Product Ciphers

Substitute, then transpose, then repeat. Confusion and diffusion together: the shape DES and AES inherit.

Compositiondemo

Objectives

Follow a message through several substitute-then-transpose rounds.
Distinguish confusion from diffusion by which stage produces each.
Explain why iterating both is stronger than either one alone.

50%

Substitution hides which letter. Transposition hides where it was. Do both, repeatedly.

Neither stage is new. The substitution is the general monoalphabetic cipher and the transposition is the rail fence. A product cipher is what you get by alternating two ciphers you already have, so both keys are yours to set.

Substitution key (26 letters, each used once)

Type a keyword, then fill in the rest: its letters first, then every letter it did not use, counting down from Z.

✓ valid permutation

plain

cipher

Plaintext

Rounds (substitute, then transpose)

Rails

round 0: plaintext

WEHAV EAMOL EABOR TTHED EAL

round 1a: monoalphabetic substitution

FUZPG UPSNV UPRNK IIZUD UPV

round 1b: rail fence, 3 rails

FGNRI UUPUS VPNIZ DPZPU KUV

round 2a: monoalphabetic substitution

CTQKY HHMHJ GMQYA DMAMH WHG

round 2b: rail fence, 3 rails

CYHQM WTKHM JMYDA HHQHG AMG

Confusion and diffusion. Substitution complicates the relation between key and ciphertext; transposition spreads each plaintext letter over many ciphertext letters. Neither alone is enough. Iterating both is the design of DES and AES.

step 1/2

CPE 645 / CS 685

Product Ciphers

Columnar Transposition

Steganography