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RSA (Rivest-Shamir-Adleman)
The first practical public-key cryptosystem. It relies on the mathematical difficulty of factoring large prime numbers. It is the "workhorse" of the internet, used for secure web browsing (SSL/TLS), email security, and digital signatures.
ECC (Elliptic Curve Cryptography)
A modern approach that uses the geometry of curves rather than large numbers. It is highly efficient, providing the same security as RSA but with much smaller keys, making it perfect for mobile devices and smart cards.
Diffie-Hellman
This is not for encryption; it is for Key Exchange. It allows two parties who have never met to securely agree on a shared password (symmetric key) over an insecure public network.
DHE (Diffie-Hellman Ephemeral)
A key exchange method where a new temporary key is generated for every single connection and then immediately thrown away. Because the key is never saved to a hard drive, it provides "Perfect Forward Secrecy"
ECDHE (Elliptic Curve Diffie-Hellman Ephemeral)
The upgraded, modern version of DHE. It does the exact same thing (creates temporary keys for every session) but uses Elliptic Curve math. This makes it much faster and more efficient for mobile phones than standard DHE.
DSA
An older government standard used only for digital signatures (verifying who sent a message), never for encryption.
PGP / GPG
Not an algorithm itself, but a software suite/standard that uses both Asymmetric (RSA/ECC) and Symmetric keys to secure email and files.