MESSAGE

plaintext

encode/encipher decode/decipher

ZXYCTHI MESSAGE

plaintext

ciphertext

algorithm algorithm

Cryptography“art or science concerning the principles, means and methods for rendering plain information unintelligible and for restoring encrypted information to intelligible form.” -- National Information System Security Glossary (NSTISSC)

-- a readable form for a message (e.g. English text)xaiettlnp

tcxiepthre -- a scrambled version of some plaintext message intended to protect the message’s confidentiality and/or integrity

dcnoee -- translate from plaintext to ciphertext

dceoed -- translate from ciphertext back to plaintext

pihcenre -- synonym for encode (technically, encodes a single symbol/character)

pihcdere -- synonym for decode (technically, decodes a single symbol)

ysterocmptsy-- a collection of algorithms for encryption and decryption

niprnecyto -- the act of encoding

niprdecyto -- the act of decoding

ytapopcghyrr -- the study of cryptosystems (the science of secret writing)

hpicer -- a particular cryptosystem

MESSAGE

plaintext

encode/encipher decode/decipher

ZXYCTHI MESSAGE

plaintext

ciphertext

E( plaintext ) = ciphertext

Inverse FunctionFunction

E-1( ciphertext ) = plaintext

Encryption AlgorithmEach letter (Lp) is replaced by the letter from the following function:

E(Lp) = (Lp + 3) mod 26

letters are numbered from zero (A≈0, B≈1, …Z≈25)

Example

HI MOM SEND DOLLARS

KL PRP VHQG GROODUV

plaintext

ciphertext

Decryption AlgorithmEach letter (Lc) is replaced by the letter from the following function:

D(Lc) =

Simple Caesar CipherE(Lp) = (Lp + 3) mod 26

Generalized Caesar CipherECaesar(Lp, k) = (Lp + k) mod 26

Key“a sequence of random or pseudorandom bits used initially to set up and periodically change the operations performed in crypto-equipment for the purpose of encrypting or decrypting electronic signals...” -- National Information System Security Glossary (NSTISSC)

plaintext ciphertext

encryption algorithm decryption algorithm

plaintext

plaintext ciphertext

encryption algorithm decryption algorithm

plaintext

Symmetric Encryption

Asymmetric Encryption

Is the Caesar Cipher (keyed version) symmetric or asymmetric?

Symmetric encryption is also known as ________ key encryption,because the key must be kept private from…

EncodeECaesar(Lp, k) = (Lp + k) mod 26

DecodeDCaesar(Lc, k) =

code breaker

rot13(Lp) = ECaesar(Lp, 13)

Note that rot13 = rot13-1 (i.e. rot13 decodes any message encoded with rot13)

In general, what is DCaesar(Ln, k) in terms of ECaesar(Ln, k) ?

Cryptanalysis“operations performed in converting encrypted messages to plain text without initial knowledge of the crypto-algorithm and/or key employed in the encryption.” -- National Information System Security Glossary (NSTISSC)

code breakerCommon Cryptanalysis Attacks

Attack Type Cryptanalysis Knowledge

ciphertext only • encryption algorithm (less the key)• ciphertext to be deciphered

known plaintext • encryption algorithm (less the key)• ciphertext to be deciphered• a segment of plaintext with corresponding ciphertext

chosen plaintext • encryption algorithm (less the key)• ciphertext to be deciphered• a segment of plaintext selected by cryptanalyst with corresponding ciphertext

How difficult is cryptanalysis on a keyed Caesar cipher?

T U R K E Y

substitutionA substitution cipher forms ciphertext from replacing plaintext bit patternswith other bit patterns.

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

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

Example (Caesar cipher with key = 1)

D( )

E( )

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

Another ExampleUse a word as key. Encode using word followed by remaining alphabet.

A simple (mono-alphabetic) substitution always maps the same bit pattern consistently.

Cryptanalysis of this second example?

Non-alphabeticComputers have no need to use alphabets - bit strings are easier.

Non-sequentialThere is nothing to suggest that alphabetic ordering be used at all. (Why notuse every third letter in the alphabet?)

There is a need to use a proper permutation. Why?

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

brute force (for mono-alphabetic substitution)

alphabetic frequency cryptanalysis (Cryptography and Data Security, Denning, 1982.)

There are 26! simple substitution ciphers from the English alphabet.

Suppose you know only that the cipher uses some tabular mono-alphabetic substitution.

Digrams and trigrams can be analyzed in similar fashion.

1) The amount of required secrecy should determine the amount of encrypting/decrypting work.

In 1949 Shannon proposed the following characteristics of a good cipher:

2) The choice of keys and the enciphering algorithm should be free from complexity.

3) The implementation of the process should be as simple as possible.

4) Errors in ciphering should not propagate, corrupting other message parts.

5) The size of the ciphertext should be no larger than its corresponding plaintext.

Today’s priorities:1) The encryption/decryption algorithm must be proven to be mathematically sound.

2) The algorithm must have been analyzed by experts for its vulnerability.

3) The algorithm must have stood the “test of time”.

4) Time to encode/decode must still be acceptable.

Tableau

(basis for well-known polyalphabetic substitution ciphers)

Use a string as key, repeatedly. The key letters serve as row indices for enciphering.

