Research_Theory_Design_and_MethodsWalden_UniversityJournal

Research Theory, Design, and Methods Walden University

Journal Articles

Locate your program below for the assigned journal articles to use for the Discussion assignments in Weeks 3, 4, 5, and 7. Please follow the instructions in the week’s unit and find these articles in the Walden Library .

If your program is not listed, your Instructor will post an announcement with your assigned journal articles.

You will focus on one article in each of these weeks for your Main Question Post; however, you are expected to read and familiarize yourself with all of the articles listed to effectively participate in the discussion. Consult the particular week’s Discussion area for instructions on completing the assignment.

For quick access, press CTRL + left-click on your program’s link below.

Criminal Justice

CRIMINAL JUSTICE

Week 4

(Riddick is my last name)

If your last name starts with M through Z, use Article A.

Article A:

Forster, M., Grigsby, T. J., Unger, J. B., & Sussman, S. (2015). Associations between gun violence exposure, gang associations, and youth aggression: Implications for prevention and intervention programs. Journal of Criminology, doi:http://dx.doi.org/10.1155/2015/963750

Required Readings

Babbie, E. (2017). Basics of social research (7th ed.). Boston, MA: Cengage Learning.

· Chapter 4, “Research Design”

Burkholder, G. J., Cox, K. A., Crawford, L. M., & Hitchcock, J. H. (Eds.). (2020). Research designs and methods: An applied guide for the scholar-practitioner. Thousand Oaks, CA: Sage.

· Chapter 20, “Writing the Research Proposal”

Purpose Statement Checklist

Use the following criteria to evaluate an author’s purpose statement.

Look for indications of the following:

• Does the statement begin with signaling words?

• Does the statement identify the research approach (quantitative,

qualitative, or mixed)?

• Does the statement clearly state the intent of the study?

• Does the statement mention the participants?

• Does the statement mention the research site?

• Is the statement framed in a way that is consistent with the identified

problem?

If the study is qualitative, does the purpose statement do as follows?

• Focus on a single phenomenon

• Use an action verb to convey how learning will take place

• Use neutral, nondirectional language

• Provide a general definition of the central phenomenon

If the study is quantitative, does the purpose statement do as follows?

• Identify the variables under study

• Provide a general definition of each key variable

• Use words that connect the variables

• Identify a theory

If the study is mixed methods, does the purpose statement do as follows?

• Discuss the reason(s) for mixing both quantitative and qualitative data

• Include the characteristics of a good qualitative purpose statement (as

listed above)

• Include the characteristics of a good quantitative purpose statement (as listed above)

• Indicate the specific method of collecting both quantitative and qualitative data

Cryptography and Network Security:

Principles and Practice Eighth Edition

Chapter 6

Advanced Encryption Standard

Finite Field Arithmetic (1 of 2)

• In the Advanced Encryption Standard (A E S) all operations are

performed on 8-bit bytes

• The arithmetic operations of addition, multiplication, and division

are performed over the finite field G F(28)

• A field is a set in which we can do addition, subtraction,

multiplication, and division without leaving the set

• Division is defined with the following rule:

– a /b = a (b−1 )

• An example of a finite field (one with a finite number of

elements) is the set Zp consisting of all the integers {0, 1, . . . . ,

p − 1}, where p is a prime number and in which arithmetic is

carried out modulo p

Finite Field Arithmetic (2 of 2)

• If one of the operations used in the algorithm is division, then we need

to work in arithmetic defined over a field

– Division requires that each nonzero element have a multiplicative

inverse

• For convenience and for implementation efficiency we would like to

work with integers that fit exactly into a given number of bits with no

wasted bit patterns

– Integers in the range 0 through 2n – 1, which fit into an n-bit word

• The set of such integers, Z2 n, using modular arithmetic, is not a field

– For example, the integer 2 has no multiplicative inverse in Z2 n, that

is, there is no integer b, such that 2b mod 2n = 1

• A finite field containing 2n elements is referred to as G F(2n)

