conventional encryption: algorithms

1Conventional Encryption: Algorithms

Cryptography & Network Security H. Yoon

Conventional Encryption: Algorithms

• Some of the most important symmetric block ciphers in current use

– Triple DES

– IDEA

– Blowfish

– RC5

– CAST-128

– RC2



Multiple Encryption with DES

• Double DES

• C = EK2[EK1[P]]; D = DK1[DK2[C]]• 112 bit key is safe from brute force attack• Need to examine if K3 s.t. EK2[EK1[P]] =

EK3[P]• The answer is No!! (Proved in 1992)

• # of mappings between 64-bit blocks = 264! =10347380000000000000000

• DES defines one mapping for each different key, for a total # of mappings: 256 <1017

– If DES is used twice with different keys, it will produce one of the many mappings that is not defined by a single application of DES

Triple DES



Meet In The Middle Attack

• Let X = EK1(P). Clearly X = DK2(C)

• Given a known <P, C>, construct a table of size 256 with all values of K1 and EK1(P)

• Sort on EK1(P)

• Now decrypt C with all values of K2. Check all results against table

• Any match is a candidate <K1, K2> pair – If this pair is checked with another plaintext-ciphertext pair, it can

be determined with the probability 1-2-16 (If this pair is correct with another plaintext-ciphertext pair, it is a correct key with the probability 1-2-16 )

• Total effort is O(256), not 2112 (Not much better than the 255 required for single DES)

Triple DES



Triple DES• C = EK3(DK2(EK1(P)))

• No cryptographic significance to middle decrypt operation– backwards compatible with existing single DES (K1 = K2 = K3)

• Two-key Triple DES (K1 = K3) or three-key triple DES

• Security of Triple DES – no known practical attacks

– brute force search impossible

– meet-in-the-middle attacks need 256 plaintext-ciphertext pairs per key

• A popular current

alternative

• Major disadvantage is

speed (3x slower)

Triple DES



International Data Encryption Algorithm (IDEA)

• Xuejia Lai and James Massey, ETH (Swiss Federal Institute of Technology), 1991

• Patented – patent is held by Ascom-Tech

– Non-commercial use of IDEA is free. Commercial licenses can be obtained by contacting Ascom-Tech

• Used in PGP

• 128-bit key, 64-bit block

• Variant Feistel network (not Feistel)

• Eight rounds + final transformation

IDEA



IDEA Basic Operations• Uses three operations. Each operation is performed on

two 16-bit inputs to produce a single 16-bit output– Bit-by-bit XOR ( )

– (Unsigned 16-bit integers) addition modulo 216 ( )

– (Unsigned 16-bit integers) multiplication modulo 216 + 1 (except that a block of all zeros is treated as representing 216 ( )

• Three operations are incompatible in the sense that– No pair of the three operations satisfies a distributive law. e.g.,

a (b c) (a b) (a c)

– No pair of the three operations satisfies an associative law. e.g.,

a (b c) (a b) c

• In IDEA, confusion is achieved by using these three separate operations in combination

– Provides a complex transformation of the input, making cryptanalysis much more difficult (than with a DES which uses just a single XOR)

IDEA



IDEA Basic Operations - Examples• Examples for 2-bit operands

IDEA



IDEA Basic Building Block, MAIDEA

• Basic building block is the Multiplication/Addition (MA) structure

– F1,F2: Two 16-bit values derived from

the plaintext

– Z5,Z6: Two 16-bit subkeys derived from

the key

– G1,G2: Two 16-bit outputs

• In IDEA, diffusion is provided by MA– Each output bit depends on every bit of

inputs (plaintext-derived inputs and

subkey inputs)

– This MA structure is repeated eight times,

providing very effective diffusion



Overall IDEA Encryption StructureIDEA



Single Round of IDEA (1st Round)IDEA

Transformation

Sub-encryption



Output Transformation Stage of IDEAIDEA



IDEA

Subkey Generation

• 52 16-bit subkeys are generated from the 128-bit key

• The first eight subkeys, Z1, Z2, …, Z8, are taken directly from the key

• Then a circular left shift of 25 bit positions is applied to the key, and the next eight keys are extracted.