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 ZB C D E F G H I J K L M N O P Q R S T U V W X Y Z AC D E F G H I J K L M N O P Q R S T U V W X Y Z A BD E F G H I J K L M N O P Q R S T U V W X Y Z A B CE F G H I J K L M N O P Q R S T U V W X Y Z A B C DF G H I J K L M N O P Q R S T U V W X Y Z A B C D EG H I J K L M N O P Q R S T U V W X Y Z A B C D E FH I J K L M N O P Q R S T U V W X Y Z A B C D E F GI J K L M N O P Q R S T U V W X Y Z A B C D E F G HJ K L M N O P Q R S T U V W X Y Z A B C D E F G H IK L M N O P Q R S T U V W X Y Z A B C D E F G H I JL M N O P Q R S T U V W X Y Z A B C D E F G H I J KM N O P Q R S T U V W X Y Z A B C D E F G H I J K LN O P Q R S T U V W X Y Z A B C D E F G H I J K L MO 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. . .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

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

abcdefghijklmno z

ExampleA B C D E F G H I J K L M N O P Q R S T U V W X Y ZB C D E F G H I J K L M N O P Q R S T U V W X Y Z AC D E F G H I J K L M N O P Q R S T U V W X Y Z A BD E F G H I J K L M N O P Q R S T U V W X Y Z A B CE F G H I J K L M N O P Q R S T U V W X Y Z A B C DF G H I J K L M N O P Q R S T U V W X Y Z A B C D EG H I J K L M N O P Q R S T U V W X Y Z A B C D E FH I J K L M N O P Q R S T U V W X Y Z A B C D E F GI J K L M N O P Q R S T U V W X Y Z A B C D E F G HJ K L M N O P Q R S T U V W X Y Z A B C D E F G H IK L M N O P Q R S T U V W X Y Z A B C D E F G H I JL M N O P Q R S T U V W X Y Z A B C D E F G H I J KM N O P Q R S T U V W X Y Z A B C D E F G H I J K LN O P Q R S T U V W X Y Z A B C D E F G H I J K L MO 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. . .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

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

abcdefghijklmno z

HI MOM SEND DOLLARS plaintext

ciphertextTQ XYY APXP LZVXICC

mi lkm ilkm ilkmilk key = milk

Cryptanalysis of such a cipher?

Encryption Algorithm

• Designed by British scientist Sit Charles Wheatstone (1854) and promoted by Baron Playfair of St. Andrews.

• a dual-alphabetic substitution cipher

• uses a key consisting of a string of unique characters (e.g. SECURITY)

1) Build 5 by 5 table beginning with key followed by remaining alphabet (combine I/J).

S E C U RI/J T Y A BD F G H KL M N O PQ V W X Z

3) Each pair of letters (Lleft, Lright) from modified plaintext is replaced as follows:a) If Lleft in same row as Lright, then replace each with letter in next column to its right.

(e.g. for pair “FK” substitute “GD”)

2) Insert X between repeated letters in plaintext. (e.g. “BALLOON” becomes “BALXLOXON”

b) If Lleft in same column as Lright, then replace each with letter in row beneath. (e.g. for pair “VT” substitute “EF”)

c) If Lleft and Lright in different rows and colums, then replace each with the table letter from its own row and the other letter’s column. (e.g. for pair “UN” substitute “CO”)

Example

HI MOM SEND DOLLARS plaintext

S E C U RI/J T Y A BD F G H KL M N O PQ V W X Z

HI MO MS EN DX DO LX LA RS

ciphertextDA NP LE CM HQ HL OQ TB SE

Still vulnerable to digram and single-character frequency attacks.

• the invention of an Army Signal Corp officer, Joseph Mauborgne.

• provably unbreakable!

• algorithm: a Vignère cipher using a random key of infinite length.

The standard Vignère cipher can be broken by analyzing the period of the repeating key.

One-Time Pad

What’s the catch?

It is possible to use a book cipher - a pad of key that are used then discarded.

Created by Gilbert Vernam (Bell Labs)

Vernam cipher

Use paper tape (teletype) to deliver an arbitrarily-long non-repeating sequence of keys.

Another alternative is to use a table (e.g. of sine values) or a book.

Encode/decode by numeric function rather than Vignère table.

Example 1: use XOR to encode and decode.

SymboSymboll

DecimaDecimall

Bit Bit StringString

PlaintePlaintextxt ‘‘RR ’’ 8282

0101001010100100

KeyKey 15150000111000011111

EVernam(‘R’,15)

Example 2: Encode with addition mod 256.EVernam(‘R’,15)

What is DVernam(X,K)?

= 01010010 0001111 =

= (82 + 15) mod 256 =

substitute or transpose or productA substitution cipher forms ciphertext from replacing plaintext bit patternswith other bit patterns.

A transposition cipher forms ciphertext from rearranging plaintext bit sequences.

stream or blockA stream cipher transforms plaintext one small subsequence (bit, byte, letter) at a time.

A block cipher transforms a larger units of plaintext (usually 64 or 128 bits).

A product cipher uses both substitution and transposition.

Encipher by arranging plaintext in two rows, as illustrated below.Rail Fence Transposition

Arrange plaintext row by row in 2D grid and select cipher text from columns.Use a key to determine column order.

Tabular Transposition

HMMEDOLR IOSNDLAS plaintext (in diagonal rows)

ciphertextHMMEDOLRIOSNDLAS

A rail fence cypher is trivial to cryptanalyze, much like an Caesar cipher.

HIMOMSENDDOLLARS

plaintext (in 5-letter rows)

35241 key

ciphertextMDRMNLHSOSODRIEL

The prior tabular transposition is still extremely vulnerable to attack by digram frequency analysis. A repeated transposition improves the cipher.

HIMOMSENDDOLLARS

plaintext (in 5-letter rows)

35241 key

ciphertextNSERSRMLOLMOIDHD

MDRMNLHSOSODRIEL

after first transposition

Cryptanalysis of such a cipher?