– Every polynomial in G F(2n) can be represented by an n-bit

number

Figure 6.1 A E S Encryption Process

Figure 6.2 A E S Data Structures

Table 6.1 A E S Parameters

Key Size (words/bytes/bits) 4/16/128 6/24/192 8/32/256

Plaintext Block Size (words/bytes/bits) 4/16/128 4/16/128 4/16/128

Number of Rounds 10 12 14

Round Key Size (words/bytes/bits) 4/16/128 4/16/128 4/16/128

Expanded Key Size (words/bytes) 44/176 52/208 60/240

Figure 6.3 A E S Encryption and Decryption

Detailed Structure (1 of 2)

• Processes the entire data block as a single matrix during

each round using substitutions and permutation

• The key that is provided as input is expanded into an array

of forty-four 32-bit words, w[i]

• Four different stages are used:

– Substitute bytes – uses an S-box to perform a byte-by-

byte substitution of the block

– ShiftRows – a simple permutation

– MixColumns – a substitution that makes use of

arithmetic over GF(28)

– AddRoundKey – a simple bitwise X O R of the current

block with a portion of the expanded key

Detailed Structure (2 of 2)

• The cipher begins and ends with an AddRoundKey stage

• Can view the cipher as alternating operations of X O R

encryption (AddRoundKey) of a block, followed by

scrambling of the block (the other three stages), followed

by X O R encryption, and so on

• Each stage is easily reversible

• The decryption algorithm makes use of the expanded key

in reverse order, however the decryption algorithm is not

identical to the encryption algorithm

• State is the same for both encryption and decryption

• Final round of both encryption and decryption consists of

only three stages

Figure 6.4 A E S Encryption Round

Figure 6.5 A E S Byte-Level Operations

Table 6.2 AES S-Boxes (1 of 2)

Table 6.2 AES S-Boxes (2 of 2)

Figure 6.6 Construction of S-Box and IS-Box

S-Box Rationale

• The S-box is designed to be resistant to known

cryptanalytic attacks

• The Rijndael developers sought a design that has a low

correlation between input bits and output bits and the

property that the output is not a linear mathematical

function of the input

• The nonlinearity is due to the use of the multiplicative

inverse

Figure 6.7 A E S Row and Column Operations

Shift Row Rationale

• More substantial than it may first appear

• The State, as well as the cipher input and output, is treated

as an array of four 4-byte columns

• On encryption, the first 4 bytes of the plaintext are copied

to the first column of State, and so on

• The round key is applied to State column by column

– Thus, a row shift moves an individual byte from one

column to another, which is a linear distance of a

multiple of 4 bytes

• Transformation ensures that the 4 bytes of one column are

spread out to four different columns

Mix Columns Rationale

• Coefficients of a matrix based on a linear code with

maximal distance between code words ensures a good

mixing among the bytes of each column

• The mix column transformation combined with the shift row

transformation ensures that after a few rounds all output

bits depend on all input bits

AddRoundKey Transformation

• The 128 bits of State are

bitwise XORed with the 128

bits of the round key

• Operation is viewed as a

columnwise operation

between the 4 bytes of a

State column and one word

of the round key

– Can also be viewed as

a byte-level operation

• Rationale:

– Is as simple as possible

and affects every bit of

State

– The complexity of the

round key expansion

plus the complexity of

the other stages of A E S

ensure security

Figure 6.8 Inputs for Single A E S Round

A E S Key Expansion

• Takes as input a four-word (16 byte) key and produces a linear

array of 44 words (176) bytes

– This is sufficient to provide a four-word round key for the

initial AddRoundKey stage and each of the 10 rounds of the

cipher

• Key is copied into the first four words of the expanded key

– The remainder of the expanded key is filled in four words at

a time

• Each added word w[i] depends on the immediately preceding

word, w[i – 1], and the word four positions back, w[i – 4]

– In three out of four cases a simple X O R is used

– For a word whose position in the w array is a multiple of 4, a

more complex function is used

Figure 6.9 A E S Key Expansion

Key Expansion Rationale (1 of 2)

• The Rijndael developers designed the expansion key

algorithm to be resistant to known cryptanalytic attacks

• Inclusion of a round-dependent round constant eliminates

the symmetry between the ways in which round keys are

generated in different rounds

Key Expansion Rationale (2 of 2)

• The specific criteria that were used are:

– Knowledge of a part of the cipher key or round key does

not enable calculation of many other round-key bits

– An invertible transformation

– Speed on a wide range of processors

– Usage of round constants to eliminate symmetries

– Diffusion of cipher key differences into the round keys

– Enough nonlinearity to prohibit the full determination of

round key differences from cipher key differences only

– Simplicity of description

Table 6.3 Example Round Key

Calculation

Description Value

i (decimal) 36

temp = w[i − 1] 7F8D292F

RotWord (temp) 8D292F7F

SubWord (RotWord (temp)) 5DA515D2

Rcon (9) 1B000000

SubWord (RotWord (temp)) ⊕ Rcon (9) 46A515D2

w[i − 4] EAD27321

w[i] = w[i − 4] ⊕ SubWord (RotWord (temp)) ⊕ Rcon (9) AC7766F3

Table 6.4 Key Expansion for A E S Example (1 of 3)

Key Words Auxiliary Function

w0 = 0f 15 71 c9

w1 = 47 d9 e8 59

w2 = 0c b7 ad d6

w3 = af 7f 67 98

RotWord (w3) = 7f 67 98 af = x1

SubWord (x1) = d2 85 46 79 = y1

Rcon (1) = 01 00 00 00

y1 ⊕ Rcon (1) = d3 85 46 79 = z1

w4 = w0 ⊕ z1 = dc 90 37 b0 w5 = w4 ⊕ w1 = 9b 49 df e9 w6 = w5 ⊕ w2 = 97 fe 72 3f w7 = w6 ⊕ w3 = 38 81 15 a7

RotWord (w7) = 81 15 a7 38 = x2

SubWord (x2) = 0c 59 5c 07 = y2

Rcon (2) = 02 00 00 00

y2 ⊕ Rcon (2) = 0e 59 5c 07 = z2

w8 = w4 ⊕ z2 = d2 c9 6b b7 w9 = w8 ⊕ w5 = 49 80 b4 5e w10 = w9 ⊕ w6 = de 7e c6 61 w11 = w10 ⊕ w7 = e6 ff d3 c6

RotWord (w11) = ff d3 c6 e6 = x3

SubWord (x3) = 16 66 b4 83 = y3

Rcon (3) = 04 00 00 00

y3 ⊕ Rcon (3) = 12 66 b4 8e = z3

Table 6.4 Key Expansion for A E S Example (2 of 3)

Key Words Auxiliary Function

w12 = w8 ⊕ z3 = c0 af df 39 w13 = w12 ⊕ w9 = 89 2f 6b 67 w14 = w13 ⊕ w10 = 57 51 ad 06 w15 = w14 ⊕ w11 = b1 ae 7e c0

RotWord (w15) = ae 7e c0 b1 = x4

SubWord (x4) = e4 f3 ba c8 = y4

Rcon (4) = 08 00 00 00

y4 ⊕ Rcon (4) = ec f3 ba c8 = 4

w16 = w12 ⊕ z4 = 2c 5c 65 f1 w17 = w16 ⊕ w13 = a5 73 0e 96 w18 = w17 ⊕ w14 = f2 22 a3 90 w19 = w18 ⊕ w15 = 43 8c dd 50

RotWord (w19) = 8c dd 50 43 = x5

SubWord (x5) = 64 c1 53 1a = y5

Rcon(5) = 10 00 00 00

y5 ⊕ Rcon (5) = 74 c1 53 1a = z5

w20 = w16 ⊕ z5 = 58 9d 36 eb w21 = w20 ⊕ w17 = fd ee 38 7d w22 = w21 ⊕ w18 = 0f cc 9b ed w23 = w22 ⊕ w19 = 4c 40 46 bd

RotWord (w23) = 40 46 bd 4c = x6

SubWord (x6) = 09 5a 7a 29 = y6

Rcon(6) = 20 00 00 00

y6 ⊕ Rcon(6) = 29 5a 7a 29 = z6

Table 6.4 Key Expansion for A E S Example (3 of 3)

Key Words Auxiliary Function

w24 = w20 ⊕ z6 = 71 c7 4c c2 w25 = w24 ⊕ w21 = 8c 29 74 bf w26 = w25 ⊕ w22 = 83 e5 ef 52 w27 = w26 ⊕ w23 = cf a5 a9 ef

