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s-prg - STREAM CIPHERS and PRGs 1 16 Stateful Generators...

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STREAM CIPHERS and PRGs 1/16
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Stateful Generators Initially, St is a random seed G St St X Operation: G G G St[1] St[2] St[3] St[0] X[1] X[2] X[3] X [1] X [2] X [3] ... is the output sequence and should be “pseudorandom”. 2/16
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Notation ( X [1] ... X [ m ] , St ) G ( St , m ) means we Run G with starting state St for m steps Let X [1] ... X [ m ] be the output blocks produced Let St be the updated state G X[1] St G St X[m] ... 3/16
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Usage for Encryption Alice maintains a state St A and Bob maintains a state St B . Initially: St A = St B is a random seed. E ( M [1] ... M [ m ]) ( X [1] ... X [ m ] , St A ) G ( St A , m ) for i = 1 ,..., m do C [ i ] X [ i ] M [ i ] D ( C [1] ... C [ m ]) ( X [1] ... X [ m ] , St B ) G ( St B , m ) for i = 1 ,..., m do M [ i ] X [ i ] C [ i ] Note that the states must be synchronized! 4/16
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Usage for Pseudorandom Bit Generation G is initialized with a random seed and its outputs are then used coins for any purpose needing randomness, including: Keys IVs for block-cipher based encryption Nonces Simulations 5/16
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Methods Linear Congruential Generators (LCGs) Linear Feedback Shift Registers (LFSRs) These have
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