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    Encryption

    DIGITAL COMMUNICATIONS

    Lectured by Assoc. Prof. Dr.Thuong Le-Tien

    Oct, 2011

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    Data Encryption

    Encryption is the transformation of plain text into ciphertext;

    decryption is the inverse of this process.

    The cipher is the set of transformation, and the keys are the

    transformation parameter.

    There are two type of ciphers: Block encryption is where

    fixed blocks of plaintext are operated on in a combinatorial

    Fashion, and stream encryption is similar to convolution

    Encoding in that all segments of the plaintext are processed

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    Secret key system

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    Public/private key system

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    1 2 3 4 5

    1 A B C D E

    2 F G H IJ K

    3 L M N O P

    4 Q R S T U

    5 V W X Y Z

    Polybius square

    Plain text : N O W I S T H E T I M E

    Cipher text: 33 43 25 42 34 44 32 51 44 42 23 51

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    Key: TYPETYPETYPE

    Plain text : NOWISTHETIME

    Cipher text : GMLMLRWIMGBITrithemius progressive key

    A b c d e f g h i j k l m n o p q r s t u v w x y z

    0 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

    1 B C D E F G H I J K L M N O P Q R S T U V W X Y Z A

    2 C D E F G H I J K L M N O P Q R S T U V W X Y Z A B

    3 D E F G H I J K L M N O P Q R S T U V W X Y Z A B C

    4 E F G H I J K L M N O P Q R S T U V W X Y Z A B C D

    5 F G H I J K L M N O P Q R S T U V W X Y Z A B C D E

    6 G H I J K L M N O P Q R S T U V W X Y Z A B C D E F

    7 H I J K L M N O P Q R S T U V W X Y Z A B C D E F G

    8 I J K L M N O P Q R S T U V W X Y Z A B C D E F G H

    9 J K L M N O P Q R S T U V W X Y Z A B C D E F G H I

    10 K L M N O P Q R S T U V W X Y Z A B C D E F G H I J

    11 L M N O P Q R S T U V W X Y Z A B C D E F G H I J K

    12 M N O P Q R S T U V W X Y Z A B C D E F G H I J K L

    13 N O P Q R S T U V W X Y Z A B C D E F G H I J K L M

    14 O P Q R S T U V W X Y Z A B C D E F G H I J K L M N

    15 P Q R S T U V W X Y Z A B C D E F G H I J K L M N O

    16 Q R S T U V W X Y Z A B C D E F G H I J K L M N O P17 R S T U V W X Y Z A B C D E F G H I J K L M N O P Q

    18 S T U V W X Y Z A B C D E F G H I J K L M N O P Q R

    19 T U V W X Y Z A B C D E F G H I J K L M N O P Q R S

    20 U V W X Y Z A B C D E F G H I J K L M N O P Q R S T

    21 V W X Y Z A B C D E F G H I J K L M N O P Q R S T U

    22 W X Y Z A B C D E F G H I J K L M N O P Q R S T U V

    23 X Y Z A B C D E F G H I J K L M N O P Q R S T U V W

    24 Y Z A B C D E F G H I J K L M N O P Q R S T U V W X

    25 Z A B C D E F G H I J K L M N O P Q R S T U V W X Y

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    Permutation examples (a) straight (b) expanded(c) compressed

    Figure 13.4-3

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    S-box exampleFigure 13.4-4

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    DES flowchartFigure 13.4-5

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    Substitute and permute blockFigure 13.4-6