• This procedure is repeated until all 52 subkeys are generated



IDEA

IDEA Decryption

• Use the same structure (algorithm) as the encryption, but with different subkeys

• Decryption subkeys U1, …, U52 are derived from encryption subkeys



IDEA

Encryption and Decryption Subkeys

• Zj-1: multiplicative inverse; Zj Zj

-1 = 1

• -Zj : additive inverse; -Zj Zj = 0



Blowfish

• Designed by Bruce Schneier, 1993

• Freely available (Unpatented; Royalty-free; No license required; Free source code available)

• Used in SSH, OpenBSD, IPSec

• Block cipher: 64-bit block

• Variable key length; 32 bits to 448 bits

• Fast encryption (much faster than DES and IDEA)

• Compact

• Simple

Blowfish



Subkey and S-Box Generation

• The key ranging from 32 bits to 448 bits (1 to 14 32-bit words) is stored in a K-array:

K1, K2, …, Kj 1 j 14

• The 18 32-bit subkeys are stored in the P-array: P1, P2, …, P18

• There are 4 S-boxes, each with 8x32(=256) 32-bit entries

• P-array and then 4 S-boxes are initialized with fractional part of :

Blowfish

S1,0, S1,1, …, S1,255

S2,0, S2,1, …, S2,255

S3,0, S3,1, …, S3,255

S4,0, S4,1, …, S4,255

P1= 243F6A8816

P2= 85A308D316

S4,254= 578FDFE316

S4,255= 3AC372E616



Subkey and S-Box Initialization

• P-array is XORed with K-array (reusing K-array if necessary): P1 = P1 K1, P2 = P2 K2, …, Pj = Pj Kj, Pj+1 = Pj+1 K1, Pj+2 = Pj+2 K2, …

• Then update P-array and S-boxes as follows:

Where EP,S[Y] is the ciphertext produced by encrypting Y using Blowfish with the P and S arrays

• 521 executions in total are required to produce the final P and S arrays

Blowfish

P1, P2 = EP,S[0]P3, P4 = EP,S[P1 || P2] P17, P18 = EP,S[P15 || P16]S1,0, S1,1 = EP,S[P17 || P18] S4,254, S4,255 = EP,S[P4,252 || P4,253]



Blowfish Encryption/Decryption

• Slight variant of classic Feistel network

– L and R are both processed in each round

– 16 rounds

– Two extra XORs at the end

Blowfish



Single Blowfish Round• Uses addition modulo 232 and XOR

• Round function processes four bytes– F(a, b, c, d) = ((S1,a + S2,b) S3,c) + S4,d

– Followed by Feistel swap

Blowfish



Characteristics of Blowfish• Key-dependent S-Boxes

• Operations are performed on both halves of data

• Time-consuming subkey generation process– Makes it bad for rapid key switching, but makes brute force expensive

• Perfect avalanche effect

• Fast

Blowfish



RC5

• Designed by Ronald Rivest (MIT Prof.) for RSA Data Security

• Secret-key block cipher

• Parameterized algorithm

• Features– Data-dependent rotations

– Variable block size

– Variable key size

– Variable number of rounds

RC5



Motivations

• Suitable for hardware and software• Fast• Adaptable to processors of different word lengths• Variable number of rounds• Variable-length key• Simple• Low memory usage• High security• Emphasis of data-dependent rotations

RC5



Parameterization

• RC5 is word-oriented– Two-word input and two-word output

• Representation– Word size: w (16,32,64)

– Number of rounds: r (0,1, …, 255)

– Number of bytes in key K: b (0,1, …, 255)

– RC5 algorithm notation: RC5-w/r/b

• RC5 algorithm example: RC5-32/16/7– Similar to DES

– Two 32-bit word inputs and outputs

– 16 rounds

– 7-byte (56-bit) key

• RC5-32/12/16– “nominal” version

RC5



Key Expansion• RC5 performs complex operations on the secret key t

o generate a total of t subkeys, which are stored in S array, S[0],S[1], …, S[t-1]

• Each subkey is one word (w bits) in length

• Two subkeys are used in each round, and two more subkeys are used outside the r-round t = 2r+2

