Asymmetric Cryptography and Hashes

Vocabulary flashcards covering hash functions, asymmetric encryption schemes (RSA, ECC), digital signatures, key exchange protocols, and post-quantum cryptography based on Lecture 04.

Hash Function

A function that takes arbitrary-length data as input and produces a fixed-length output, often referred to as a hash value or digest.

Preimage resistance

A characteristic of hash functions where, given a hash value $H(m)$, it should be computationally infeasible to find the original input $m$.

Second preimage resistance

A characteristic of hash functions where, given an input $m$, it should be infeasible to find a different input $m'$ such that $H(m) = H(m')$.

Collision resistance

A characteristic of hash functions where it should be infeasible to find any pair of distinct inputs $m$ and $m'$ that yield the same hash output.

MD5

A common hash function with a 128-bit output length that is now considered insecure due to vulnerabilities like chosen-prefix collision attacks.

Argon2

A secure hash function used for password hashing, supporting output lengths of 128, 256, or 512 bits.

Chosen-prefix collision attack

An attack where an attacker selects two different prefixes and computes collision blocks such that the hash of both resulting messages is identical; demonstrated against MD5.

Asymmetric Cryptography

A cryptographic system where the sender and receiver use different, mathematically linked keys (a public key and a private key).

Public Key

A non-secret key distributed publicly and used for encryption or signature verification.

Private Key

A secret key stored securely by the owner and used for decryption or creating digital signatures.

RSA

The most widely used asymmetric encryption scheme, based on the mathematical difficulty of prime factorization.

RSA Key Generation

A process involving choosing two large primes $p$ and $q$, computing $n = p \times q$, finding $\varphi(n) = (p - 1) \times (q - 1)$, and selecting exponents $e$ and $d$.

Square-then-Multiply

A practical optimization for computing exponentials in RSA, reducing the number of multiplications required for operations like $m^e \pmod n$.

Hybrid Encryption Scheme

A system that uses asymmetric cryptography to securely exchange a symmetric key, which is then used for the efficient encryption of the actual data.

Key Encapsulation Mechanism (KEM)

A mechanism that generates a symmetric key and an encapsulated ciphertext of that key using the receiver's public key.

Digital Signature

A cryptographic tool used to attest to the authenticity, integrity, and non-repudiation of data using a private key to sign and a public key to verify.

Qualified electronic signature

A type of signature based on digital signatures using keys from a trusted authority, legally equivalent to a physical handwritten signature.

EUF-CMA

Existential Unforgeability under adaptive Chosen Message Attack; the gold standard for signature security ensuring an attacker cannot generate any valid message+signature pair.

Digital Signature Algorithm (DSA)

An alternative to RSA signatures that uses public parameters $p$, $q$, and $g$ and relies on the discrete logarithm problem.

Elliptic Curve Cryptography (ECC)

An asymmetric cryptographic approach based on operations on elliptic curves, offering similar security to RSA but with significantly smaller key sizes.

Certificate Authority (CA)

A trusted third party that verifies an entity's identity and issues a digital certificate binding that identity to a public key.

Diffie-Hellman (DH) Key Exchange

A protocol that allows two parties to agree on a shared secret key over an insecure channel using the discrete logarithm problem.

Forward Secrecy

A property where the compromise of long-term private keys does not compromise the confidentiality of past session keys, often achieved via Ephemeral Diffie-Hellman.

Shor's algorithm

A quantum algorithm that can break RSA, DH, and ECC in polynomial time by solving integer factorization and discrete logarithm problems.

Grover's algorithm

A quantum algorithm that speeds up brute-force attacks by a factor of $2$, requiring larger keys for symmetric algorithms like AES to remain secure.

Store-now-decrypt-later

A threat model where an attacker records encrypted traffic today to decrypt it in the future once sufficiently powerful quantum computers are available.