The document provides an overview of cipher techniques including:
- Classical techniques like transposition ciphers, substitution ciphers including the Caesar and Playfair ciphers, and polyalphabetic ciphers like the Vigenere cipher.
- Modern techniques like stream ciphers which encrypt bits one at a time using a pseudorandom keystream, and block ciphers which encrypt blocks of text.
- It also discusses cryptanalysis techniques for analyzing ciphers and discusses how to build more secure systems using techniques like the one-time pad or combining multiple ciphers.
2. Road Map
Basic Terminology
Cryptosystem
Classical Cryptography
Algorithm Types and Modes
Data Encryption Standard
Other Stream & Block Ciphers
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3. Basic Terminology
plaintext - the original message
ciphertext - the coded message
cipher - algorithm for transforming plaintext to ciphertext
key - info used in cipher known only to sender/receiver
encipher (encrypt) - converting plaintext to ciphertext
decipher (decrypt) - recovering ciphertext from plaintext
cryptography - study of encryption principles/methods
cryptanalysis (codebreaking) - the study of principles/ methods
of deciphering ciphertext without knowing key
cryptology - the field of both cryptography and cryptanalysis
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4. Cryptosystem
A cryptosystem is a five-tuple (P,C,K,E,D),
where the following are satisfied:
1. P is a finite set of possible plaintexts.
2. C is a finite set of possible ciphertexts.
3. K, the key space, is a finite set of possible
keys
4. ∀K∈K, ∃EK∈E (encryption rule), ∃DK∈D
(decryption rule).
Each EK: P→C and DK: C→P are functions
such that ∀x∈P, DK(EK(x)) = x.
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5. Cryptography
Cryptography
Symmetric / private key / single key
Asymmetric / public-key / two - key
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8. Requirements
Two requirements for secure use of
symmetric encryption:
a strong encryption algorithm
a secret key known only to sender / receiver
Y = EK(X)
X = DK(Y)
assume encryption algorithm is known
implies a secure channel to distribute key
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10. Types of Cryptanalytic Attacks
adversary needs
strongest attack ciphertext only
only know algorithm / ciphertext, statistical, can
identify plaintext, or worse: the key
known plaintext
know/suspect plaintext & ciphertext to attack
cipher
chosen plaintext
select plaintext and obtain ciphertext to attack
cipher
chosen ciphertext
select ciphertext and obtain plaintext to attack
adversary’s attacks cipher
can be weaker chosen text
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select either plaintext or ciphertext to en/decrypt 10
to
11. Brute Force Search
always possible to simply try every key
most basic attack, proportional to size of key
space
assume either know / recognise plaintext
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12. Transposition Ciphers
Consider classical transposition or
permutation ciphers
these hide the message by rearranging the
letter order
without altering the actual letters used
can recognise these since have the same
frequency distribution as the original text
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13. Rail Fence cipher
writemessage letters out diagonally over a
number of rows
then read off cipher row by row
eg. write message out as:
m e m a t r h t g p r y
e t e f e t e o a a t
giving ciphertext
MEMATRHTGPRYETEFETEOAAT
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14. Row Transposition Ciphers
a more complex scheme
write letters of message out in rows over a
specified number of columns
then reorder the columns according to some
key before reading off the rows
Key: 4 3 1 2 5 6 7
Plaintext: a t t a c k p
o s t p o n e
d u n t i l t
w o a m x y z
Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ
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15. Classical Substitution Ciphers
where letters of plaintext are replaced by
other letters or by numbers or symbols
or if plaintext is viewed as a sequence of bits,
then substitution involves replacing plaintext
bit patterns with ciphertext bit patterns
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16. Caesar Cipher
earliest known substitution cipher
by Julius Caesar
first attested use in military affairs
replaces each letter by 3rd letter after it
example:
meet me after the toga party
PHHW PH DIWHU WKH WRJD SDUWB
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17. Caesar Cipher
can define transformation as:
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
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
mathematically give each letter a number
a b c d e f g h i j k l m
0 1 2 3 4 5 6 7 8 9 10 11 12
n o p q r s t u v w x y Z
13 14 15 16 17 18 19 20 21 22 23 24 25
then have Caesar cipher as:
C = E(p) = (p + k) mod (26)
p = D(C) = (C – k) mod (26)
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18. Monoalphabetic Cipher
rather than just shifting the alphabet
could shuffle (jumble) the letters arbitrarily