• In key expansion, magic constants are used– Pw = Odd((e 2)2w); e=2.718281828…. (base of natural logarithms)

– Qw = Odd(( 1)2w); =1.618033988…. (golden ratio = (1+sqr(5))/2)

» Odd(x): odd integer nearest to x

– Example

RC5

w 16 32 64Pw B7E1 B7E15163 B7E151628AED2A6BQw 9E37 9E3779B9 9E3779B97F4A7C15



Key Expansion Algorithm

• Step-1: Convert secret key bytes to words– b byte key K, (K[0], K[1], …, K[b-1]) is converted to

word array L[0], L[1], …, L[c-1]

• Step-2: Initialize subkey array S (S[0], S[1], …, S[t-1])S[0] = Pw;

for i=1 to t-1 do

s[i] = s[i-1] + Qw;

• Step-3: Mix the secret key into subkey array S

RC5

i=j=X=Y=0;

Do 3*max(t, c) times:

X=S[i]=(S[i]+X+Y)<<<3;

Y=L[j]=(L[j]+X+Y)<<<(X+Y);

i=(i+1) mod t;

j=(j+1) mod c;

Note: <<< cyclic rotate left



RC5 Key ExpansionRC5



RC5 EncryptionRC5

LE0 = A + S[0];RE0 = B + S[1];for i = 1 to r do LEi = ((LEi-1 REi-1) <<< REi-1) + S[2i]; REi = ((REi-1 LEi) <<< LEi) + S[2i+1];

• RC5 uses 3 primitive operations– Addition, Subtraction (of words): modulo 2w

– Bitwise XOR

– Left, right circular rotation

• Encryption



RC5 DecryptionRC5

for i = r downto 1 do RDi-1 = ((RDi – S[2i+1] >>> LDi) LDi) ; LDi-1 = ((LDi – S[2i] >>> Rdi-1) RDi-1) ;B = RD0 - S[1];A = LD0 - S[0];



CAST-128• Developed by Carlisle Adams and Stafford Tavares• Used in IPSec• 64-bit block, 40- to 128-bit keys (in 8-bit increments)• Classical Feistel network structure

– Sixteen rounds– Two subkeys per round, one 32-bit (Kmi), one 5-bit (Kri)– Three different round functions– Four operations: addition(+) and subtraction(-) modulo 232, XOR, and (

variable) circular left rotate (<<<)– 5-bit subkey (Kri) determines rotate amount

• Encryption

• Decryption: same as encryption with the keys applied in reverse order

CAST-128

L0||R0 = Plaintextfor i = 1 to 16 do Li = Ri-1 Ri = Li-1 Fi[Ri-1, Kmi, Kri];Ciphertext = L16||R16



CAST-128 Round Function FCAST-128

Rounds 1,4 I=(Kmi+ Ri-1)<<<Kri) 7,10,13,16 F=((S1[Ia]S2[Ib])-S3[Ic])+S4[Id]Rounds 2,5 I=(KmiRi-1)<<<Kri) 8,11,14 F=((S1[Ia]-S2[Ib])+S3[Ic])S4[Id]Rounds 3,6 I=(Kmi-Ri-1)<<<Kri) 9,12,15 F=((S1[Ia]+S2[Ib])S3[Ic])-S4[Id]

IIa Ib Ic Id

Definition of F



CAST-128 S-Boxes

• CAST-128 uses 8 S-boxes

• Four of these, S-box 1 thru S-box 4 are used in the encryption/decryption process

• S-box 5 thru S-box 8 are used in the subkey generation

• S-boxes contain fixed (predefined) values

• Each S-box contains 256 32-bit values

CAST-128



CAST-128 Subkey Generation

• Label the 128-bit (16-byte) key as:x0x1x3x4x5x6x7x8xAxBxCxDxExF

• Symbol DefinitionsKm1, …, Km16 Sixteen 32-bit masking subkeys (one per round)

Kr1, …, Kr16 Sixteen 32-bit rotate subkeys (one per round), of which

only the least significant 5 bits of each are used

z0, …, zF Intermediate (temporary) bytes

K1, …, K32 Intermediate (temporary) words

• K1 thru K32 are calculated from the key using S-boxes 5 thru 8 (See next pages)

