Traceroute Assignment

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• Traceroute Assignment

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• Base64 Encoding
• The SMTP protocol only allows 7 bit ASCII data,
  so how can you send me a picture of Avril
  Lavigne, which is an 8 bit binary JPEG file?
• 
  Encode it.

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• But back to Base64 encoding

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• The encoding method used is simple and elegant.
  Each group of 3 bytes is encoded as 4 bytes, each
  containing only 6 bits of data. These are sent as
  7-bit ASCII.
• Why is it called BASE64? Because 6 bits gives us
  decimal numbers in the range 0-63, by assigning a
  character to each decimal value (64 of them), we
  can encode any number in the range 0-63 by just
  one single character. Base 64 requires 64
  symbols, just as decimal (base 10) requires 10
  symbols and hexadecimal (base 16), requires 16
  symbols.

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• The Base64 Alphabet (values given in
  decimal)
• 0 A 17 R 34 i
  51 z
• 1 B 18 S 35 j
  52 0
• 2 C 19 T 36 k
  53 1
• 3 D 20 U 37 l
  54 2
• 4 E 21 V 38 m
  55 3
• 5 F 22 W 39 n
  56 4
• 6 G 23 X 40 o
  57 5
• 7 H 24 Y 41 p
  58 6
• 8 I 25 Z 42 q
  59 7
• 9 J 26 a 43 r
  60 8
• 10 K 27 b 44 s
  61 9
• 11 L 28 c 45 t
  62
• 12 M 29 d 46 u
  63 /
• 13 N 30 e 47 v
• 14 O 31 f 48 w
  (pad)
• 15 P 32 g 49 x

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• We take 3 bytes and encode to 4 bytes
•  
• 3 bytes to encode 10101111 11001010 11101010
•  
• 24 bit stream 101011111100101011101010
•  
• Four 6-bit values 101011 111100 101011
  101010
• decimal value 43 60 43 42
• Base64 character r 8 r q
•  
• We then use the table to send the ASCII codes for
  each BASE64 character.

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• The Base64 Alphabet (values given in
  decimal)
• 0 A 17 R 34 i
  51 z
• 1 B 18 S 35 j
  52 0
• 2 C 19 T 36 k
  53 1
• 3 D 20 U 37 l
  54 2
• 4 E 21 V 38 m
  55 3
• 5 F 22 W 39 n
  56 4
• 6 G 23 X 40 o
  57 5
• 7 H 24 Y 41 p
  58 6
• 8 I 25 Z 42 q
  59 7
• 9 J 26 a 43 r
  60 8
• 10 K 27 b 44 s
  61 9
• 11 L 28 c 45 t
  62
• 12 M 29 d 46 u
  63 /
• 13 N 30 e 47 v
• 14 O 31 f 48 w
  (pad)
• 15 P 32 g 49 x

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• There is a slight problem when the bit stream to
  be encoded is not an exact multiple of 3.
• In this case, zeros are added to make the last
  group of bytes (ie 1 or 2 bytes) up to a multiple
  of 6 bits.
• One or two padding characters () are added to
  make the encoded data a multiple of 4 bytes.

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• For example
•  
• 4 bytes to encode 10101111 11001010 11101010
  00100011
•  
• 32 bit stream 10101111110010101110101000100
  011
•  
• Six 6-bit values 101011 111100 101011 101010
  001000 110000
• decimal value 43 60 43 42
  08 48
• Base64 characters r 8 r q I
  w
• Add padding r 8 r q I
  w
•  
• In this case four zeros are added, then two
  padding characters.

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• The Base64 Alphabet (values given in
  decimal)
• 0 A 17 R 34 i
  51 z
• 1 B 18 S 35 j
  52 0
• 2 C 19 T 36 k
  53 1
• 3 D 20 U 37 l
  54 2
• 4 E 21 V 38 m
  55 3
• 5 F 22 W 39 n
  56 4
• 6 G 23 X 40 o
  57 5
• 7 H 24 Y 41 p
  58 6
• 8 I 25 Z 42 q
  59 7
• 9 J 26 a 43 r
  60 8
• 10 K 27 b 44 s
  61 9
• 11 L 28 c 45 t
  62
• 12 M 29 d 46 u
  63 /
• 13 N 30 e 47 v
• 14 O 31 f 48 w
  (pad)
• 15 P 32 g 49 x

