RSA
RSA is a public-key cryptosystem based on the computational difficulty of factoring large composite integers and supporting encryption and digital signatures.
Software Security for Developers
RSA is a public-key cryptographic algorithm based on the computational difficulty of factoring large integers.
- How it is used
- Secures application communication, encrypts keys, signs data, and supports TLS-related public-key operations.
- How deep it goes
- Explains key pairs, factoring, padding, hybrid workflows, and Java usage while deferring mathematical proofs and production certificates.
- Examples
- Uses ACME warehouse and payments services, refunds.json, Java key generation, chunked OAEP encryption, and SHA256withRSA signatures.
- What you can do after
- Apply RSA via Java libraries to generate keys, encrypt and decrypt data, wrap AES keys, and create or verify signatures.
Secure APIs
RSA is a public-key cryptosystem based on the computational difficulty of factoring large integers.
- How it is used
- Uses RSA to issue JWTs with private-key signatures and to encrypt JWE content-encryption keys.
- How deep it goes
- Explains RSA through JWT signing, key generation, private-key loading, and JWE placement, without developing factoring mathematics.
- Examples
- Demonstrates OpenSSL key generation, Python key loading, and PyJWT issuance of a PS256-signed token.
- What you can do after
- Apply it via OpenSSL, cryptography, and PyJWT to generate RSA keys and issue PS256-signed JWTs.
Real-World Cryptography
RSA is a public-key cryptosystem based on the difficulty of factoring large composite integers and supporting encryption and digital signatures.
- How it is used
- Uses RSA for asymmetric encryption, digital signatures, and encapsulating symmetric keys in hybrid exchanges.
- How deep it goes
- Explains public-key roles and modular exponentiation with e, d, and N, while warning that naive implementations and standards can fail.
- Examples
- Uses Queen Alice’s encrypted chest, signed trust statement, modular example m = 2, and symmetric-key encapsulation.
- What you can do after
- Evaluate RSA encryption, signatures, and key encapsulation while recognizing the risks of naive implementations and changing protocol preferences.
Hacking Cryptography
RSA is a public-key cryptosystem whose security relies on the difficulty of factoring a product of large primes.
- How it is used
- Uses integer factorization as a trapdoor for public-key encryption and message exchange.
- How deep it goes
- Explains key notation and modular encryption and decryption, then emphasizes implementation failures without detailing individual exploits.
- Examples
- Uses trial division of 764,512, Alice-and-Bob message exchange, RSA equations, and shared-prime weak-key detection.
- What you can do after
- Evaluate RSA implementations for factoring strength, randomness failures, deterministic encryption, and unsafe private exponents.
Related concepts
- factorizationuses · Factorization is the decomposition of a mathematical object, such as an integer or joint distribution, into simpler multiplicative factors.
- rsa-pssused by · RSA-PSS is a probabilistic RSA digital-signature scheme using the probabilistic signature scheme encoding specified by PKCS #1.
- digital signatureimplements · A digital signature is cryptographic data generated with a private key and verified with corresponding public information to authenticate data or its signer and detect alteration.
- quantum computercontrasts with · A quantum computer is a computing device that processes information using quantum-mechanical states and operations.
- textbook rsaincludes · Textbook RSA is an unpadded RSA method that directly applies modular exponentiation to a message representative for encryption or signing.
- hybrid encryptionuses · Hybrid encryption combines asymmetric cryptography or key exchange for protecting a symmetric key with symmetric authenticated encryption for protecting data.
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