Classical Encryption Techniques

Week 6-wend

One-Time Pad

if a 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

can only use the key once though

problems in generation & safe distribution of key

One-Time Pad

if a 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

can only use the key once though

problems in generation & safe distribution of key

One-Time Pad

Random Bytesk

P

C= P k

P= C kP= P k k

Random Bytesk

If the streams of random bytes are: • Identical• Truly Random Then the cipher text is also truly random. This scheme is unbreakable, even if infinite computational resources are available to the Cryptanalyst.

One-time Pads

One-time Pads:

Step 1 - Write the Plaintext above the key

T H E B R I T I S H A R E C O M I N GD K J F O I S J O G I J P A P D I G N

Step 2 - Determine an algorithm

(m + k) MOD 26

One-time Pads

Step 3 - Perform the encryption

(T(19)+D(03)=22) MOD 26 = 22 = W(H(07)+K(10)=17) MOD 26 = 17 = R(E(04)+J(09)=13) MOD 26 = 13 = N(B(01)+F(05)=06) MOD 26 = 06 = G………

………

(C(02)+A(00)=02) MOD 26 = 02 = C(O(14)+P(15)=29) MOD 26 = 03 = D(M(12)+D(03)=15) MOD 26 = 15 = P(I(08)+I(08)=16) MOD 26 = 16 = Q(N(13)+G(06)=19) MOD 26 = 19 = T(G(06)+N(13)=19) MOD 26 = 19 = T

One-time Pads

now we can determine that our CT is "WRNGFQLRGNIATCDPQTT". This is not vulnerable to simple frequency analysis because the same letter is not encrypted the same way twice (unless, of course, it aligns with the same key character twice). It should also be invulnerable to index of coincidence attacks because your key is not repeated; it is the length of the text.

Decryption is also quite straightforward. It follows the formulaM= (c – k +26) MOD 26

One-time Pads

(W(22)-D(03)= 19 +26) MOD 26 = 19 = T(R(17)-K(10)= 07 +26) MOD 26 = 07 = H(N(13)-J(09)= 04 +26) MOD 26 = 04 = E(G(06)-F(05)= 01 +26) MOD 26 = 01 = B(F(05)-O(14)=-09 +26) MOD 26 = 17 = R(Q(16)-I(08)= 08 +26) MOD 26 = 08 = I……………………(P(15)-D(03)= 12 +26) MOD 26 = 12 = M(Q(16)-I(08)= 08 +26) MOD 26 = 08 = I(T(19)-G(06)= 13 +26) MOD 26 = 13 = N(T(19)-N(13)= 06 +26) MOD 26 = 06 = G

We can see the original message here: "The British are coming".

One-Time Pad

Because of the Key Management problem the One-Time pad (or Vernam Cipher) was not widely used, except by the Russians who used it very successfully during WWII and after.

Transposition Ciphers

now 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

12

Row Transposition Ciphers

a more complex transpositionwrite letters of message out in rows over a specified number of columnsthen reorder the columns according to some key before reading off the rowsKey: 3 4 2 1 5 6 7Plaintext: 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 zCiphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ

Block cipher vs Stream cipher

A block cipher: is an encryption/decryption scheme in which a block of plaintext is treated as a whole and used to produce a ciphertext block of equal length. Typically, a block size of 64 or 128 bits is used

A stream cipher: is an encryption/decryption scheme that encrypts a digital data stream one bit or one byte at a time.

Substitution & Permutation

Substitution: Each plaintext element or group of elements is uniquely replaced by a corresponding ciphertext element or group of elements.

Permutation(Transposition ): A sequence of plaintext elements is replaced by a permutation of that sequence. That is, no elements are added or deleted or replaced in the sequence, i.e. the order in which the elements appear in the sequence is changed.

Stream Encryption Algorithms Block Encryption Algorithms

Advantages

• Speed of transformation. Because each symbol is encrypted without regard for any other plaintext symbols, each symbol can be encrypted as soon as it is read. Thus, the time to encrypt a symbol depends only on the encryption algorithm itself, not on the time it takes to receive more plaintext.

• Low error propagation. Because each symbol is separately encoded, an error in the encryption process affects only that character.

• High diffusion. Information from the plain-text is diffused into several ciphertext symbols. One ciphertext block may depend on several plaintext letters.

• Immunity to insertion of symbols. Because blocks of symbols are enciphered, it is impossible to insert a single symbol into one block. The length of the block would then be incorrect. The length of the block would then be incorrect, and the decipherment would quickly reveal the insertion.

Disadvantages

• Low diffusion. Each symbol is separately enciphered. Therefore, all the information of that symbol is contained in one symbol of the ciphertext.

• Susceptibility to malicious insertions and modifications. Because each symbol is separately enciphered, an active interceptor who has broken the code can splice together pieces of previous messages and transmit a spurious new message that may look authentic.

• Slowness of encryption. The person or machine using a block cipher must wait until an entire block of plaintext symbols has been received before starting the encryption process.

• Error propagation. An error will affect the transformation of all other characters in the same block.

Product Ciphers

ciphers using substitutions or transpositions are not secure because of language characteristics

hence consider using several ciphers in succession to make harder, but:

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

Rotor Machines

before modern ciphers, rotor machines were most common complex ciphers in use

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

Hagelin Rotor Machine

Rotor Machine Principles

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

advantage is can obscure encryption use

Summary

have considered:

classical cipher techniques and terminology monoalphabetic substitution ciphers cryptanalysis using letter frequencies polyalphabetic ciphers transposition ciphers product ciphers and rotor machines stenography