to it After the message is obtained in the necessary numeric format, it can be encrypted by raising it to the 2 e’th power modulo of n The resulting cipher text of the encryption will be integer values ranging between 0 and n – 1.

E NCRYPTION AND DECRYPTION Decryption: When the receiver gets the cipher text (C), it is decrypted using the private key (d, n). The cipher text is raised to another power d and then modulo n which gives back the plain text.

APPLICATIONS RSA is used in security protocols such as: IPSEC/IKE - IP data security TLS/SSL - transport data security (web) PGP - security SSH - terminal connection security SILC - conferencing service security

A PPLICATIONS Digital Signature: To verify the origin of the document and identity of the sender Based on both the document and the signer's private key Sender encrypts the message with the public key of the intended recipient Then encrypts the "digital fingerprint" of the document with his or her own private key Anyone with access to the public key of the signer may verify the signature

A TTACKS ON RSA Searching the Message Space If the message space is small, then one could simply try to encrypt every possible message block, until a match is found with one of the ciphertext blocks. Guessing d Known ciphertext attack. The attacker know both the private and public key. They then try to crack the key to discover the private exponent d. Cycle Attack Encrypt the ciphertext repeatedly and count the iterations, continue till the original text is found

A TTACKS ON RSA Common Modulus A weakness where users within an organization share a public modulus. Eavesdropping is easier Faulty Encryption During exchange of public keys, man in middle changes specific bits in the public key Low Exponent Based on Chinese Remainder Theorem, where if same message is encrypted 3 times with different types of moduli, we can retrieve the message

C ONCLUSION RSA has many advantages over symmetric key encryption, but it is considerably slower RSA Security claims that 1024 bit keys suffice for the current period and 2048 keys can be adopted in future After 2030, 3072-bit keys should be used

T HANK Y OU !