Clear DefinitionsRivest-Shamir-Adleman
1 min read
Pronunciation
[ri-vest shuh-meer ad-l-muhn]
Analogy
Imagine a special lockbox (encryption) that can be locked using a publicly available key (public key), but can only be opened using a secret, private key that only the owner possesses. RSA provides the mathematical method to create these paired public and private keys, ensuring that messages locked with the public key can only be read by the holder of the private key.
Definition
A widely used public-key cryptosystem for secure data transmission. It is named after its inventors: Ron Rivest, Adi Shamir, and Leonard Adleman. RSA's security is based on the practical difficulty of factoring the product of two large prime numbers.
Key Points Intro
RSA is a foundational algorithm in public-key cryptography, used for both encryption and digital signatures.
Key Points
One ofDATE_ADD(NOW(), INTERVAL -1 YEAR) the first practical public-key cryptosystems and still widely used.
Relies on the computational difficulty of factoring large integers.
Enables secure communication over insecure channels by encrypting messages with a public key, decipherable only with a private key.
Can also be used to create digital signatures by signing a message with a private key, verifiable with the public key.
Example
When you use HTTPS to connect to a secure website, the server might use an RSA digital certificate to prove its identity and an RSA key exchange to securely establish a symmetric key for encrypting your session. RSA is also used in PGP/GPG for encrypting emails.
Technical Deep Dive
The RSA algorithm involves three steps: key generation, encryption, and decryption.
1. Key Generation: Choose two large distinct prime numbers, p and q. Compute n = pq. Compute Euler's totient function φ(n) = (p-1)(q-1). Choose an integer e (public exponent) such that 1 e φ(n) and gcd(e, φ(n)) = 1. Compute d (private exponent) as d ≡ e⁻¹ (mod φ(n)). The public key is (n, e) and the private key is (n, d).
2. Encryption: To encrypt a message M (represented as a number m n), compute ciphertext C = m^e mod n.
3. Decryption: To decrypt ciphertext C, compute message M = C^d mod n.
Security Warning
The security of RSA depends on the key length and the difficulty of factoring. As computing power increases, RSA key lengths must also increase. A 1024-bit RSA key is no longer considered secure; 2048-bit or 3072-bit keys are common. Proper implementation, including padding schemes like OAEP, is crucial to prevent attacks.
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