each plaintext letter maps to a different random
ciphertext letter
hence key is 26 letters long
Plain: abcdefghijklmnopqrstuvwxyz
Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN
Plaintext: ifwewishtoreplaceletters
Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA
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19. Playfair Cipher
not even the large number of keys in a
monoalphabetic cipher provides security
one approach to improving security was to
encrypt multiple letters
the Playfair Cipher is an example
invented by Charles Wheatstone in 1854, but
named after his friend Baron Playfair
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20. Playfair Key Matrix
a 5X5 matrix of letters based on a keyword
(I and J aren’t distinguished)
fill in letters of keyword (sans duplicates)
fill rest of matrix with other letters
eg. using the keyword MONARCHY
MONAR
CHYBD
EFGIK
LPQST
UVWXZ
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21. Encrypting and Decrypting
plaintext encrypted two letters at a time:
1. each letter is replaced by the one in its row in the column
of the other letter of the pair, eg. “hs" encrypts to "BP",
and “ea" to "IM" or "JM" (as desired). Except when that
doesn’t work!
2. if a pair is a repeated letter, insert a filler like 'X', eg.
"balloon" transformed to "ba lx lo on"
3. if both letters fall in the same row, replace each with
letter to right (wrapping back to start from end), eg.
“ar" encrypts as "RM"
4. if both letters fall in the same column, replace each with
the letter below it (again wrapping to top from bottom),
eg. “mu" encrypts to "CM"
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22. Polyalphabetic Ciphers
another approach to improving security is to use
multiple cipher alphabets
called polyalphabetic substitution ciphers
makes cryptanalysis harder with more alphabets to
guess and flatter frequency distribution
use a key to select which alphabet is used for each
letter of the message
use each alphabet in turn
repeat from start after end of key is reached
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23. Vigenère Cipher
simplest polyalphabetic substitution cipher is
the Vigenère Cipher
effectively multiple caesar ciphers
key is multiple letters long K = k1 k2 ... kd
ith letter specifies ith alphabet to use
use each alphabet in turn
repeat from start after d letters in message
decryption simply works in reverse
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24. Example
write the plaintext out
write the keyword repeated above it
use each key letter as a caesar cipher key
encrypt the corresponding plaintext letter
eg using keyword deceptive
key: deceptivedeceptivedeceptive
plaintext: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGRZGVTWAVZHCQYGLMGJ
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25. Autokey Cipher
ideally want a key as long as the message
Vigenère proposed the autokey cipher
with keyword is prefixed to message as key
knowing keyword can recover the first few letters
use these in turn on the rest of the message
but still have frequency characteristics to attack
eg. given key deceptive
key: deceptivewearediscoveredsav
plaintext: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLA
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26. One-Time Pad
ifa truly random key as long as the message
is used, the cipher will be secure
called a One-Time pad
is unbreakable since ciphertext bears no
statistical relationship to the plaintext
since for any plaintext & any ciphertext
there exists a key mapping one to other
unconditional security! why look any
further??
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27. Product Ciphers
ciphers using substitutions or transpositions are not
secure because of language characteristics
hence consider using several ciphers in succession
to make harder (Shannon)
two substitutions make a more complex substitution
two transpositions make more complex transposition
but a substitution followed by a transposition makes a new
much harder cipher
this is bridge from classical to modern ciphers
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28. Rotor Machines
before modern ciphers, rotor machines were most
common product cipher
were widely used in WW2
German Enigma, Allied Hagelin, Japanese Purple
implemented a very complex, varying substitution
cipher
used a series of cylinders, each giving one
substitution, which rotated and changed after each
letter was encrypted
with 3 cylinders have 263=17576 alphabets
3! rearrangements of cylinders in Enigma
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29. Steganography
an alternative to encryption
hides existence of message
using only a subset of letters/words in a longer
message marked in some way
using invisible ink
hiding in LSB in graphic image or sound file
has drawbacks
high overhead to hide relatively few info bits
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30. Algorithm Types and Modes
An Algorithm type defines what size of plain
text should be encrypted in each step of
algorithm
An Algorithm mode defines the details of the
cryptographic algorithm, once the type is
decided.
