RSA Encryption: Full Form and Overview
RSA stands for Rivest-Shamir-Adleman, named after its inventors:
- Ron Rivest
- Adi Shamir
- Leonard Adleman
What is RSA Encryption?
RSA is a widely used public-key cryptographic system that enables secure data transmission and digital signatures. It is based on the mathematical properties of prime numbers and modular arithmetic.
Key Features of RSA Encryption:
- Asymmetric Encryption: Utilizes a pair of keys – a public key for encryption and a private key for decryption.
- Security: The security of RSA is based on the difficulty of factoring large composite numbers.
- Widely Used: Commonly used in securing sensitive data, such as:
- Online transactions
- Email communication
- Digital certificates
How RSA Works:
- Key Generation:
- Two large prime numbers (p and q) are chosen.
- Compute ( n = p times q ).
- Calculate the totient: ( phi(n) = (p-1)(q-1) ).
- Choose a public exponent ( e ) such that ( 1 < e < phi(n) ) and ( e ) is coprime to ( phi(n) ).
Calculate the private exponent ( d ) such that ( d times e equiv 1 mod phi(n) ).
Encryption:
- The plaintext message is converted into an integer ( m ) (where ( m < n )).
Ciphertext ( c ) is generated using the formula:
[
c equiv m^e mod n
]Decryption:
- The original message is retrieved using the formula:
[
m equiv c^d mod n
]
Applications of RSA:
- Secure Web Browsing (HTTPS): Ensures safe online transactions.
- Digital Signatures: Verifies the authenticity of a message or document.
- Data Encryption: Protects sensitive information during transmission.
Advantages of RSA:
- Robust Security: Considered secure against many types of attacks.
- Widely Adopted: Standard in many security protocols.
Disadvantages of RSA:
- Performance: Slower than symmetric encryption algorithms.
- Key Size: Requires larger keys to maintain security, leading to increased computational overhead.
In summary, RSA encryption is a cornerstone of modern digital security, facilitating safe communication over the internet. Its combination of security and ease of use makes it a fundamental technology in protecting sensitive data.