Diffie-Hellman comparison

One hidden product, three algebraic worlds.

These systems preserve the hidden scalar relationship a * b. The operations and public inputs are visible, but a, b, and the raw product a * b remain private. What changes is the encoded result: g^(ab), abP, or e(P,Q)^(ab), and who is meant to compute it.

Publicoperator, g/P/Q, public keys

Privatea, b, raw a * b

Encoded resultDH/ECDH: private to Alice and Bob; pairing: often public

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Ordinary DH

Numbers in a finite group

shared = g^(ab)

Alice applies her secret exponent to Bob's public value. Bob does the symmetric calculation.

ECDH / X25519

Points on an elliptic curve

shared = abP

The same hidden product appears as scalar multiplication of a public base point.

Pairings

Public map into GT

shared-like value = e(P,Q)^(ab)

The result moves into a target group, and public keys can often be combined publicly.

Bitcoin address

Hash a secp256k1 public key

Base58Check(0x00 || HASH160(pubkey))

Legacy P2PKH addresses use SHA-256, RIPEMD-160, a version byte, and a checksum.

Ethereum address

Take the last 20 bytes

last20(Keccak256(pubkey_x || pubkey_y))

Ethereum hashes the uncompressed secp256k1 public key without the leading 0x04 byte.

Comparison matrix

Same hidden product, different algebraic worlds.

System	Protocol shape	Public starting object	Private input(s)	Public output(s)	Calculation	Result	Main algebra or hash rule	Where result lives	Typical use
Ordinary Diffie-Hellman	Two-party key agreement	Generator number g	Alice secret a and Bob secret b	Alice publishes g^a; Bob publishes g^b	Alice computes (g^b)^a; Bob computes (g^a)^b	g^(ab)	(g^a)^b = g^(ab)	Number/group element	Older finite-field DH
Elliptic-Curve Diffie-Hellman / X25519	Two-party key agreement	Public curve point P	Alice secret a and Bob secret b	Alice publishes aP; Bob publishes bP	Alice computes a(bP); Bob computes b(aP)	abP	a(bP) = abP	Elliptic-curve point	Modern secure connections
Pairing version	Public pairing relation or scheme-specific key/proof check	Two public curve points, often P in G1 and Q in G2	Scheme scalars such as a and b	Could publish aP and bQ, depending on scheme	Often compute e(aP, bQ)	e(P,Q)^(ab)	e(aP,bQ) = e(P,Q)^(ab)	Target group element, usually written GT	Identity-based crypto, BLS signatures, zk-SNARKs
Bitcoin key/address	Single-account key pair and address derivation	secp256k1 generator point G	One account private scalar k	Public key K = kG, usually compressed for P2PKH	HASH160(compressed public key), then Base58Check	Bitcoin address, for example P2PKH	address = Base58Check(0x00 \|\| RIPEMD160(SHA256(K)))	Base58Check address string	Receiving funds and identifying spend conditions
Ethereum key/address	Single-account key pair and address derivation	secp256k1 generator point G	One account private scalar k	Uncompressed public key K = kG = 0x04 \|\| x \|\| y	Keccak256(x \|\| y), then take the last 20 bytes	Ethereum account address	address = last20(Keccak256(public_key_without_04))	20-byte address, usually hex with optional EIP-55 checksum casing	Account identity for balances, transactions, and contracts

Intentional capability

Pairings do not reveal the ECDH shared point.

In ordinary ECDH, an outsider seeing P, aP, and bP should not derive abP. In a pairing-friendly setting, a public observer may compute e(aP,bQ). That reveals a related target-group value, not a, b, or abP.

Technology	What it intentionally lets you do
X25519	Only Alice and Bob derive abP
Pairings	Publicly combine points into e(P,Q)^(ab)
BLS signatures	Verify a signature relation with pairings
zk-SNARKs	Verify algebraic proof relations efficiently
Identity-based encryption	Derive public keys from identities such as an email address