Week 3: Block ciphers
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1 Week 3: Block ciphers Jay Daigle Occidental College September 13, 2018 Jay Daigle (Occidental College) Week 3: September 13, / 12
2 Jay Daigle (Occidental College) Week 3: September 13, / 12
3 Definition A block cipher encrypts fixed-sized blocks of ciphertext, rather than single letters at a time. Jay Daigle (Occidental College) Week 3: September 13, / 12
4 Permutation ciphers Jay Daigle (Occidental College) Week 3: September 13, / 12
5 Permutation ciphers Permutation cipher We choose a block size n, and as a key choose an element k S n, which is a permutation on an alphabet of n letters. Jay Daigle (Occidental College) Week 3: September 13, / 12
6 Permutation ciphers Permutation cipher We choose a block size n, and as a key choose an element k S n, which is a permutation on an alphabet of n letters. To encrypt, we break our plaintext into blocks of size n, padding the final block with nonsense characters if necessary. Then we permute each block according to the key k. Jay Daigle (Occidental College) Week 3: September 13, / 12
7 Permutation ciphers Permutation cipher We choose a block size n, and as a key choose an element k S n, which is a permutation on an alphabet of n letters. To encrypt, we break our plaintext into blocks of size n, padding the final block with nonsense characters if necessary. Then we permute each block according to the key k. To decrypt, we take the inverse permutation k 1 and apply this to each ciphertext block. Jay Daigle (Occidental College) Week 3: September 13, / 12
8 Permutation ciphers Jay Daigle (Occidental College) Week 3: September 13, / 12
9 Permutation ciphers Fourscore and seven years ago Jay Daigle (Occidental College) Week 3: September 13, / 12
10 Permutation ciphers Fourscore and seven years ago Block size five Jay Daigle (Occidental College) Week 3: September 13, / 12
11 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). Jay Daigle (Occidental College) Week 3: September 13, / 12
12 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago Jay Daigle (Occidental College) Week 3: September 13, / 12
13 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
14 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
15 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
16 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
17 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
18 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU Jay Daigle (Occidental College) Week 3: September 13, / 12
19 Permutation ciphers Fourscore and seven years ago Block size five and key k = (12345) (23514). fours corea ndsev enyea rsago RFOSU ECOAR ENDVS EENAY GRSOA. Jay Daigle (Occidental College) Week 3: September 13, / 12
20 Modular Arithmetic and Matrices Jay Daigle (Occidental College) Week 3: September 13, / 12
21 Modular Arithmetic and Matrices [ ] 1 ( [ ]) 1 [ ] a b a b d b = det = c d c d c a 1 ad bc [ d b c a ]. Jay Daigle (Occidental College) Week 3: September 13, / 12
22 The Hill Cipher Jay Daigle (Occidental College) Week 3: September 13, / 12
23 The Hill Cipher Lester Hill s patented cipher machine Jay Daigle (Occidental College) Week 3: September 13, / 12
24 The Hill Cipher Jay Daigle (Occidental College) Week 3: September 13, / 12
25 The Hill Cipher Hill Cipher We first choose a block size n. We choose a key, which is a n n matrix K with entries in Z/26Z (that is, integers modulo 26). We require that gcd(26, det K) = 1. We divide our message into blocks of length n. We write each plaintext block as a column vector B (Z/26Z) n. The corresponding ciphertext block is given by KB. To decrypt, we compute K 1 in Z/26Z. Given a ciphertext block C, the corresponding plaintext block is K 1 C. Jay Daigle (Occidental College) Week 3: September 13, / 12
26 The Hill Cipher Jay Daigle (Occidental College) Week 3: September 13, / 12
27 The Hill Cipher It was a dark and stormy night. Jay Daigle (Occidental College) Week 3: September 13, / 12
28 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT Jay Daigle (Occidental College) Week 3: September 13, / 12
29 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT Jay Daigle (Occidental College) Week 3: September 13, / 12
30 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT K [ ] 8 = 19 [ ] [ ] 17 0 Jay Daigle (Occidental College) Week 3: September 13, / 12
31 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT K [ ] 8 = 19 [ ] [ ] 17 0 K [ ] [ ] = [ ] 14 6 Jay Daigle (Occidental College) Week 3: September 13, / 12
32 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT [ ] [ ] [ ] K = [ ] [ ] [ ] K = K [ ] [ ] = [ ] 14 6 Jay Daigle (Occidental College) Week 3: September 13, / 12
33 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = Jay Daigle (Occidental College) Week 3: September 13, / 12
34 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = Jay Daigle (Occidental College) Week 3: September 13, / 12
35 The Hill Cipher It was a dark and stormy night. IT WA SA DA RK AN DS TO RM YN IG HT [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = [ ] [ ] [ ] K = RA OG CM JP JA NA BZ TT LF HQ EA OV Jay Daigle (Occidental College) Week 3: September 13, / 12
36 The Hill Cipher Jay Daigle (Occidental College) Week 3: September 13, / 12
37 The Hill Cipher how are you today Jay Daigle (Occidental College) Week 3: September 13, / 12
38 The Hill Cipher how are you today ZWS ENI USP LJVEU Jay Daigle (Occidental College) Week 3: September 13, / 12
39 The Hill Cipher how are you today ZWS ENI USP LJVEU Jay Daigle (Occidental College) Week 3: September 13, / 12
40 The Hill Cipher how are you today ZWS ENI USP LJVEU Jay Daigle (Occidental College) Week 3: September 13, / 12
41 Diffusion and Confusion Jay Daigle (Occidental College) Week 3: September 13, / 12
42 Diffusion and Confusion Claude Shannon Picture CC BY-SA 2.0 de by Konrad Jacobs Jay Daigle (Occidental College) Week 3: September 13, / 12
43 Diffusion and Confusion Jay Daigle (Occidental College) Week 3: September 13, / 12
44 Diffusion and Confusion Definition An encryption method has good diffusion if changing one character of the plaintext changes several characters of the ciphertext, and vice versa. Jay Daigle (Occidental College) Week 3: September 13, / 12
45 Diffusion and Confusion Definition An encryption method has good diffusion if changing one character of the plaintext changes several characters of the ciphertext, and vice versa. Definition An encryption method has good confusion if the key does not relate straightforwardly to the ciphertext, but each part of the ciphertext depends on many parts of the key. Jay Daigle (Occidental College) Week 3: September 13, / 12
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