• Then subkeys are defined asfor i = 1 to 16 do

Kmi = Ki;

Kri = K16+i;

CAST-128



z0z1z2z3 = x0x1x2x3 S5[xD] S6[xF] S7[xC] S8[xE] S7[x8] z4z5z6z7 = x8x9xAxB S5[z0] S6[z2] S7[z1] S8[z3] S8[xA]z8z9zAzB = xCxDxExF S5[z7] S6[z6] S7[z5] S8[z4] S5[x9] zCzDzEzF = x4x5x6x7 S5[zA] S6[z9] S7[zB] S8[z8] S6[xB] K1 = S5[z8] S6[z9] S7[z7] S8[z6] S5[z2] K2 = S5[zA] S6[zB] S7[z5] S8[z4] S6[z6]K3 = S5[zC] S6[zD] S7[z3] S8[z2] S7[z9]K4 = S5[zE] S6[zF] S7[z1] S8[z0] S8[zC] x0x1x2x3 = z8z9zAzB S5[z5] S6[z7] S7[z4] S8[z6] S7[z0] x4x5x6x7 = z0z1z2z3 S5[x0] S6[x2] S7[x1] S8[x3] S8[z2] x8x9xAxB = z4z5z6z7 S5[x7] S6[x6] S7[x5] S8[x4] S5[z1] xCxDxExF = zCzDzEzF S5[xA] S6[x9] S7[xB] S8[x8] S6[z3] K5 = S5[x3] S6[x2] S7[xC] S8[xD] S5[x8] K6 = S5[x1] S6[x0] S7[xE] S8[xF] S6[xD] K7 = S5[x7] S6[x6] S7[x8] S8[x9] S7[x3] K8 = S5[x5] S6[x4] S7[xA] S8[xB] S8[x7] z0z1z2z3 = x0x1x2x3 S5[xD] S6[xF] S7[xC] S8[xE] S7[x8] z4z5z6z7 = x8x9xAxB S5[z0] S6[z2] S7[z1] S8[z3] S8[xA] z8z9zAzB = xCxDxExF S5[z7] S6[z6] S7[z5] S8[z4] S5[x9] zCzDzEzF = x4x5x6x7 S5[zA] S6[z9] S7[zB] S8[z8] S6[xB] K9 = S5[z3] S6[z2] S7[zC] S8[zD] S5[z9] K10 = S5[z1] S6[z0] S7[zE] S8[zF] S6[zC] K11 = S5[z7] S6[z6] S7[z8] S8[z9] S7[z2] K12 = S5[z5] S6[z4] S7[zA] S8[zB] S8[z6] x0x1x2x3 = z8z9zAzB S5[z5] S6[z7] S7[z4] S8[z6] S7[z0] x4x5x6x7 = z0z1z2z3 S5[x0] S6[x2] S7[x1] S8[x3] S8[z2] x8x9xAxB = z4z5z6z7 S5[x7] S6[x6] S7[x5] S8[x4] S5[z1] xCxDxExF = zCzDzEzF S5[xA] S6[x9] S7[xB] S8[x8] S6[z3] K13 = S5[x8] S6[x9] S7[x7] S8[x6] S5[x3] K14 = S5[xA] S6[xB] S7[x5] S8[x4] S6[x7] K15 = S5[xC] S6[xD] S7[x3] S8[x2] S7[x8] K16 = S5[xE] S6[xF] S7[x1] S8[x0] S8[xD]