RotWord (w27) = a5 a9 ef cf = x7

SubWord (x7) = 06 d3 bf 8a = y7 Rcon (7) = 40 00 00 00 y7 ⊕ Rcon(7) = 46 d3 df 8a = z7

w28 = w24 ⊕ z7 = 37 14 93 48 w29 = w28 ⊕ w25 = bb 3d e7 f7 w30 = w29 ⊕ w26 = 38 d8 08 a5 w31 = w30 ⊕ w27 = f7 7d a1 4a

RotWord (w31) = 7d a1 4a f7 = x8

SubWord (x8) = ff 32 d6 68 = y8 Rcon (8) = 80 00 00 00 y8 ⊕ Rcon(8) = 7f 32 d6 68 = z8

w32 = w28 ⊕ z8 = 48 26 45 20 w33 = w32 ⊕ w29 = f3 1b a2 d7 w34 = w33 ⊕ w30 = cb c3 aa 72 w35 = w34 ⊕ w32 = 3c be 0b 3

RotWord (w35) = be 0b 38 3c = x9

SubWord (x9) = ae 2b 07 eb = y9 Rcon (9) = 1B 00 00 00 y9 ⊕ Rcon (9) = b5 2b 07 eb = z9

w36 = w32 ⊕ z9 = fd 0d 42 cb w37 = w36 ⊕ w33 = 0e 16 e0 1c w38 = w37 ⊕ w34 = c5 d5 4a 6e w39 = w38 ⊕ w35 = f9 6b 41 56

RotWord (w39) = 6b 41 56 f9 = x10

SubWord (x10) = 7f 83 b1 99 = y10 Rcon (10) = 36 00 00 00 y10 ⊕ Rcon (10) = 49 83 b1 99 = z10

w40 = w36 ⊕ z10 = b4 8e f3 52 w41 = w40 ⊕ w37 = ba 98 13 4e w42 = w41 ⊕ w38 = 7f 4d 59 20 w43 = w42 ⊕ w39 = 86 26 18 76

Table 6.5 A E S Example (1 of 2) Start of Round After SubBytes After ShiftRows After MixColumns Round Key

01 89 fe 76

23 ab dc 54

45 cd ba 32

67 ef 98 10

0f 47 0c af

15 d9 b7 7f

71 e8 ad 67

c9 59 d6 98

0e ce f2 d9

36 72 6b 2b

34 25 17 55

ae b6 4e 88

ab 8b 89 35

05 40 7f f1

18 3f f0 fc

e4 4e 2f c4

ab 8b 89 35

40 7f f1 05

f0 fc 18 3f

c4 e4 4e 2f

b9 94 57 75

e4 8e 16 51

47 20 9a 3f

c5 d6 f5 3b

dc 9b 97 38

90 49 fe 81

37 df 72 15

b0 e9 3f a7

65 0f c0 4d

74 c7 e8 d0

70 ff e8 2a

75 3f ca 9c

4d 76 ba e3

92 c6 9b 70

51 16 9b e5

9d 75 74 de

4d 76 ba e3

c6 9b 70 92

9b e5 51 16

de 9d 75 74

8e 22 db 12

b2 f2 dc 92

df 80 f7 c1

2d c5 1e 52

d2 49 de e6

c9 80 7e ff

6b b4 c6 d3

b7 5e 61 c6

5c 6b 05 f4

7b 72 a2 6d

b4 34 31 12

9a 9b 7f 94

4a 7f 6b bf

21 40 3a 3c

8d 18 c7 c9

b8 14 d2 22

4a 7f 6b bf

40 3a 3c 21

c7 c9 8d 18

22 b8 14 d2

b1 c1 0b cc

ba f3 8b 07

f9 1f 6a c3

1d 19 24 5c

c0 89 57 b1

af 2f 51 ae

df 6b ad 7e

39 67 06 c0

71 48 5c 7d

15 dc da a9

26 74 c7 bd

24 7e 22 9c

a3 52 4a ff

59 86 57 d3

f7 92 c6 7a

36 f3 93 de

a3 52 4a ff

86 57 d3 59

c6 7a f7 92

de 36 f3 93

d4 11 fe 0f

3b 44 06 73

cb ab 62 37

19 b7 07 ec

2c a5 f2 43

5c 73 22 8c

65 0e a3 dd

f1 96 90 50

f8 b4 0c 4c

67 37 24 ff

ae a5 c1 ea

e8 21 97 bc

41 8d fe 29

85 9a 36 16

e4 06 78 87

9b fd 88 65

41 8d fe 29

9a 36 16 85

78 87 e4 06

65 9b fd 88

2a 47 c4 48

83 e8 18 ba

84 18 27 23

eb 10 0a f3

58 fd 0f 4c

9d ee cc 40

36 38 9b 46

eb 7d ed bd

Table 6.5 A E S Example (2 of 2)