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    58 50 42 34 26 18 10 2

    60 52 44 36 28 20 12 4

    62 54 46 38 30 22 14 664 56 48 40 32 24 16 8

    57 49 41 33 25 17 9 1

    59 51 43 35 27 19 11 3

    61 53 45 37 29 21 13 5

    63 55 47 39 31 23 15 7

    Initial permutation

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    32 1 2 3 4 5

    4 5 6 7 8 9

    8 9 10 11 12 1312 13 14 15 16 17

    16 17 18 19 20 21

    20 21 22 23 24 25

    24 25 26 27 28 29

    28 29 30 31 32 1

    16 7 20 21

    29 12 28 17

    1 15 23 26

    5 18 31 10

    2 8 24 14

    32 27 3 9

    19 13 30 6

    22 11 4 25

    E Box

    P Box

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    15

    S BoxCot

    Hang 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

    0 14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7

    S11 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8

    2 4 1 14 8 13 6 2 11 1 5 12 9 7 3 10 5 0

    3 15 12 8 2 4 9 1 7 5 11 3 14 10 0 6 13

    0 15 1 8 14 6 11 3 4 9 7 2 13 12 0 5 10

    S21 3 13 4 7 15 2 8 14 1 2 0 1 10 6 9 11 5

    2 0 14 7 11 10 4 13 1 5 8 12 6 9 3 2 15

    3 13 8 10 1 3 15 4 2 11 6 7 12 0 5 14 9

    0 10 0 9 14 6 3 15 5 1 13 12 17 11 4 2 8

    S31 13 7 0 9 3 4 6 10 2 8 5 14 1 2 11 15 1

    2 13 6 4 9 8 15 3 0 11 1 2 12 5 10 14 7

    3 1 10 13 0 6 9 8 7 4 15 14 3 11 5 2 12

    0 7 13 14 3 0 6 9 10 1 2 8 5 11 12 4 15

    S41 13 8 11 5 6 15 0 3 4 7 2 12 1 10 14 9

    2 10 6 9 0 12 11 7 13 1 5 1 3 14 5 2 8 4

    3 3 15 0 6 10 1 13 8 9 4 5 11 12 7 2 14

    0 2 12 4 1 7 10 11 6 8 5 3 15 1 3 0 14 9

    S51 14 11 2 12 4 7 13 1 5 0 15 10 3 9 8 6

    2 4 2 1 11 10 13 7 8 15 9 12 5 6 3 0 14

    3 11 8 12 7 1 14 2 13 6 15 0 9 10 4 5 3

    0 12 1 10 15 9 2 6 8 0 13 3 4 14 7 5 11

    S61 10 15 4 2 7 12 9 5 6 1 13 14 0 11 3 8

    2 9 14 1 5 5 2 8 12 3 7 0 4 10 1 13 11 6

    3 4 3 2 12 9 5 15 0 11 14 1 7 6 0 8 13

    0 4 11 2 14 1 5 0 8 13 3 12 9 7 5 10 6 1

    S71 13 0 11 7 4 9 1 10 1 4 3 5 12 2 15 8 6

    2 1 4 11 13 1 2 3 7 14 1 0 15 6 8 0 5 9 2

    3 6 11 13 8 1 4 10 7 9 5 0 15 14 2 3 12

    0 13 2 8 4 6 15 11 1 10 9 3 14 5 0 12 7

    S81 1 15 1 3 8 10 3 7 4 12 5 6 11 0 14 9 2

    2 7 11 4 1 9 12 14 2 0 6 10 13 1 5 3 5 8

    3 2 1 14 7 4 10 8 13 15 12 9 0 3 5 6 11

    b0, b5 for rows; b1, b2, b3, b4 for columns

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    Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

    Key generator flowchartFigure 13.4-7

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    Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

    32 to 48 bit expansionFigure 13.4-8

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    Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

    Details of 48 to 32-bit S-boxFigure 13.4-9

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    In cryptography, the Advanced Encryption Standard (AES)

    is a symmetric-key encryption standard adopted by the U.S.

    government.

    The standard comprises threeblock ciphers, AES-128, AES-

    192 and AES-256, adopted from a larger collection originally

    published as Rijndael. Each of these ciphers has a 128-bit

    block size, with key sizes of 128, 192 and 256 bits,

    respectively.

    The AES ciphers have been analyzed extensively and are nowused worldwide, as was the case with its predecessor, the Data

    Encryption Standard (DES).

    AES

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    Description of the cipherAES is based on a design principle known as a Substitution

    permutation network. It is fast in both software and

    hardware.[6] Unlike its predecessor, DES, AES does not use a

    Feistel network.

    AES has a fixedblock size of 128bits and a key size of 128,192, or 256 bits, whereas Rijndael can be specified with

    block and key sizes in any multiple of 32 bits, with a

    minimum of 128 bits. The blocksize has a maximum of 256

    bits, but the keysize has theoretically no maximum.

    AES operates on a 44 array of bytes, termed the state

    (versions of Rijndael with a larger block size have additional

    columns in the state). Most AES calculations are done in a

    special finite field.

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    High-level description of the algorithm

    KeyExpansionround keys are derived from the cipher key using Rijndael's key schedule

    * Initial Round

    AddRoundKeyeach byte of the state is combined with

    the round key using bitwise xor

    * RoundsSubBytesa non-linear substitution step where each

    byte is replaced with another according to a lookup table.

    ShiftRowsa transposition step where each row of the

    state is shifted cyclically a certain number of steps.

    MixColumnsa mixing operation which operates on the

    columns of the state, combining the four bytes in each column.AddRoundKey

    * Final Round (no MixColumns)

    SubBytes

    ShiftRows

    AddRoundKey

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