classic crypto slides based on those developed by dr. lawrie brown at the australian defence force...
TRANSCRIPT
Classic CryptoClassic Crypto
Slides based on those developed by Dr. Slides based on those developed by Dr. Lawrie Brown at the Australian Defence Lawrie Brown at the Australian Defence Force Academy, University College, Force Academy, University College, UNSWUNSW
See See http://www.williamstallings.com/Crypto/Cryhttp://www.williamstallings.com/Crypto/Crypto4e.htmlpto4e.html
Symmetric EncryptionSymmetric Encryption
or conventional / or conventional / private-keyprivate-key / single-key / single-key sender and recipient share a common keysender and recipient share a common key all classical encryption algorithms are all classical encryption algorithms are
private-keyprivate-key was only type prior to invention of public-was only type prior to invention of public-
key in 1970’skey in 1970’s and by far most widely usedand by far most widely used
Some Basic TerminologySome Basic Terminology
plaintextplaintext - original message - original message ciphertextciphertext - coded message - coded message ciphercipher - algorithm for transforming plaintext to ciphertext - algorithm for transforming plaintext to ciphertext keykey - info used in cipher known only to sender/receiver - info used in cipher known only to sender/receiver encipher (encrypt)encipher (encrypt) - converting plaintext to ciphertext - converting plaintext to ciphertext decipher (decrypt)decipher (decrypt) - recovering ciphertext from plaintext - recovering ciphertext from plaintext cryptographycryptography - study of encryption principles/methods - study of encryption principles/methods cryptanalysis (codebreaking)cryptanalysis (codebreaking) - study of principles/ - study of principles/
methods of deciphering ciphertext methods of deciphering ciphertext withoutwithout knowing key knowing key cryptologycryptology - field of both cryptography and cryptanalysis - field of both cryptography and cryptanalysis
Symmetric Cipher ModelSymmetric Cipher Model
RequirementsRequirements
two requirements for secure use of two requirements for secure use of symmetric encryption:symmetric encryption: a strong encryption algorithma strong encryption algorithm a secret key known only to sender / receivera secret key known only to sender / receiver
mathematically have:mathematically have:Y Y = E= EKK((XX))
X X = D= DKK((YY)) assume encryption algorithm is knownassume encryption algorithm is known implies a secure channel to distribute keyimplies a secure channel to distribute key
CryptographyCryptography
characterize cryptographic system by:characterize cryptographic system by: type of encryption operations usedtype of encryption operations used
• substitution / permutation / productsubstitution / permutation / product number of keys usednumber of keys used
• single-key or private / two-key or publicsingle-key or private / two-key or public way in which plaintext is processedway in which plaintext is processed
• block / streamblock / stream
CryptanalysisCryptanalysis
objective to recover key not just messageobjective to recover key not just message general approaches:general approaches:
cryptanalytic attackcryptanalytic attack brute-force attackbrute-force attack
Cryptanalytic AttacksCryptanalytic Attacks ciphertext onlyciphertext only
only know algorithm & ciphertext, is statistical, only know algorithm & ciphertext, is statistical, know or can identify plaintext know or can identify plaintext
known plaintextknown plaintext know/suspect plaintext & ciphertextknow/suspect plaintext & ciphertext
chosen plaintextchosen plaintext select plaintext and obtain ciphertextselect plaintext and obtain ciphertext
chosen ciphertextchosen ciphertext select ciphertext and obtain plaintextselect ciphertext and obtain plaintext
chosen textchosen text select plaintext or ciphertext to en/decryptselect plaintext or ciphertext to en/decrypt
More DefinitionsMore Definitions unconditional securityunconditional security
no matter how much computer power or time no matter how much computer power or time is available, the cipher cannot be broken is available, the cipher cannot be broken since the ciphertext provides insufficient since the ciphertext provides insufficient information to uniquely determine the information to uniquely determine the corresponding plaintext corresponding plaintext
computational securitycomputational security given limited computing resources (eg time given limited computing resources (eg time
needed for calculations is greater than age of needed for calculations is greater than age of universe), the cipher cannot be broken universe), the cipher cannot be broken
Brute Force SearchBrute Force Search
always possible to simply try every key always possible to simply try every key most basic attack, proportional to key size most basic attack, proportional to key size assume either know / recognise plaintextassume either know / recognise plaintext
Key Size (bits) Number of Alternative Keys
Time required at 1 decryption/µs
Time required at 106 decryptions/µs
32 232 = 4.3 109 231 µs = 35.8 minutes 2.15 milliseconds
56 256 = 7.2 1016 255 µs = 1142 years 10.01 hours
128 2128 = 3.4 1038 2127 µs = 5.4 1024 years 5.4 1018 years
168 2168 = 3.7 1050 2167 µs = 5.9 1036 years 5.9 1030 years
26 characters (permutation)
26! = 4 1026 2 1026 µs = 6.4 1012 years 6.4 106 years
Classical Substitution Classical Substitution CiphersCiphers