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31. Algorithm Types
Stream Ciphers
Block Ciphers
Algorithm Modes
ElectronicCode Book Work On Block Cipher
Cipher Block Chaining
Cipher FeedBack
Work On Block Ciphers acting as
Output FeedBack Stream Cipher
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32. Stream, Block Ciphers
E encipherment function
Ek(b) encipherment of message b with key k
In what follows, m = b1b2 …, each bi of fixed length
Block cipher
Ek(m) = Ek(b1)Ek(b2) …
Stream cipher
k = k1k2 …
Ek(m) = Ek1(b1)Ek2(b2) …
If k1k2 … repeats itself, cipher is periodic and the kength of
its period is one cycle of k1k2 …
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33. Stream Ciphers
Often (try to) implement one-time pad by
xor’ing each bit of key with one bit of
message
Example:
m = 00101
k = 10010
c = 10111
But how to generate a good key?
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34. Synchronous Stream Ciphers
n-stage Linear Feedback Shift Register:
consists of
n bit register r = r0…rn–1
n bit tap sequence t = t0…tn–1
Use:
Use rn–1 as key bit
Compute x = r0t0 ⊕ … ⊕ rn–1tn–1
Shift r one bit to right, dropping rn–1, x becomes r0
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35. Operation
…
r0 … rn–1 ⊕ bi
…
ci
r0´ … rn–1´ ri´ = ri–1,
0<i≤n
r0t0 + … + rn–1tn–1
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36. Example
4-stage LFSR; t = 1001
r ki new bit computation new r
0010 0 01⊕00⊕10⊕01 = 0 0001
0001 1 01⊕00⊕00⊕11 = 1 1000
1000 0 11⊕00⊕00⊕01 = 1 1100
1100 0 11⊕10⊕00⊕01 = 1 1110
1110 0 11⊕10⊕10⊕01 = 1 1111
1111 1 11⊕10⊕10⊕11 = 0 0111
0111 1 11⊕10⊕10⊕11 = 1 1011
Key sequence has period of 15 (010001111010110)
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37. NLFSR
n-stage Non-Linear Feedback Shift Register:
consists of
n bit register r = r0…rn–1
Use:
Use rn–1 as key bit
Compute x = f(r0, …, rn–1); f is any function
Shift r one bit to right, dropping rn–1, x becomes r0
Note same operation as LFSR but more general
bit replacement function
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39. Self-Synchronous Stream
Cipher
Takekey from message itself (autokey)
Example: Vigenère, key drawn from plaintext
key XTHEBOYHASTHEBA
plaintext THEBOYHASTHEBAG
ciphertext QALFPNFHSLALFCT
Problem:
Statistical regularities in plaintext show in key
Once you get any part of the message, you can
decipher more
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40. Another Example
Take key from ciphertext (autokey)
Example: Vigenère, key drawn from
ciphertext
key XQXBCQOVVNGNRTT
plaintext THEBOYHASTHEBAG
ciphertext QXBCQOVVNGNRTTM
Problem:
Attacker gets key along with ciphertext, so
deciphering is trivial
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41. Block Cipher
Block Cipher – treat a
block of plaintext as a whole
Feistel Cipher
DES/3DES/AES
Stream coding – encrypt one
bit or byte at a time
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42. Block Ciphers
Encipher, decipher multiple bits at once
Each block enciphered independently
Problem: identical plaintext blocks produce
identical ciphertext blocks
Example: two database records
MEMBER: HOLLY INCOME $100,000
MEMBER: HEIDI INCOME $100,000
Encipherment:
ABCQZRME GHQMRSIB CTXUVYSS RMGRPFQN
ABCQZRME ORMPABRZ CTXUVYSS RMGRPFQN
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43. Solutions
Insert information about block’s position into
the plaintext block, then encipher
Cipher block chaining:
Exclusive-or current plaintext block with previous
ciphertext block:
c0 = Ek(m0 ⊕ I)
ci = Ek(mi ⊕ ci–1) for i > 0
where I is the initialization vector
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44. Algorithm Modes
ElectronicCode Book Work On Block Cipher
Cipher Block Chaining
Cipher FeedBack
Work On Block Ciphers acting as
Output FeedBack Stream Cipher
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45. ECB (Electronic CodeBook) Mode
Encryption: for 1≤j≤t, cj <= EK(xj).
