CSCI284-162 Spring 2007

GWU

Stream Ciphers

04/19/23 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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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?

04/19/23 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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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)

04/19/23 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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Definition: Synchronous Stream Cipher

P: plaintextC: ciphertextK: keyspace(so far exactly that in block ciphers)L: keystream alphabetg: keystream generator

z1,z2,… = g(K) where K K, and zi L

ezi: P C

dzi: C P

dzi(ezi

(x)) = x

04/19/23 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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Examples from ciphers we have already seen?

• Shift? Affine? Substitution? Vigenère? Permutation?

04/19/23 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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Periodic Stream Cipher?

• Security?

• Binary addition as XOR, easy to implement in hardware.

• Encryption and decryption are the same operations: addition of the bit

04/19/23 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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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

04/19/23 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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Hardware implementationLinear Feedback Shift Register (LFSR)

….Delay Delay Delay

m

Cm-1 Cm-2 C0

C1

….

zi+m = j=0m-1 cizi+j

zizi+m

Key = (c0, c1, …cm-1, z0, z1, …zm-1)

04/19/23 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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Shrinking Generator

Y = f(X, Z) / * X, Y, Z, (pseudo) random-number sequences *//* X and Z from an LFSR with different keys */

j := 0For every i

If (Xi == 1) /* Clock is ON */Yj = Zi /* Output other sequence */j +=1

EndifEnd i

Disadvantage?

04/19/23 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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Shrinking Generator: Examples

04/19/23 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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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

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Examples

04/19/23 CS284-162/Spring07/GWU/Vora/ Stream Ciphers

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Is the one-time pad with a pseudo-random key perfectly secret?