Making “Good” Encryption Making “Good” Encryption AlgorithmsAlgorithms

Substitution algorithms “hide” the Substitution algorithms “hide” the plaintext and dissipate high letter plaintext and dissipate high letter frequenciesfrequencies

Transposition algorithms scramble Transposition algorithms scramble texttext

Many “good” algorithms combine Many “good” algorithms combine both techniquesboth techniques

Shannon’s Characteristics of Shannon’s Characteristics of “Good” Ciphers“Good” Ciphers

Amount of secrecy needed should Amount of secrecy needed should determine the amount of labor appropriate determine the amount of labor appropriate for encryption/decryption.for encryption/decryption.

Set of keys and enciphering algorithm Set of keys and enciphering algorithm should be free from complexity.should be free from complexity.

Implementation should be simpleImplementation should be simple Errors in ciphering should not propogate.Errors in ciphering should not propogate. Size of ciphertext should be no larger than Size of ciphertext should be no larger than

the size of the plaintextthe size of the plaintext

Properties of “Trustworthy” Properties of “Trustworthy” Encryption SystemsEncryption Systems

Based on sound mathematicsBased on sound mathematics Been analyzed by competent experts Been analyzed by competent experts

and found to be soundand found to be sound Stood the “test of time”Stood the “test of time”

Three Examples:Three Examples:• DES (data encryption standard)DES (data encryption standard)• RSA (Rivest-Shamir-Adelman)RSA (Rivest-Shamir-Adelman)• AES (Advanced Encryption Standard)AES (Advanced Encryption Standard)

Symmetric and Asymmetric Symmetric and Asymmetric Encryption SystemsEncryption Systems

Symmetric requires one “secret” key that Symmetric requires one “secret” key that is used for encryption AND decryption (e.g. is used for encryption AND decryption (e.g. Caesar cipher might use a “key” of 3 to Caesar cipher might use a “key” of 3 to indicate shift by 3)indicate shift by 3)

As long as key remains secret, As long as key remains secret, authenticationauthentication is provided is provided

Problem is key distribution; if there are n Problem is key distribution; if there are n users, we need n * (n-1)/2 unique keysusers, we need n * (n-1)/2 unique keys

Symmetric and Asymmetric Symmetric and Asymmetric Encryption SystemsEncryption Systems

Asymmetric requires two keys one of Asymmetric requires two keys one of which is a “public key”which is a “public key”

The public key is used for encryption The public key is used for encryption and the “private” key is used for and the “private” key is used for decryptiondecryption

If there are n users, there are n If there are n users, there are n public keys that everyone knows and public keys that everyone knows and n private keys known only to the usern private keys known only to the user

Stream and Block CiphersStream and Block Ciphers Stream ciphers – convert one symbol Stream ciphers – convert one symbol

of plaintext immediately into a of plaintext immediately into a symbol of ciphertextsymbol of ciphertext

Transformation depends on the Transformation depends on the plaintext symbol, the key, and the plaintext symbol, the key, and the algorithmalgorithm

Error can affect all text after the Error can affect all text after the errorerror

Stream and Block CiphersStream and Block Ciphers Block cipher encrypts a Block cipher encrypts a groupgroup of plaintext of plaintext

symbols as symbols as oneone block (e.g. columnar block (e.g. columnar transposition)transposition)

StreamStream BlockBlock

AdvantagesAdvantages Speed of Speed of transformationtransformationLow error propagationLow error propagation

High diffusionHigh diffusionImmunity to insertation Immunity to insertation of symbolsof symbols

disadvantagesdisadvantages Low diffusionLow diffusionSusceptibility to Susceptibility to malicious insertations malicious insertations and modificationsand modifications

Slowness of encryptionSlowness of encryptionError propagationError propagation

Confusion and DiffusionConfusion and Diffusion ConfusionConfusion – interceptor cannot – interceptor cannot

predict what will happen to the predict what will happen to the ciphertext by changing one character ciphertext by changing one character in the plaintextin the plaintext

DiffusionDiffusion – information from single – information from single plaintext is distributed over the plaintext is distributed over the entire ciphertextentire ciphertext

CryptanalysisCryptanalysis Ciphertext OnlyCiphertext Only – requires analysis using – requires analysis using

probabilities, distributions, and probabilities, distributions, and characteristics of the available ciphertext, characteristics of the available ciphertext, plus any publicly known informationplus any publicly known information

Full or Partial PlaintextFull or Partial Plaintext – knows some – knows some plaintext and ciphertext (C & P in C = E(P) ); plaintext and ciphertext (C & P in C = E(P) ); only needs to determine the algorithm; can only needs to determine the algorithm; can use use probable plaintextprobable plaintext analysis analysis

Ciphertext of Any PlaintextCiphertext of Any Plaintext – analyst can – analyst can insert data into plaintext to be encryptedinsert data into plaintext to be encrypted

CryptanalysisCryptanalysis Algorithm and Ciphertext Algorithm and Ciphertext – analyst runs – analyst runs

the algorithm on massive amounts of the algorithm on massive amounts of plaintext to try and match one with the plaintext to try and match one with the ciphertext and deduce the sender’s ciphertext and deduce the sender’s encryption keyencryption key

Ciphertext and PlaintextCiphertext and Plaintext – try and – try and determine the encryption keydetermine the encryption key

WeaknessesWeaknesses – cryptanalysis often – cryptanalysis often succeeds because of human error and/or succeeds because of human error and/or carelessnesscarelessness

Elementary Tips for Frequency AnalysisElementary Tips for Frequency Analysis Count frequenciesCount frequencies

• j,k,q,x,z have frequency less than 1%j,k,q,x,z have frequency less than 1%• e should have frequency greater than 10% (19% in German)e should have frequency greater than 10% (19% in German)• Italian has 3 letters with frequency > 10% and 9 letters with Italian has 3 letters with frequency > 10% and 9 letters with

frequency < 1%frequency < 1% In English, look for repeated letters (ss, ee, tt, ff, ll, mm, oo)In English, look for repeated letters (ss, ee, tt, ff, ll, mm, oo) If ciphertext contains spaces, look for one, two, three letter If ciphertext contains spaces, look for one, two, three letter

words (a, I, of, to, in, it, is, be, as, at, so, we, he, by, or, on, words (a, I, of, to, in, it, is, be, as, at, so, we, he, by, or, on, do, if, me, my, up, an, go, no, us, am, the, and)do, if, me, my, up, an, go, no, us, am, the, and)

Tailor table of frequencies to message you are trying to Tailor table of frequencies to message you are trying to decipher (e.g. military messages omit pronouns and decipher (e.g. military messages omit pronouns and articles)articles)

Be willing to guess and use experienceBe willing to guess and use experience If the frequency of the ciphertext matches frequency table, If the frequency of the ciphertext matches frequency table,

the cipher is transpositonthe cipher is transpositon

Taken from Appendix B of Taken from Appendix B of The Code BookThe Code Book by Simon Singh, by Simon Singh, Doubleday, 1999.Doubleday, 1999.