where where letters of plaintext are replaced by letters of plaintext are replaced by other letters or by numbers or symbolsother letters or by numbers or symbols
or if plaintext is or if plaintext is viewed as a sequence of viewed as a sequence of bits, then substitution involves replacing bits, then substitution involves replacing plaintext bit patterns with ciphertext bit plaintext bit patterns with ciphertext bit patternspatterns
Caesar CipherCaesar Cipher
earliest known substitution cipherearliest known substitution cipher by Julius Caesar by Julius Caesar first attested use in military affairsfirst attested use in military affairs replaces each letter by 3rd letter onreplaces each letter by 3rd letter on example:example:
meet me after the toga partymeet me after the toga partyPHHW PH DIWHU WKH WRJD SDUWBPHHW PH DIWHU WKH WRJD SDUWB
Caesar CipherCaesar Cipher
can define transformation as: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 za 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 CD 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 numbermathematically give each letter a numbera b c d e f g h i j k l m n o p q r s t u v w x y za 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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
then have Caesar cipher as:then have Caesar cipher as:c c = E(= E(pp) = () = (p p + + kk) mod (26)) mod (26)
p p = D(c) = (c – = D(c) = (c – kk) mod (26)) mod (26)
Cryptanalysis of Caesar Cryptanalysis of Caesar Cipher Cipher
only have 26 possible ciphers only have 26 possible ciphers A maps to A,B,..Z A maps to A,B,..Z
could simply try each in turn could simply try each in turn a a brute force searchbrute force search given ciphertext, just try all shifts of lettersgiven ciphertext, just try all shifts of letters do need to recognize when have plaintextdo need to recognize when have plaintext eg. break ciphertext "GCUA VQ DTGCM"eg. break ciphertext "GCUA VQ DTGCM"
Monoalphabetic CipherMonoalphabetic Cipher
rather than just shifting the alphabet rather than just shifting the alphabet could shuffle the letters arbitrarily could shuffle the letters arbitrarily each plaintext letter maps to a different random each plaintext letter maps to a different random
ciphertext letter ciphertext letter hence key is 26 letters long hence key is 26 letters long
Plain: abcdefghijklmnopqrstuvwxyzPlain: abcdefghijklmnopqrstuvwxyzCipher: DKVQFIBJWPESCXHTMYAUOLRGZNCipher: DKVQFIBJWPESCXHTMYAUOLRGZN
Plaintext: ifwewishtoreplacelettersPlaintext: ifwewishtoreplacelettersCiphertext: WIRFRWAJUHYFTSDVFSFUUFYA Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA
Monoalphabetic Cipher Monoalphabetic Cipher SecuritySecurity
now have a total of 26! >= 4 x 10^{26} now have a total of 26! >= 4 x 10^{26} keys keys
with so many keys, might think is secure with so many keys, might think is secure but would be but would be !!!WRONG!!!!!!WRONG!!! problem is language characteristicsproblem is language characteristics
Language Redundancy and Language Redundancy and CryptanalysisCryptanalysis
human languages are human languages are redundantredundant eg "th lrd s m shphrd shll nt wnt" eg "th lrd s m shphrd shll nt wnt" letters are not equally commonly used letters are not equally commonly used in English E is by far the most common letter in English E is by far the most common letter
followed by T,R,N,I,O,A,S followed by T,R,N,I,O,A,S
other letters like Z,J,K,Q,X are fairly rare other letters like Z,J,K,Q,X are fairly rare have tables of single, double & triple letter have tables of single, double & triple letter
frequencies for various languagesfrequencies for various languages
English Letter FrequenciesEnglish Letter Frequencies
Use in CryptanalysisUse in Cryptanalysis key concept - monoalphabetic substitution key concept - monoalphabetic substitution
ciphers do not change relative letter frequencies ciphers do not change relative letter frequencies discovered by Arabian scientists in 9discovered by Arabian scientists in 9 thth century century calculate letter frequencies for ciphertextcalculate letter frequencies for ciphertext compare counts/plots against known values compare counts/plots against known values if caesar cipher look for common peaks/troughs if caesar cipher look for common peaks/troughs
peaks at: A-E-I triple, NO pair, RST triplepeaks at: A-E-I triple, NO pair, RST triple troughs at: JK, X-Ztroughs at: JK, X-Z
for for monoalphabetic must identify each lettermonoalphabetic must identify each letter tables of common double/triple letters helptables of common double/triple letters help
Example CryptanalysisExample Cryptanalysis
given ciphertext:given ciphertext:UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZUZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSXEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
count relative letter frequencies (see text)count relative letter frequencies (see text) guess P & Z are e and tguess P & Z are e and t guess ZW is th and hence ZWP is theguess ZW is th and hence ZWP is the proceeding with trial and error finally get:proceeding with trial and error finally get:
it was disclosed yesterday that several informal butit was disclosed yesterday that several informal butdirect contacts have been made with politicaldirect contacts have been made with politicalrepresentatives of the viet cong in moscowrepresentatives of the viet cong in moscow
Polyalphabetic CiphersPolyalphabetic Ciphers