CAST-128 Subkey GenerationCAST-128



z0z1z2z3 = x0x1x2x3 S5[xD] S6[xF] S7[xC] S8[xE] S7[x8] z4z5z6z7 = x8x9xAxB S5[z0] S6[z2] S7[z1] S8[z3] S8[xA] z8z9zAzB = xCxDxExF S5[z7] S6[z6] S7[z5] S8[z4] S5[x9] zCzDzEzF = x4x5x6x7 S5[zA] S6[z9] S7[zB] S8[z8] S6[xB] K17 = S5[z8] S6[z9] S7[z7] S8[z6] S5[z2] K18 = S5[zA] S6[zB] S7[z5] S8[z4] S6[z6] K19 = S5[zC] S6[zD] S7[z3] S8[z2] S7[z9] K20 = S5[zE] S6[zF] S7[z1] S8[z0] S8[zC] x0x1x2x3 = z8z9zAzB S5[z5] S6[z7] S7[z4] S8[z6] S7[z0] x4x5x6x7 = z0z1z2z3 S5[x0] S6[x2] S7[x1] S8[x3] S8[z2] x8x9xAxB = z4z5z6z7 S5[x7] S6[x6] S7[x5] S8[x4] S5[z1] xCxDxExF = zCzDzEzF S5[xA] S6[x9] S7[xB] S8[x8] S6[z3] K21 = S5[x3] S6[x2] S7[xC] S8[xD] S5[x8] K22 = S5[x1] S6[x0] S7[xE] S8[xF] S6[xD] K23 = S5[x7] S6[x6] S7[x8] S8[x9] S7[x3] K24 = S5[x5] S6[x4] S7[xA] S8[xB] S8[x7] z0z1z2z3 = x0x1x2x3 S5[xD] S6[xF] S7[xC] S8[xE] S7[x8] z4z5z6z7 = x8x9xAxB S5[z0] S6[z2] S7[z1] S8[z3] S8[xA] z8z9zAzB = xCxDxExF S5[z7] S6[z6] S7[z5] S8[z4] S5[x9] zCzDzEzF = x4x5x6x7 S5[zA] S6[z9] S7[zB] S8[z8] S6[xB] K25 = S5[z3] S6[z2] S7[zC] S8[zD] S5[z9] K26 = S5[z1] S6[z0] S7[zE] S8[zF] S6[zC] K27 = S5[z7] S6[z6] S7[z8] S8[z9] S7[z2] K28 = S5[z5] S6[z4] S7[zA] S8[zB] S8[z6] x0x1x2x3 = z8z9zAzB S5[z5] S6[z7] S7[z4] S8[z6] S7[z0] x4x5x6x7 = z0z1z2z3 S5[x0] S6[x2] S7[x1] S8[x3] S8[z2] x8x9xAxB = z4z5z6z7 S5[x7] S6[x6] S7[x5] S8[x4] S5[z1] xCxDxExF = zCzDzEzF S5[xA] S6[x9] S7[xB] S8[x8] S6[z3] K29 = S5[x8] S6[x9] S7[x7] S8[x6] S5[x3] K30 = S5[xA] S6[xB] S7[x5] S8[x4] S6[x7] K31 = S5[xC] S6[xD] S7[x3] S8[x2] S7[x8] K32 = S5[xE] S6[xF] S7[x1] S8[x0] S8[xD]