Decryption: for 1≤j≤t, xj <= DK(cj).
Identical plaintext (under the same key) result in
identical ciphertext
blocks are enciphered independently of other
blocks
bit errors in a single ciphertext affect decipherment
of that block only
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46. ECB Mode (Cont’d)
xj
n
key E E-1 key
n
x’j = xj
cj
encipherment decipherment
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47. CBC (Cipher-Block Chaining)
Mode
C0=IV Cj
C j-1
n key
xj ⊕ E-1
⊕
C j-1
key E
Cj
<Encipherment> n X’j = xj
<Decipherment>
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48. CBC Mode (Cont’d)
Encryption: c0 ← IV, cj ← EK(cj−1⊕ xj)
Decryption: c0 ← IV, xj ← cj−1 ⊕ E−1K(cj)
chaining causes ciphertext cj to depend on all preceding
plaintext
a single bit error in cj affects decipherment of blocks cj and
cj+1
self-synchronizing: error cj (not cj+1, cj+2) is correctly
decrypted to xj+2.
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49. CFB-r(Cipher FeedBack) Mode
r-bit Shift r-bit Shift
I1=IV
key E key E
leftmost r bits Oj leftmost r bits Oj
xj ci ci xj
Encipherment Decipherment
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50. OFB(Output FeedBack) Mode
with full(or r-bit) feedback
Ij r-bit Shift Ij r-bit Shift
I1=IV
key E key E
Leftmost r-bits Oj Leftmost r-bits Oj
xj cj cj xj
Encipherment Deciphering
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51. Data Encryption
Standard
The Data Encryption Standard (DES)
specifies a FIPS approved
cryptographic algorithm as required
by FIPS 140-1.(Federal Information
Processing Standards 140-1)
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55. The permuted input block is then the input
to a complex key-dependent computation.
The output of that computation (preoutput)
is then subjected to the next permutation
which is the inverse of the initial
permutation.
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57. Let K be a block of 48 bits chosen from the
64-bit (how? explained next). Then the
output L'R' of an iteration with input LR is
defined by:
L' = R
R' = L (+) f (R,K)
L'R' is the output of the 16th iteration then
R'L' is the preoutput block.
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74. The permutation function P yields a 32-
bit output from a 32-bit input by
permuting the bits of the input block
P 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
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75. Primitive functions for the data
encryption algorithm
The choice of the primitive functions KS,
S1, ..., S8 and P is critical to the strength of an
encipherment resulting from the algorithm
The recommended set of functions are
described as S1, ..., S8 and P in the
algorithm.
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76. Deciphering
The permutation IP-1 applied to the
preoutput block is the inverse of the
initial permutation IP applied to the
input.
