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Stream Ciphers

Stream Ciphers. CSCI284-162 Spring 2007 GWU. One-time pad is best. But key too long to be practical Can we use a pseudo-random key then, which would be generated from a short truly random string?. Stream Ciphers.

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Stream Ciphers

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  1. Stream Ciphers CSCI284-162 Spring 2007 GWU

  2. One-time pad is best • But key too long to be practical • Can we use a pseudo-random key then, which would be generated from a short truly random string? CS284-162/Spring07/GWU/Vora/ Stream Ciphers

  3. Stream Ciphers • Message does not consist of words of symbols, but an (unending) stream of symbols. • A key stream (not a single key) encrypts the stream of symbols y1y2… = ez1(x1)ez2(x2)… Synchronous: when keystream generated by a key, independent of plaintext z1,z2,… = g(K) CS284-162/Spring07/GWU/Vora/ Stream Ciphers

  4. Definition: Synchronous Stream Cipher P: plaintext C: ciphertext K: keyspace (so far exactly that in block ciphers) L: keystream alphabet g: keystream generator z1,z2,… = g(K) where K K, and ziL ezi: P C dzi: C  P dzi(ezi(x)) = x CS284-162/Spring07/GWU/Vora/ Stream Ciphers

  5. Examples from ciphers we have already seen? • Shift? Affine? Substitution? Vigenère? Permutation? CS284-162/Spring07/GWU/Vora/ Stream Ciphers

  6. Periodic Stream Cipher? • Security? • Binary addition as XOR, easy to implement in hardware. • Encryption and decryption are the same operations: addition of the bit CS284-162/Spring07/GWU/Vora/ Stream Ciphers

  7. Example: Linear recurrenceProb 1.18 and 1.19 (text) zi+4 = (zi + zi+1 + zi+2 + zi+3) mod 2 Of degree 4. Why linear? Start with some z1, z2, z3, z4 0 1 0 1 0 0 1 0 1 0 0 1 Period? Security? Try two other initialization vectors Same with zi+4 = (zi + zi+3) mod 2 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

  8. Hardware implementationLinear Feedback Shift Register (LFSR) Key = (c0, c1, …cm-1, z0, z1, …zm-1) zi+m zi …. Delay Delay Delay Cm-1 Cm-2 C1 C0  ….  zi+m = j=0m-1 cizi+j m CS284-162/Spring07/GWU/Vora/ Stream Ciphers

  9. Shrinking Generator Y = f(X, Z) / * X, Y, Z, (pseudo) random-number sequences */ /* X and Z from an LFSR with different keys */ j := 0 For every i If (Xi == 1) /* Clock is ON */ Yj = Zi /* Output other sequence */ j +=1 Endif End i Disadvantage? CS284-162/Spring07/GWU/Vora/ Stream Ciphers

  10. Shrinking Generator: Examples CS284-162/Spring07/GWU/Vora/ Stream Ciphers

  11. Stop-and-go Generator Y = f(X, Z) x_pos = 0; /* mark stop position */ Forall i If(Zi == 1) /* Go. */ x_pos += 1 Endif Yi := Xx_pos /* Hold onto output value */ End i CS284-162/Spring07/GWU/Vora/ Stream Ciphers

  12. Examples CS284-162/Spring07/GWU/Vora/ Stream Ciphers

  13. Is the one-time pad with a pseudo-random key perfectly secret? CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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