Modern cryptography fundamentally relies on mathematical concepts rather than secret algorithms, distinguishing it from classical cryptography which often depended on confidentiality of the methods used.
The primary types of cryptographic systems are symmetric (private-key) and asymmetric (public-key) cryptography.
Symmetric cryptography requires the same key for both encryption and decryption, while asymmetric uses a pair of keys—a public key for encryption and a private key for decryption.
The concept of a "one-way function" is essential in modern cryptography.
A one-way function is easy to compute in one direction but hard to reverse, making it useful for creating secure hashes and digital signatures.
The security of many cryptographic systems is based on mathematical problems that are difficult to solve, such as factorizing large integers (used in RSA encryption) or calculating discrete logarithms (used in Diffie-Hellman key exchange).
The Diffie-Hellman key exchange algorithm was one of the first public-key methods developed and allows two parties to securely share a secret key over a public channel without having to meet or exchange the key directly.
Cryptography plays a crucial role in ensuring the integrity of data through hashing functions, which transform any input into a fixed-size string of characters that appears random.
Even minor changes to the input produce drastically different hashes.
Digital signatures function similarly to handwritten signatures but use mathematical techniques to ensure authenticity and non-repudiation, confirming that a message has not been altered and verifying the sender's identity.
The "padding scheme" is vital in cryptography to prevent various attacks, like the padding oracle attack, by ensuring that data blocks conform to expected sizes, thus enhancing security when encrypting data of varying lengths.
Block ciphers like AES (Advanced Encryption Standard) encrypt data in fixed-size blocks, while stream ciphers encrypt data one bit at a time.
Each has its use cases, with block ciphers often used in file encryption and stream ciphers in real-time communications.
Public key infrastructures (PKIs) are essential for managing digital certificates that verify the authenticity of public keys and prevent man-in-the-middle attacks by ensuring users can trust each other's identities.
Cryptographic protocols often involve zero-knowledge proofs, allowing one party to prove to another that they know a value without revealing the value itself, which finds applications in authentication and privacy-related systems.
Quantum computing poses a serious future threat to current cryptographic systems.
Many traditional cryptographic algorithms could potentially be broken by quantum algorithms like Shor's algorithm, which efficiently factors large numbers.
The concept of "homomorphic encryption" allows operations to be performed on encrypted data without needing to decrypt it first, which can revolutionize areas such as secure data processing in cloud computing.
Secure multi-party computation (MPC) permits parties to jointly compute a function over their inputs while keeping those inputs private, finding applications in fields such as finance and privacy-preserving data analysis.
Hash functions are designed to be collision-resistant, meaning it should be computationally infeasible to find two different inputs that produce the same hash output, crucial for many security mechanisms.
The "Kerckhoffs's principle" states that a cryptographic system should remain secure even if everything about the system, except the key, is public knowledge, emphasizing the importance of key security over system secrecy.
Modern cryptography is part of a broader field known as "cryptology," which includes both cryptography (the creation of secure communication techniques) and cryptanalysis (the study of how to break those techniques).
Advances in cryptographic research have led to the concept of "post-quantum cryptography," which seeks to develop cryptographic systems resistant to the potential threats posed by quantum computers.
The notion of "security proofs" in modern cryptography is important, where cryptographic schemes provide formal assurances about their security properties under certain assumptions, transitioning cryptography from art to science.
Digital currencies, often based on blockchain technology, utilize cryptographic techniques to secure transactions, control the creation of additional units, and verify the transfer of assets without a central authority.