R = L'
L = R' (+) f (L', K)
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77. Other Stream Ciphers
RC4
Variable key size stream cipher
Proprietary for 7 years (1987 - 1994)
In 1994 source code was posted to mailing list
Works in OFB
Encryption is 10 times faster than DES
SEAL (Software-optimized Encryption ALgorithm)
length-increasing pseudorandom function which maps a 32-bit sequence
number n to an L-bit keystream under control of a 160-bit secret key a
In the preprocessing stage, the key is stretched into larger tables using the
table-generation function Ga (based on SHA-1)
Subsequent to this preprocessing, keystream generation requires about 5
machine instructions per byte
order of magnitude faster than DES
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78. Other Block Ciphers
FEAL
Fast N-round block cipher
Suffers a lot of attacks, and hence introduce new attacks
on block ciphers
Japan standard
IDEA
64-64-128-8
James Massey
Using algebraic functions (mult mod 2n+1, add mod 2n)
SAFER, RC-5, AES
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79. Thank You
reachable at
naasir_k@donboscoit.ac.in
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Notas do Editor
Briefly review some terminology used throughout the course.
Detail 5 ingredients of the symmetric cipher model: plaintext encryption algorithm – performs substitutions/transformations on plaintext secret key – control exact substitutions/transformations used in encryption algorithm ciphertext decryption algorithm – inverse of encryption algorithm
Basert på enveis funksjoner Offentlige nøkler kan sender over usikret media, mens private nøkler skal holdes hemmelige. Forskjell fra symmetrisk pga privat skal kun 1 person vite mens ved secret er det flere enn 1 person som kjenner til nøklen. Vanskeligheten ligger i sikker utveksling av offentlig nøkkel Hvem som helst kan lese det som krypteres med privat nøkkel (autentisering) Bare eier av den private nøkkel kan lese det som krypteres med den offentlige nøkkelen (kryptering) RSA. Diffie-Hellman
Generally assume that the algorithm is known. This allows easy distribution of s/w and h/w implementations. Hence assume just keeping key secret is sufficient to secure encrypted messages. Have plaintext X, ciphertext Y, key K, encryption alg Ek, decryption alg Dk.
Deep crack, EFF ’98: 88x10^9 encr/s -> approx 5 days. They solved a 56 bit key in 3 days.
Transposition Ciphers form the second basic building block of ciphers. The core idea is to rearrange the order of basic units (letters/bytes/bits) without altering their actual values.
Example message is: "meet me after the toga party" with a rail fence of depth 2. How do you cryptanalyze this? Freq analysis shows expected distribution with expected letters, so you have to suspect transpositions
Transposition ciphers often are block ciphers…
In this section and the next, we examine a sampling of what might be called classical encryption techniques. A study of these techniques enables us to illustrate the basic approaches to symmetric encryption used today and the types of cryptanalytic attacks that must be anticipated. The two basic building blocks of all encryption techniques: substitution and transposition. We examine these in the next two sections. Finally, we discuss a system that combine both substitution and transposition.
Substitution ciphers form the first of the fundamental building blocks. The core idea is to replace one basic unit (letter/byte) with another. Whilst the early Greeks described several substitution ciphers, the first attested use in military affairs of one was by Julius Caesar, described by him in Gallic Wars (cf. Kahn pp83-84). Still call any cipher using a simple letter shift a caesar cipher , not just those with shift 3. Note: when letters are involved, the following conventions are used in this course: Plaintext is always in lowercase; ciphertext is in uppercase; key values are in italicized lowercase.
This mathematical description uses modulo arithmetic (ie clock arithmetic). Here, when you reach Z you go back to A and start again. Mod 26 implies that when you reach 26, you use 0 instead (ie the letter after Z, or 25 + 1 goes to A or 0). Example: howdy (7,14,22,3,24) encrypted using key f (5) is MTBID
Definition: each character is independently encrypted (hence, a single rewriting alphabet is used)
Consider ways to reduce the "spikyness" of natural language text, since if just map one letter always to another, the frequency distribution is just shuffled. One approach is to encrypt more than one letter at once. Playfair cipher is an example of doing this.
Have here the rules for filling in the 5x5 matrix, L to R, top to bottom, first with keyword after duplicate letters have been removed, and then with the remain letters, with I/J used as a single letter. This example comes from Dorothy Sayer's book "Have His Carcase", in which Lord Peter Wimsey solves this, and describes the use of a probably word attack.
