Glossary of Terms
A cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner. Also known as Public-Key Cryptography. Enables encryption, digital signatures, and key exchange without pre-sharing a secret key.
An encryption algorithm that operates on fixed-length groups of bits, called blocks. Asymmetric algorithms like RSA operate mathematically on integers representing blocks.
Trying all possible private keys. Countered by using very large key sizes (e.g., 2048 bits or more for RSA).
An asymmetric protocol used to establish a shared secret (symmetric key) between two parties over an insecure channel. It does not encrypt messages itself but enables secure key establishment.
An application of asymmetric cryptography used to verify the authenticity and integrity of a message. The sender signs (encrypts a hash of the message) with their private key, and anyone can verify using the sender's public key.
A U.S. federal standard for digital signatures based on the Digital Signature Algorithm (DSA), which is an asymmetric algorithm but cannot be used for encryption, only signing.
An approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. Provides equivalent security to RSA with much smaller key sizes, leading to better performance.
An asymmetric key encryption algorithm based on the Diffie-Hellman key exchange, using the difficulty of the discrete logarithm problem. Can be used for both encryption and digital signatures.
To send a confidential message, the sender encrypts it using the recipient's public key. Only the recipient, with their corresponding private key, can decrypt the message.
In number theory, for a positive integer n, the totient φ(n) is the number of positive integers less than or equal to n that are relatively prime to n (i.e., share no common factors other than 1). For RSA, if n = p*q (p, q are prime), then φ(n) = (p-1)*(q-1).
A whole number (not a fraction). In RSA, the plaintext and ciphertext are treated as large integers for mathematical operations.
An application of asymmetric cryptography where two parties cooperate to securely establish a shared secret key (typically a symmetric key for later bulk encryption) over an insecure channel. Examples: Diffie-Hellman, RSA key transport.
A system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus. Operations like 'mod n' find the remainder after division by n. Central to RSA and Diffie-Hellman.
A mathematical function that is easy to compute in one direction (e.g., encrypting with a public key) but computationally infeasible to reverse (e.g., decrypting without the private key, or finding the private key from the public key).
An encryption program that provides cryptographic privacy and authentication for data communication. PGP is often used for signing, encrypting, and decrypting texts, e-mails, files, directories, and whole disk partitions and to increase the security of e-mail communications. It typically uses a hybrid approach (asymmetric for key exchange/signing, symmetric for bulk encryption).
A natural number greater than 1 that has no positive divisors other than 1 and itself. The security of RSA relies on the difficulty of factoring the product of two large prime numbers.
In asymmetric cryptography, the key of the key pair that is kept secret by the owner. Used for decryption (in public-key encryption) or signing (in digital signatures).
In asymmetric cryptography, the key of the key pair that can be shared openly. Used for encryption (in public-key encryption) or verifying signatures (in digital signatures).
See Asymmetric Cryptography.
Two integers are relatively prime (or coprime) if their greatest common divisor (GCD) is 1. In RSA, the public exponent 'e' must be relatively prime to φ(n).
A widely used public-key cryptosystem for secure data transmission. Named after its inventors Rivest, Shamir, and Adleman. Can be used for both encryption and digital signatures.
A symmetric key used for encrypting messages during a single communication session only. Often established using an asymmetric key exchange method like Diffie-Hellman or RSA.
An attack based on information gained from the physical implementation of a cryptosystem, rather than theoretical weaknesses. Examples include timing analysis, power monitoring, or electromagnetic leaks. RSA can be vulnerable if not implemented carefully.