Start of Round After SubBytes After ShiftRows After MixColumns Round Key

72 ba cb 04

1e 06 d4 fa

b2 20 bc 65

00 6d e7 4e

40 f4 1f f2

72 6f 48 2d

37 b7 65 4d

63 3c 94 2f

40 f4 1f f2

6f 48 2d 72

65 4d 37 b7

2f 63 3c 94

7b 05 42 4a

1e d0 20 40

94 83 18 52

94 c4 43 fb

71 8c 83 cf

c7 29 e5 a5

4c 74 ef a9

c2 bf 52 ef

0a 89 c1 85

d9 f9 c5 e5

d8 f7 f7 fb

56 7b 11 14

67 a7 78 97

35 99 a6 d9

61 68 68 0f

b1 21 82 fa

67 a7 78 97

99 a6 d9 35

68 0f 61 68

fa b1 21 82

ec 1a c0 80

0c 50 53 c7

3b d7 00 ef

b7 22 72 e0

37 bb 38 f7

14 3d d8 7d

93 e7 08 a1

48 f7 a5 4a

db a1 f8 77

18 6d 8b ba

a8 30 08 4e

ff d5 d7 aa

b9 32 41 f5

ad 3c 3d f4

c2 04 30 2f

16 03 0e ac

b9 32 41 f5

3c 3d f4 ad

30 2f c2 04

ac 16 03 0e

b1 1a 44 17

3d 2f ec b6

0a 6b 2f 42

9f 68 f3 b1

48 f3 cb 3c

26 1b c3 be

45 a2 aa 0b

20 d7 72 38

f9 e9 8f 2b

1b 34 2f 08

4f c9 85 49

bf bf 81 89

99 1e 73 f1

af 18 15 30

84 dd 97 3b

08 08 0c a7

99 1e 73 f1

18 15 30 af

97 3b 84 dd

a7 08 08 0c

31 30 3a c2

ac 71 8c c4

46 65 48 eb

6a 1c 31 62

fd 0e c5 f9

0d 16 d5 6b

42 e0 4a 41

cb 1c 6e 56

cc 3e ff 3b

a1 67 59 af

04 85 02 aa

a1 00 5f 34

4b b2 16 e2

32 85 cb 79

f2 97 77 ac

32 63 cf 18

4b b2 16 e2

85 cb 79 32

77 ac f2 97

18 32 63 cf

b4 ba 7f 86

8e 98 4d 26

f3 13 59 18

52 4e 20 76

ff 08 69 64

0b 53 34 14

84 bf ab 8f

4a 7c 43 b9

Table 6.6 Avalanche Effect in A E S:

Change in Plaintext (1 of 2)

Round Number of Bits

that Differ

0123456789abcdeffedcba9876543210

0023456789abcdeffedcba9876543210

0 0e3634aece7225b6f26b174ed92b5588

0f3634aece7225b6f26b174ed92b5588

1 657470750fc7ff3fc0e8e8ca4dd02a9c

c4a9ad090fc7ff3fc0e8e8ca4dd02a9c

2 5c7bb49a6b72349b05a2317ff46d1294

fe2ae569f7ee8bb8c1f5a2bb37ef53d5

3 7115262448dc747e5cdac7227da9bd9c

ec093dfb7c45343d689017507d485e62

4 f867aee8b437a5210c24c1974cffeabc

43efdb697244df808e8d9364ee0ae6f5

5 721eb200ba06206dcbd4bce704fa654e

7b28a5d5ed643287e006c099bb375302

Table 6.6 Avalanche Effect in A E S:

Change in Plaintext (2 of 2)