CAST-128 Subkey GenerationCAST-128



CAST-128 S-Box S1CAST-128

S-Box S1 30fb40d4 9fa0ff0b 6beccd2f 3f258c7a 1e213f2f 9c004dd3 6003e540 cf9fc949 bfd4af27 88bbbdb5 e2034090 98d09675 6e63a0e0 15c361d2 c2e7661d 22d4ff8e 28683b6f c07fd059 ff2379c8 775f50e2 43c340d3 df2f8656 887ca41a a2d2bd2d a1c9e0d6 346c4819 61b76d87 22540f2f 2abe32e1 aa54166b 22568e3a a2d341d0 66db40c8 a784392f 004dff2f 2db9d2de 97943fac 4a97c1d8 527644b7 b5f437a7 b82cbaef d751d159 6ff7f0ed 5a097a1f 827b68d0 90ecf52e 22b0c054 bc8e5935 4b6d2f7f 50bb64a2 d2664910 bee5812d b7332290 e93b159f b48ee411 4bff345d fd45c240 ad31973f c4f6d02e 55fc8165 d5b1caad a1ac2dae a2d4b76d c19b0c50 882240f2 0c6e4f38 a4e4bfd7 4f5ba272 564c1d2f c59c5319 b949e354 b04669fe b1b6ab8a c71358dd 6385c545 110f935d 57538ad5 6a390493 e63d37e0 2a54f6b3 3a787d5f 6276a0b5 19a6fcdf 7a42206a 29f9d4d5 f61b1891 bb72275e aa508167 38901091 c6b505eb 84c7cb8c 2ad75a0f 874a1427 a2d1936b 2ad286af aa56d291 d7894360 425c750d 93b39e26 187184c9 6c00b32d 73e2bb14 a0bebc3c 54623779 64459eab 3f328b82 7718cf82 59a2cea6 04ee002e 89fe78e6 3fab0950 325ff6c2 81383f05 6963c5c8 76cb5ad6 d49974c9 ca180dcf 380782d5 c7fa5cf6 8ac31511 35e79e13 47da91d0 f40f9086 a7e2419e 31366241 051ef495 aa573b04 4a805d8d 548300d0 00322a3c bf64cddf ba57a68e 75c6372b 50afd341 a7c13275 915a0bf5 6b54bfab 2b0b1426 ab4cc9d7 449ccd82 f7fbf265 ab85c5f3 1b55db94 aad4e324 cfa4bd3f 2deaa3e2 9e204d02 c8bd25ac eadf55b3 d5bd9e98 e31231b2 2ad5ad6c 954329de adbe4528 d8710f69 aa51c90f aa786bf6 22513f1e aa51a79b 2ad344cc 7b5a41f0 d37cfbad 1b069505 41ece491 b4c332e6 032268d4 c9600acc ce387e6d bf6bb16c 6a70fb78 0d03d9c9 d4df39de e01063da 4736f464 5ad328d8 b347cc96 75bb0fc3 98511bfb 4ffbcc35 b58bcf6a e11f0abc bfc5fe4a a70aec10 ac39570a 3f04442f 6188b153 e0397a2e 5727cb79 9ceb418f 1cacd68d 2ad37c96 0175cb9d c69dff09 c75b65f0 d9db40d8 ec0e7779 4744ead4 b11c3274 dd24cb9e 7e1c54bd f01144f9 d2240eb1 9675b3fd a3ac3755 d47c27af 51c85f4d 56907596 a5bb15e6 580304f0 ca042cf1 011a37ea 8dbfaadb 35ba3e4a 3526ffa0 c37b4d09 bc306ed9 98a52666 5648f725 ff5e569d 0ced63d0 7c63b2cf 700b45e1 d5ea50f1 85a92872 af1fbda7 d4234870 a7870bf3 2d3b4d79 42e04198 0cd0ede7 26470db8 f881814c 474d6ad7 7c0c5e5c d1231959 381b7298 f5d2f4db ab838653 6e2f1e23 83719c9e bd91e046 9a56456e dc39200c 20c8c571 962bda1c e1e696ff b141ab08 7cca89b9 1a69e783 02cc4843 a2f7c579 429ef47d 427b169c 5ac9f049 dd8f0f00 5c8165bf



RC2

• Developed by Ron Rivest (RSA Data Security)

• 64-bit block cipher

• Variable key size (from one byte up to 128 bytes)

• Designed to be easy to implement on 16-bit microprocessor

– Use 16-bit word, 16-bit arithmetic (addition, XOR, AND, ~, rotate)

• Non-Feistel

• 18 rounds (mixing/mashing)

• Used in S/MIME

RC2



RC2 Key Expansion• RC2 assumes 128 (64 word) byte key buffer

– For byte operation, key array is L[0], …, L[127]; each L[i] is a byte– For word operation, key array is K[0], …, K[63]; each K[i] is a 16-bit word– These are alternative views of the same key buffer

• Key expansion– Assume that exactly T bytes of key are supplied, 1 T 128– The purpose of key expansion algorithm is to modify the key buffer so

that each bit of the expanded key depends in a complicated way on every bit of the supplied input key

– Key expansion begins by placing the supplied T-byte key into bytes L[0], …, L[T-1] of the key buffer

– L array is then computed making use of an auxiliary array P– P array is a random permutation of values of 0,…,255, which is

constructed based on =3.14159… (See next page)– The computation is

RC2

for i = T to 127 doL[i] = P[L[i-1] + L[i-T]];

L[128-T] = P[L[128-T]]For i = 127 – T down to 0 do

L[i]=P[L[i+1] L[i+T]];



PiTable (P-array)RC2

Here is the P array in hexadecimal notation:

