RSA

By:

Abhishek Naik

Viswanath Chennuru

CPSC 624

CONTENTS

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

WHAT 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

WHY 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

WHAT IS PUBLIC KEY ENCRYPTION ?

WHAT 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

STEPS IN RSA

Key generation

Encryption

Transmitting

Decryption

KEY 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.

KEY GENERATION IN RSA

Choose a large, random integer d such that it is a relative prime to z.

i.e. if gcd (d, z) = 1

The integer e is computed using p, q and d to be the multiplicative inverse of “d modulo z”.

i.e.

The public key is (e, n) and the private key is (d, n).

ENCRYPTION 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.

ENCRYPTION 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 - email security SSH - terminal connection security SILC - conferencing service security

APPLICATIONS 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

ATTACKS 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

ATTACKS 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

CONCLUSION

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

THANK YOU !