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• Example Email Message with GIF attachment -
  BASE64 encoded
•   
• MIME-Version 1.0
• Content-Type Multipart/mixed BOUNDARY"Part10510
  241718.A"
• --Part10510241718.A
• Content-Type Text/Plain charset"us-ascii"
• This email contains an attachment - a small GIF
  file.
•  
• Jim
• ----------------------
•  
• --Part10510241718.A
• Content-Type Image/gif name"pin.gif"
• Content-Transfer-Encoding base64
• Content-Disposition attachment
  filename"pin.gif"
•  
• R0lGODlhDgARAPIAAAAAAL8AAICAgP8AAP///wAAAAAAAAAAAC
  H5BAEAAAQA
• LAAAAAAOABEAAAM/SArRoRAy5yIBMwwynqTb1kjMtHHeFWRal2
  JUTAZCPJJA

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• CRC Cyclic Redundancy Check
•  
• Errors happen!
• One simple method of error checking is to do a
  checksum. All the bytes in the message are added
  up and the result is transmitted with the
  message. The receiver does the sum again and
  compares the result with the transmitted
  checksum. This can detect lots of errors, but it
  is easy to see that one bit changed in one byte
  could be cancelled out by one bit changed in
  another byte. This is not a very secure method
  of error checking.
•  
• The CRC is extensively used for error checking in
  many network protocols.

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• It is based on some very complex mathematics,
  concerned with polynomial arithmetic. If you wish
  to investigate the theory behind CRC, this is a
  good starting point http//www.ross.net/crc/link
  s.html
•  
• Why polynomial arithmetic? In any number system,
  numbers can be considered as polynomials, in our
  familiar decimal system, the number 3807 can be
  expressed as
• 3103810201017100
• Things are actually simplified if we are working
  in binary, as the coefficients can only be 0 or
  1. So if we consider the binary number 101101.
  This is
•   125024123122021120 or
  x5x3x21

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• The CRC works by division, rather than addition.
  The data (the transmitted message) is considered
  to be a big binary number, which could be
  represented as a polynomial. This polynomial is
  divided by another, carefully chosen, polynomial
  to give a result which is used to check the data,
  in the same way as a checksum.
•  
• By using a division algorithm, this method of
  error checking can detect many more errors than a
  simple checksum.

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• Rather than using a straightforward binary
  division, the CRC uses modulo-2 arithmetic. This
  means effectively doing a normal long division,
  but with a few strange rules. In modulo-2
  arithmetic, subtraction and addition are
  identical, since there are no carries. The
  logical function is actually XOR.
•  
• Deciding if the divisor goes into the current
  part of the dividend simply depends if the MSB is
  the same(1). So 1111 would go into 1000.

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• Example from the book
• Data to be checked 101110
• Generator polynomial 1001 (x31)
•  
• The data is first multiplied by 23, since the
  generator polynomial is of order 3, done by
  adding 3 zeros 101110000
•  
• Next this value is divided by the generator
  polynomial (1001), by long division, using
  modulo-2 arithmetic, where subtraction becomes
  the XOR function
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•  
• 101011
• ---------------
• 1001 101110000
• 1001
• ----
• 101
• 000
• ----
• 1010
• 1001
• ----
• 110
• 000
• ----
• 1100
• 1001
• ----
• 1010

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• The value actually transmitted is the data plus
  the remainder ie, in this case 101110011
• When the CRC is calculated at the receiver the
  value should be zero, as the remainder value has
  been added to the original data.

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•  
• 101011
• ---------------
• 1001 101110000
• 1001
• ----
• 101
• 000
• ----
• 1000
• 1001
• ----
• 110
• 000
• ----
• 1100
• 1001
• ----
• 1010

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• International standards have been established for
  various different CRC generators of different bit
  lengths. For example, this is the CRC-32-IEEE
  802.3 polynomial, used for Ethernet
• x32 x26 x23 x22 x16 x12 x11 x10
  x8 x7 x5 x4 x2 x 1 (V.42)
•  
• The CRC can always detect burst errors of fewer
  than r1 bits (where r is the order of the
  generator polynomial). There is also a good
  probability of longer burst errors being
  detected. The CRC can also detect any odd number
  of bit errors.
•  
• The CRC is easy to implement in software and is
  often implemented in hardware (using shift
  registers and xor gates).

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• The End