Round Number of Bits

that Differ

6 0ad9d85689f9f77bc1c5f71185e5fb14

3bc2d8b6798d8ac4fe36a1d891ac181a

7 db18a8ffa16d30d5f88b08d777ba4eaa

9fb8b5452023c70280e5c4bb9e555a4b

8 f91b4fbfe934c9bf8f2f85812b084989

20264e1126b219aef7feb3f9b2d6de40

9 cca104a13e678500ff59025f3bafaa34

b56a0341b2290ba7dfdfbddcd8578205

10 ff0b844a0853bf7c6934ab4364148fb9

612b89398d0600cde116227ce72433f0

Table 6.7 Avalanche Effect in A E S:

Change in Key (1 of 2)

Round Number of Bits

that Differ

0123456789abcdeffedcba9876543210

0 0e3634aece7225b6f26b174ed92b5588

0f3634aece7225b6f26b174ed92b5588

1 657470750fc7ff3fc0e8e8ca4dd02a9c

c5a9ad090ec7ff3fc1e8e8ca4cd02a9c

2 5c7bb49a6b72349b05a2317ff46d1294

90905fa9563356d15f3760f3b8259985

3 7115262448dc747e5cdac7227da9bd9c

18aeb7aa794b3b66629448d575c7cebf

4 f867aee8b437a5210c24c1974cffeabc

f81015f993c978a876ae017cb49e7eec

5 721eb200ba06206dcbd4bce704fa654e

5955c91b4e769f3cb4a94768e98d5267

Table 6.7 Avalanche Effect in A E S:

Change in Key (2 of 2)

Round Number of Bits

that Differ

6 0ad9d85689f9f77bc1c5f71185e5fb14

dc60a24d137662181e45b8d3726b2920

7 db18a8ffa16d30d5f88b08d777ba4eaa

fe8343b8f88bef66cab7e977d005a03c

8 f91b4fbfe934c9bf8f2f85812b084989

da7dad581d1725c5b72fa0f9d9d1366a

9 cca104a13e678500ff59025f3bafaa34

0ccb4c66bbfd912f4b511d72996345e0

10 ff0b844a0853bf7c6934ab4364148fb9

fc8923ee501a7d207ab670686839996b

A E S Implementation

• A E S decryption cipher is not

identical to the encryption

cipher

– The sequence of

transformations differs

although the form of the

key schedules is the

same

– Has the disadvantage

that two separate

software or firmware

modules are needed for

applications that require

both encryption and

decryption

• Two separate changes are

needed to bring the

decryption structure in line

with the encryption

structure

• The first two stages of the

decryption round need to

be interchanged

• The second two stages of

the decryption round need

to be interchanged

Interchanging InvShiftRows and Inv

SubBytes

• InvShiftRows affects the sequence of bytes in State but

does not alter byte contents and does not depend on byte

contents to perform its transformation

• InvSubBytes affects the contents of bytes in State but does

not alter byte sequence and does not depend on byte

sequence to perform its transformation

Thus, these two operations commute and can be

interchanged

Interchanging AddRoundKey and

InvMixColumns

• The transformations AddRoundKey and InvMixColumns do

not alter the sequence of bytes in State

• If we view the key as a sequence of words, then both

AddRoundKey and InvMixColumns operate on State one

column at a time

• These two operations are linear with respect to the column

input

Figure 6.10 Equivalent Inverse Cipher

Implementation Aspects (1 of 2)

• AES can be implemented very efficiently on an 8-bit

processor

• AddRoundKey is a bytewise XOR operation

• ShiftRows is a simple byte-shifting operation

• SubBytes operates at the byte level and only requires a

table of 256 bytes

• MixColumns requires matrix multiplication in the field

GF(28), which means that all operations are carried out on

bytes

Implementation Aspects (2 of 2)

• Can efficiently implement on a 32-bit processor

– Redefine steps to use 32-bit words

– Can precompute 4 tables of 256-words

– Then each column in each round can be computed

using 4 table lookups + 4 XORs

– At a cost of 4Kb to store tables

• Designers believe this very efficient implementation was a

key factor in its selection as the AES cipher

Summary

• Present an overview of the general structure of Advanced

Encryption Standard (AES)

• Understand the four transformations used in AES

• Explain the AES key expansion algorithm

• Understand the use of polynomials with coefficients in

GF(28)

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