How deeply does Hacking Cryptography cover Diffie–Hellman key exchange?

Derives public values and shared-secret equations through modular arithmetic, without implementation code or parameter-selection guidance.

Diffie–Hellman key exchange

As explained in Hacking Cryptography

Diffie–Hellman key exchange is a key-agreement protocol in which participants derive a shared secret from exchanged public values and retained private exponents.

Diffie–Hellman key exchange lets two participants derive the same secret while sharing only public values. Each chooses a private exponent, publishes its modular exponentiation, and combines the received value with its own private exponent. section 8.3.1

The exchange proceeds as follows:

Agree on a prime p and generator g. section 8.3.1
Choose private exponents a and b, then publish A = gᵃ mod p and B = gᵇ mod p. section 8.3.1
Compute S = Aᵇ mod p = Bᵃ mod p = gᵃᵇ mod p. section 8.3.1
Rely on the difficulty of recovering a private exponent from a public value: the discrete logarithm problem. section 8.3.1

A small modular example

Using p = 13 and g = 7, Alice chooses a = 3 and publishes A = 5. Bob chooses b = 9 and publishes B = 8. Alice computes 8³ mod 13 = 5; Bob computes 5⁹ mod 13 = 5. Both obtain the shared secret S = 5, while an eavesdropper sees only the public values. section 8.3.1

Table 8.1 Exponentiation table for multiplicative group modulo 13

Base \ Exponent (n)	0	1	2	3	4	5	6	7	8	9	10	11	12
\(1^n \bmod 13\)	1	1	1	1	1	1	1	1	1	1	1	1	1
\(2^n \bmod 13\)	1	2	4	8	3	6	12	11	9	5	10	7	1
\(3^n \bmod 13\)	1	3	9	1	3	9	1	3	9	1	3	9	1
\(4^n \bmod 13\)	1	4	3	12	9	10	1	4	3	12	9	10	1
\(5^n \bmod 13\)	1	5	12	8	1	5	12	8	1	5	12	8	1
\(6^n \bmod 13\)	1	6	10	8	9	2	12	7	3	5	4	11	1
\(7^n \bmod 13\)	1	7	10	5	9	11	12	6	3	8	4	2	1
\(8^n \bmod 13\)	1	8	12	5	1	8	12	5	1	8	12	5	1
\(9^n \bmod 13\)	1	9	3	1	9	3	1	9	3	1	9	3	1
\(10^n \bmod 13\)	1	10	9	12	3	4	1	10	9	12	3	4	1
\(11^n \bmod 13\)	1	11	4	5	3	7	12	2	9	8	6	10	1
\(12^n \bmod 13\)	1	12	1	12	1	12	1	12	1	12	1	12	1

Use the exponentiation table to verify the public values and shared-secret calculations modulo 13. section 8.3.1

How Hacking Cryptography covers it

liveBook manning.com

Read Hacking Cryptography on liveBook Get the book at manning.com

Also explained in

liveBook manning.com

Real-World CryptographyDiffie-Hellman key exchange is a public-key protocol that lets parties establish a shared secret over an insecure channel.
liveBook manning.com

Elliptic Curve Cryptography for DevelopersA public-key key-agreement protocol that lets parties establish a shared secret over an insecure network using private values and exchanged public values.
liveBook manning.com

Software Security for DevelopersDiffie-Hellman is a public-key key-agreement algorithm based on the computational difficulty of the discrete logarithm problem.

Compare how 4 books explain Diffie–Hellman key exchange →

Related concepts

X3DHused by · X3DH is a non-interactive key-exchange protocol that combines multiple Diffie-Hellman exchanges to establish shared keying material for asynchronous messaging.
API keyproduces · An API key is a credential used to identify or authorize a client accessing an application programming interface.
key exchangekind of · Key exchange is a cryptographic protocol by which communicating parties establish a shared secret over a communication channel without directly transmitting that secret.
elliptic-curve diffie-hellmanincludes · Elliptic-curve Diffie-Hellman is a public-key key-agreement method in which parties derive a shared secret through elliptic-curve point operations.
CPaceused by · CPace is a symmetric password-authenticated key-exchange algorithm in which parties derive a group generator from a shared password and use it for ephemeral Diffie-Hellman key exchange.

This explainer was generated by Manning's knowledge graph from the text of Hacking Cryptography. The section links point to the parts of the book it draws on.