Note the various rules, and how you wrap from right side back to left, or from bottom back to top. Decrypting of course works exactly in reverse. Can see this by working the example pairs shown, backwards.
One approach to reducing the "spikyness" of natural language text is used the Playfair cipher which encrypts more than one letter at once. We now consider the other alternative, using multiple cipher alphabets in turn. This gives the attacker more work, since many alphabets need to be guessed, and because the frequency distribution is more complex, since the same plaintext letter could be replaced by several ciphertext letters, depending on which alphabet is used. Definition: nonmonoalphabetic
Simply create a set of caesar cipher translation alphabets, then use each in turn, as shown next.
See that the key used is the keyword "DECEPTIVE" prefixed to as much of the message "WEAREDISCOVEREDSAV" as is needed. When deciphering, recover the first 9 letters using the keyword "DECEPTIVE". Then instead of repeating the keyword, start using the recovered letters from the message "WEAREDISC". As recover more letters, have more of key to recover later letters. Problem is that the same language characteristics are used by the key as the message. ie. a key of 'E' will be used more often than a 'T' etc hence an 'E' encrypted with a key of 'E' occurs with probability (0.1275)^2 = 0.01663, about twice as often as a 'T' encrypted with a key of 'T' have to use a larger frequency table, but it exists given sufficient ciphertext this can be broken.
The One-Time Pad is an evolution of the Vernham cipher, which was invented by Gilbert Vernham in 1918, and used a long tape of random letters to encrypt the message. An Army Signal Corp officer, Joseph Mauborgne, proposed an improvement using a random key that was truly as long as the message, with no repetitions, which thus totally obscures the original message. Since any plaintext can be mapped to any ciphertext given some key, there is simply no way to determine which plaintext corresponds to a specific instance of ciphertext. Can only use once though. Still have problem of safe distribution of key
Decryption of Enigma. Allies knew wiring by intercepting documents, but didn’t know the most current settings. Daily, Germans transmitted new settings in a way that reliably repeated some plaintext. Turing and others at Bletchley figured out how to use this to figure out settings. Using a huge amount of equipment and personnel they at times (not always) were able to decrypt transmissions within hours. This effort was just barely working – by adopting a little more hassle, the Germans could have made the numbers way too big for this decryption approach to work. But the Germans thought it was infeasible already.
Wildly unsubstantiated claims in Sept 2001 that Al-Qaeda had been using steganography in public bulletin board systems to communicate -- pretty silly, since we didn’t even know who the terrorists were!
Now let me explain modes of operation, Federal Information Processing Standards Publications (FIPS PUBS 81) This FIPS defines four modes of operation for the DES which may be used in a wide variety of applications. The modes specify how data will be encrypted (cryptographically protected) and decrypted (returned to original form). This recommendation specifies five confidentiality modes of operation for symmetric key block cipher algorithms, such as the algorithm specified in FIPS Pub. 197, the Advanced Encryption Standard (AES) [2]. The modes may be used in conjunction with any symmetric key block cipher algorithm that is approved by a Federal Information Processing Standard (FIPS). The five modes—the Electronic Codebook (ECB), Cipher Block Chaining (CBC), Cipher Feedback (CFB), Output Feedback (OFB), and Counter (CTR) modes—can provide data confidentiality.
There are two recommended methods for generating unpredictable IVs. The first method is to apply the forward cipher function, under the same key that is used for the encryption of the plaintext, to a nonce. The nonce must be a data block that is unique to each execution of the encryption operation. For example, the nonce may be a counter,or a message number. The second method is to generate a random data block using a FIPS-approved random number generator.
Let E denote a function which takes a block of 32 bits as input and yields a block of 48 bits as output. Let E be such that the 48 bits of its output, written as 8 blocks of 6 bits each, are obtained by selecting the bits in its inputs in order according to the following table: Each of the unique selection functions S1,S2,...,S8, takes a 6-bit block as input and yields a 4-bit block as output and is illustrated by using a table containing the recommended S1: