Cryptography Week 2: Limitations of the One Time Pad

A real world application of the 1timepad is the Red Phone of the 1980’s, with suitcases full of bits flown between moscow and DC

Limitations:

Key is as long as message Only secure if each key is used only once Therefore total length of keys shared must = total length of all messages ever want to send

Break if 2 messages to encrypt using one key

m1 -> &1 m2 -> &2

&1 XOR &2 = m1 XOR m2

Although it might not be useful, it rules out perfect secrecy

However it is useful

this reveals where m1 and m2 differ If plaintext are long can apply frequency analysis All letters begin with 01 Space is 00 XOR of 2 letters, get a byte with 00 prefix XOR of letter and space, get a byte with 01 prefix XOR of 2 spaces, get 00, but not common Therefore, can guess what is in each location Punctuation can mess this up but its uncommon so don’t worry about it

Using this method letters are guessable

not just 1 time pad, but inherent to many schemes One time pad is optimal as far as length of key goes Now relax the definition of perfect secrecy, obtain much more applicable ideas