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Elementary Cryptology

Elementary Cryptology. Algorithms or “Ciphers”. Concealment: Hide a message inside a message. Substitution: Change the symbols used to write the message. Transposition: Scramble the order of the symbols used to write the message. Concealment Ciphers or Steganography.

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Elementary Cryptology

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  1. Elementary Cryptology

  2. Algorithms or “Ciphers” Concealment: Hide a message inside a message. Substitution: Change the symbols used to write the message. Transposition: Scramble the order of the symbols used to write the message.

  3. Concealment CiphersorSteganography Steganograpy (covered writing), null cipher, open-letter cipher, conventional writing, dissimulated writing, etc.

  4. Concealment Ciphers A message is embedded (hidden) within a seemingly inocuous piece of information: A treatise to analyze campus knowledge of undergraduate tenants portrays outright sympathy totally aimed toward negligent idiots notwithstanding elegant amoral mentalities.

  5. Concealment Ciphers A message is embedded (hidden) within a seemingly inocuous piece of information: Atreatise to analyze campus knowledge of undergraduate tenants portrays outright sympathy totally aimed toward negligent idiots notwithstanding elegant amoral mentalities. attack outpost at nine am

  6. Lord Bacon’s Cipher Hold OFf uNtIl you hEar frOm mE agAin. wE May cOMpROmIse. HoldO FfuNt Ilyou hEarf rOmmE agAin wEMay cOMpR OmIse baaab baaba baaaa abaaa abaab aabaa abbaa abbab babaa The message could be concealed in markings on a piece of candy, on the palings of a picket fence, on the arrangement of a deck of cards, on published text with slightly different fonts, etc. Bacon’s Bi-literal Alphabet strike now

  7. A Steganographic Paradigm secret embedding algorithm extraction algorithm open message with embedded secret secret open message

  8. Embedding Messages in Images Steganogram: 47K bytes; Message: 6.46K bytes Original image: 47K bytes • Detecting that an image has an embedded message visually is nearly impossible. • Checking the size of the image doesn’t help. • The only hope seems to lie in deep, thorough mathematical analysis. Source:Model Based Steganography, Phil Salee, UC Davis.

  9. Breaking Concealment Ciphers These ciphers depend on the belief that they won’t be identified in a steganogram. One looks for embedded messages in data depending on the level of caution that is warranted. At times, the steganogram may be enciphered using transposition or substitution to further confuse the reader. In the event the reader can break the first cipher and read the steganogram, s/he may think that the secret has been solved.

  10. Substitution Ciphers

  11. Monoalphabetic Substitution Ciphers:The Caesar Cipher Algorithm: for each letter P in the plaintext, compute a corresponding letter C of the ciphertext using the equation below. PLAINTEXT ciphertext PLAINTEXT: HERE BE DRAGONS. ciphertext: khuh eh gudjrqs.

  12. Monoalphabetic Substitution Ciphers:The Additive Cipher The key is a positive integer value determining the shift in the cipher text alphabet. Algorithm: for each letter P in the plaintext, compute a corresponding letter C of the ciphertext using the equation below. Example: PLAINTEXT ciphertext (key: r = 6) PLAINTEXT: HERE BE DRAGONS. ciphertext: nkxk hk jxgmuty. POSSIBLE “REAL” KEY VALUES: 26. WEAK KEY: r = 0.

  13. Monoalphabetic Substitution Ciphers:The Multiplicative Cipher Algorithm: for each letter P in the plaintext, compute a corresponding letter C of the ciphertext using the equation below. Caution: We have to be careful with the choice of s: gcd(s, 26) must be 1 so that there’s a multiplicative inverse for s. PLAINTEXT ciphertext (key: s=13) PLAINTEXT ciphertext (key: s=2)

  14. Monoalphabetic Substitution Ciphers:The Multiplicative Cipher PLAINTEXT ciphertext (key s=3) gcd(3, 26) = 1 PLAINTEXT: HERE BE DRAGONS. ciphertext: vmzm dm jzasqnc. POSSIBLE “REAL” KEY VALUES: ? WEAK KEY: ?

  15. Monoalphabetic Substitution Ciphers: The Multiplicative Cipher Decription Algorithm: for each letter C in the plaintext, compute a corresponding letter P of the ciphertext using the equation below. Fine, but what is this k ? It is not (1/s), but rather the multiplicative inverse of k under modulo 26 arithmetic. You can find it by brute-force: first, substitute C in the equation above using the encipherment equation to obtain:

  16. Finding the multiplicative inverse What we want is to find some value of m* such that: Without any knowledge of number theory, we can try all values between 1 and 26 for m* in the above equation and find the value that works out. This value of m* can be used to decipher this multiplicative cipher.

  17. Monoalphabetic Substitution Ciphers: The Affine Cipher Algorithm: for each letter P in the plaintext, compute a corresponding letter C of the ciphertext using the equation below. Caution: We also have to be careful with the choice of s: gcd(s, 26) must be 1 PLAINTEXT ciphertext (key: m=5, a=8) PLAINTEXT: HERE BE DRAGONS. ciphertext: rcpc nc xpimavu. POSSIBLE “REAL” KEY VALUES: ? WEAK KEY: ?

  18. Monoalphabetic Substitution Ciphers:Random Alphabet Shuffle The key is the cipher alphabet: a 26 letter long string that determines a mapping for the substitution of letters in the plaintext. Example: PLAINTEXT ciphertext (the key is the whole alphabet) PLAINTEXT: HERE BE DRAGONS. ciphertext: elpl al gptbkjs. POSSIBLE KEY VALUES: ? WEAK KEYS: ?

  19. Fun Reading on Frequency Analysis The Adventure of the Dancing Men, Sir Arthur Conan Doyle The Gold Bug, Edgan Allan Poe

  20. References • Cryptological Mathematics, Robert E. Lewand. The Mathematical Association of America, 2000. • Cryptanalysis, Helen Fouché Gaines. Dover Publications, Inc., 1939. • The Code Book, Simon Singh. Anchor Books, 1999.

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