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One Time Pad (Vernam Cipher)

• Patrick • Rufus • Mark K. • Mark C. • Adams • Kelvin M.

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One Time Pad (Vernam Cipher)

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OTP History• First described by Frank Miller in 1882 the one-time pad was

re-invented in 1917 and patented a couple of years later. It is derived from the Vernam cipher, named after Gilbert Vernam, one of its inventors.

• Used by spies of the former USSR (Russia) during the 1960s

• Used a stack of small very thin pages, each with a series of random numbers on them. After use, a page would be destroyed immediately

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OTP-Working Mechanism•  The encryption-key has at least the same length

as the plaintext and consists of truely random numbers

• Each letter of the plaintext is 'mixed' with one element from the OTP

• This results in a ciphertext that has no relation with the plaintext when the key is unknown. At the receiving end, the same OTP is used to retrieve the original plaintext

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OTP Rules•  The OTP should consist of truely random numbers

• Precisely two copies of the OTP should exist.

• The OTP should only be used once.

• Both copies of the OTP are destroyed immediately after use.

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Why OTP is Unbreakable•  The key is atleast as long as the message• The key is truly random (not auto-generated)• Key and plain text calculated modulo 10/26/2• Each key should only be used once & destroyed

by sender and receiver• There should only be 2 copies of the key (1 for

sender and 1 for receiver)

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OTP Criticism•  Distribution of the key was a challenge• Adding numbers to the plaintext manually, is a

time-consuming task. It is therefore sometimes thought that OTPs are no longer considered practical

• Counter: Improved computing power now

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OTP Example•  Problem: Alice wishes to send the message "HELLO" to

Bob• ROE: Assume two pads of paper containing identical

random sequences of letters were somehow previously produced and securely issued to both

• Additional Info:Alice chooses the appropriate unused page from the pad.

• How: The way to do this is normally arranged for in advance, as for instance 'use the 12th sheet on 1 May', or 'use the next available sheet for the next message'. The material on the selected sheet is the key for this message. Each letter from the pad will be combined in a predetermined way with one letter of the message. It is common, but not required, to assign each letter a numerical value: e.g. "A" is 0, "B" is 1, and so on.

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OTP Example (Modulo26)•  Here, we combine the key and the message using

modular addition.

• The numerical values of corresponding message and key letters are added together, modulo 26.

• If key material begins with "XMCKL" and the message is "HELLO", then the coding would be……..

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OTP Encryption

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OTP Encryption [contd.]• If a number is larger than 25, then the remainder after

subtraction of 26 is taken in modular arithmetic fashion.

• This simply means that if your computations "go past" Z, you start again at A.

• The ciphertext to be sent to Bob is thus "EQNVZ". Bob uses the matching key page and the same process, but in reverse, to obtain the plaintext.

• Here the key is subtracted from the ciphertext, again using modular arithmetic…… 11

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OTP Decryption

• NB: If a number is negative then 26 is added to make the number positive

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OTP Cryptanalysis• Suppose Eve intercepts Alice's ciphertext: "EQNVZ".

• If Eve had infinite computing power, she would quickly find that the key "XMCKL" would produce the plaintext "HELLO", but she would also find that the key "TQURI" would produce the plaintext "LATER"

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OTP Cryptanalysis [contd]• It is possible to "decrypt" out of the ciphertext any

message whatsoever with the same number of characters, simply by using a different key, and there is no information in the ciphertext which will allow Eve to choose among the various possible readings of the ciphertext

• Thus, OTP coined, the “Perfect Cipher”

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Try This One:• Message: COME

• Key: BABY

• References:

http://www.cs.miami.edu/~burt/learning/Csc609.051/notes/02.html

http://www.cryptomuseum.com/crypto/otp.htm

http://practicalcryptography.com/ciphers/

http://en.wikipedia.org/wiki/One-time_pad15