polyalphabetic substitution cipherspolyalphabetic substitution ciphers improve security using multiple permutation improve security using multiple permutation
tables tables make cryptanalysis harder with more make cryptanalysis harder with more
permutations to guess and flatter frequency permutations to guess and flatter frequency distribution distribution
use a key to select which permutation is used for use a key to select which permutation is used for each letter of the message each letter of the message
use each permutation in turn use each permutation in turn repeat from start after end of key is reached repeat from start after end of key is reached
Vigenère CipherVigenère Cipher
simplest polyalphabetic substitution ciphersimplest polyalphabetic substitution cipher effectively multiple caesar ciphers effectively multiple caesar ciphers key is multiple letters long K = kkey is multiple letters long K = k11 k k22 ... k ... kdd
iithth letter specifies “shift-by-i” to use letter specifies “shift-by-i” to use use each shift in turn use each shift in turn repeat from start after d letters in messagerepeat from start after d letters in message decryption simply works in reverse decryption simply works in reverse
Example of Example of Vigenère CipherVigenère Cipher
write the plaintext out write the plaintext out write the keyword repeated above itwrite the keyword repeated above it use each key letter as a caesar cipher key use each key letter as a caesar cipher key encrypt the corresponding plaintext letterencrypt the corresponding plaintext letter eg using keyword eg using keyword deceptivedeceptive
key: deceptivedeceptivedeceptivekey: deceptivedeceptivedeceptive
plaintext: wearediscoveredsaveyourselfplaintext: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGRZGVTWAVZHCQYGLMGJciphertext:ZICVTWQNGRZGVTWAVZHCQYGLMGJ
One Attack MethodOne Attack Method
Just a sketch …Just a sketch … Count frequencies for letters that are 2-Count frequencies for letters that are 2-
apart, 3-apart, 4-apart, etc.apart, 3-apart, 4-apart, etc. If one of this matches frequency of If one of this matches frequency of
English, this English, this is likely to be the length d of the keyis likely to be the length d of the key then attack each monoalphabetic cipher then attack each monoalphabetic cipher
individually using same techniques as individually using same techniques as beforebefore
One-Time PadOne-Time Pad
if a truly random key as long as the message is if a truly random key as long as the message is used, the cipher will be secure used, the cipher will be secure
called a One-Time padcalled a One-Time pad is unbreakable since ciphertext bears no is unbreakable since ciphertext bears no
statistical relationship to the plaintextstatistical relationship to the plaintext since for since for any plaintextany plaintext & & any ciphertextany ciphertext there there
exists a key mapping one to otherexists a key mapping one to other can only use the key can only use the key onceonce though though problems in generation & safe distribution of keyproblems in generation & safe distribution of key
Transposition CiphersTransposition Ciphers
now consider classical now consider classical transpositiontransposition or or permutationpermutation ciphers ciphers
these hide the message by rearranging these hide the message by rearranging the letter order the letter order
without altering the actual letters usedwithout altering the actual letters used can recognise these since have the same can recognise these since have the same
frequency distribution as the original text frequency distribution as the original text
Rail Fence cipherRail Fence cipher
write message letters out diagonally over a write message letters out diagonally over a number of rows number of rows
then read off cipher row by rowthen read off cipher row by row eg. write message out as:eg. write message out as:
m e m a t r h t g p r ym e m a t r h t g p r y e t e f e t e o a a te t e f e t e o a a t
giving ciphertextgiving ciphertextMEMATRHTGPRYETEFETEOAATMEMATRHTGPRYETEFETEOAAT
Row Transposition CiphersRow Transposition Ciphers
a more complex transpositiona more complex transposition write letters of message out in rows over a write letters of message out in rows over a
specified number of columnsspecified number of columns then reorder the columns according to then reorder the columns according to
some key before reading off the rowssome key before reading off the rowsKey: 3 4 2 1 5 6 7Key: 3 4 2 1 5 6 7Plaintext: a t t a c k pPlaintext: a t t a c k p o s t p o n eo s t p o n e d u n t i l td u n t i l t w o a m x y zw o a m x y zCiphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZCiphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ
Rotor MachinesRotor Machines
before modern ciphers, rotor machines were before modern ciphers, rotor machines were most common complex ciphers in usemost common complex ciphers in use
widely used in WW2widely used in WW2 German Enigma, Allied Hagelin, Japanese PurpleGerman Enigma, Allied Hagelin, Japanese Purple
implemented a very complex, varying implemented a very complex, varying substitution ciphersubstitution cipher
used a series of cylinders, each giving one used a series of cylinders, each giving one substitution, which rotated and changed after substitution, which rotated and changed after each letter was encryptedeach letter was encrypted
with 3 cylinders have 26with 3 cylinders have 2633=17576 alphabets=17576 alphabets
Hagelin Rotor MachineHagelin Rotor Machine