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Diffie–Hellman key exchange

Diffie–Hellman key exchange or DH is a mathematical method of securely exchanging cryptographic keys over a public channel.
Used to generate a random symmetric secret key between any 2 hosts that wish to communicate securely.

Due to a new secret key used every session, this algorithm introduces forward secracy in the system which pure RSA does not. But standard DH does not provide user verification, so there’s no way to verify whether client/server had actually sent the message. Thus, it is highly susceptible to MITM attacks. Today standard DH is never used.

In TLS Cypher Suites, a version of DH called ECDHE is used for key sharing, and ECDSA or RSA is used for user authentication.

Types of keys

Ephemeral:

static:

  • long term shared secret
  • implicit authenticity (as it is guranteed that only the secret holder can encrypt the message)
  • no forward secrecy

“ephemeral, static” or “semi-static”:

  • no forward secrecy
  • one-sided authenticity

Finite Field Diffie-Hellman

A great animated video on the working on DH algorithm.
This is the working of the standard Diffie-Hellman algorithm, later formalized as Finite Field Diffie-Hellman algorithm

Finite Field DH has roughly the same key strength as RSA for the same key sizes.
So 2048-bit FFDH has same security as 2048-bit RSA

To try hands-on with numbers, refer to python’s cryptography library documentation.

ECDH

Elliptic-curve Diffie–Hellman or ECDH encryption uses DH key exchange, and elliptical curve method to generate the secret.
Have a look at this youtube video to understand the math.

Elliptical curves allow smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation such as RSA or even the standard Diffie Helman.

But a 256-bit ECDH key has approximately the same safety factor as a 128-bit aes key (which is even higher than 2048 bit RSA)

ECDHE (where final ‘E’ stands for “ephemeral”) and its variants like X25519 are widely used in TLS cypher suite for initial key exchange.

Python’s cryptography library has a seperate implementation of X25519 key exchange

ECDSA

Elliptical Curve Digital-Signature Algorithms is a family of Digital Signing and Authentication algorithms based on Elliptical curve cryptography.

Ed25519 is an implementation of ECDSA (or EdDSA to be specific) used widely for user authentication, like in ssh. It is also based on Curve25519.
To try hands-on of Ed25519 signing, refer python’s cryptography module documentation

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