0 1 2 3 4 5 6 7 8 9 a b c d e f 00: d9 78 f9 c4 19 dd b5 ed 28 e9 fd 79 4a a0 d8 9d 10: c6 7e 37 83 2b 76 53 8e 62 4c 64 88 44 8b fb a2 20: 17 9a 59 f5 87 b3 4f 13 61 45 6d 8d 09 81 7d 32 30: bd 8f 40 eb 86 b7 7b 0b f0 95 21 22 5c 6b 4e 82 40: 54 d6 65 93 ce 60 b2 1c 73 56 c0 14 a7 8c f1 dc 50: 12 75 ca 1f 3b be e4 d1 42 3d d4 30 a3 3c b6 26 60: 6f bf 0e da 46 69 07 57 27 f2 1d 9b bc 94 43 03 70: f8 11 c7 f6 90 ef 3e e7 06 c3 d5 2f c8 66 1e d7 80: 08 e8 ea de 80 52 ee f7 84 aa 72 ac 35 4d 6a 2a 90: 96 1a d2 71 5a 15 49 74 4b 9f d0 5e 04 18 a4 ec a0: c2 e0 41 6e 0f 51 cb cc 24 91 af 50 a1 f4 70 39 b0: 99 7c 3a 85 23 b8 b4 7a fc 02 36 5b 25 55 97 31 c0: 2d 5d fa 98 e3 8a 92 ae 05 df 29 10 67 6c ba c9 d0: d3 00 e6 cf e1 9e a8 2c 63 16 01 3f 58 e2 89 a9 e0: 0d 38 34 1b ab 33 ff b0 bb 48 0c 5f b9 b1 cd 2e f0: c5 f3 db 47 e5 a5 9c 77 0a a6 20 68 fe 7f c1 ad



RC2 Encryption• Encryption algorithm takes a 64-bit input stored in

R[0], R[1], R[2], R[3], and places the result back in R[0] thru R[3].

• Algorithm consists of 18 rounds of two types: mixing and mashing

• Mixing round:

RC2

R[0] = R[0] + K[j] + (R[3] & R[2]) + ((~R[3] & R[1]);R[0] = R[0] <<< 1;j = j + 1;R[1] = R[1] + K[j] + (R[0] & R[3]) + ((~R[0] & R[2]);R[1] = R[1] <<< 2;j = j + 1;R[2] = R[2] + K[j] + (R[1] & R[0]) + ((~R[1] & R[3]);R[2] = R[2] <<< 3;j = j + 1;R[3] = R[3] + K[j] + (R[2] & R[1]) + ((~R[2] & R[0]);R[3] = R[3] <<< 5;j = j + 1;

Here j is the global variable; K[j] is the first subkey word that has not yet been used



RC2 Encryption• Mashing round

• RC21. Initialize j to zero

2. Perform five mixing rounds (j = 20)

3. Perform one mashing round

4. Perform six mixing rounds (j = 44)

5. Perform one mashing round

6. Perform five mixing rounds (j=64)

• Decryption: Inverse operation of encryption with the keys used in reverse order

RC2

R[0] = R[0] + K[R[3] & 63];R[1] = R[1] + K[R[0] & 63];R[2] = R[2] + K[R[1] & 63];R[3] = R[3] + K[R[2] & 63];



Characteristics of Advanced Block Ciphers

• Variable key length– Blowfish, RC5, CAST-128, RC2

• Mixed operators– More than one arithmetic and/or Boolean operator, especially ones th

at are not associative or distributive

– These operators provide nonlinearity as an alternative to S-boxes

• Data-dependent rotation– Provide excellent confusion and diffusion

– RC5

• Key-dependent rotation– CAST-128

Key features found in advanced symmetric block ciphers (not in DES)



Characteristics of Advanced Block Ciphers

• Key-dependent S-boxes– Blowfish

• Expensive key schedule computation– Blowfish

• Variable round function (F)– CAST-128

• Variable plaintext/ciphertext block length– RC5

• Variable number of rounds– RC5

• Operation on both data halves each round– IDEA, Blowfish, RC5



Chapter 4 HW

• Prob. 4.5

• Prob. 4.8

• Prob. 4.9

• Prob. 4.13

conventional encryption: algorithms

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