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Use the key length to solve for the recurrence.The School of Teaching & Learning offers the Master of Arts in Education (M.A.E.) degree in Mathematics Education.

Can you devise a bad example (one with period N.

See for a list of maximal-period generators.

If it cycles through all of these, it’s maximal.

How many bits do we need to represent this recurrence?.

Like Vigenere with long key: hard to decrypt!.LFSR can generate sequences with long periods.How long until it repeats? (the period of the sequence).Specify initial conditions and coefficients, for example:.Linear Feedback Shift Register (LFSR) Sequences Need initial conditions (bits in register) and a function to generate more terms.Linear Feedback Shift Register (LFSR) Sequences Name comes from hardware implementation Generated bit stream Shift register b1 b2 b3 b4 … bm-1 bm To encrypt plaintext of length n, generate an n-bit sequence and XOR with the plaintext. If I’m willing to compromise some security….What’s the downside to using a one-time pad? Variation: Maurer, Rabin, Ding et al’s satellite method.Yes, for ciphertext only… Ciphertext: EOFMCKSSDKIVPSSAD Could be: thephoneisringing meetmeinthegarage … I need the whole key to decrypt.The key is a random vector of length n.Works for text (from ASCII), images, music, etc.

Represent the plaintext in binary, length n.Now consider the extreme case, the one-time pad….What does this say about our ability to do a frequency analysis?.Back to Vigenere: if the codeword were really long, say 25% as long as the entire plaintext, how many characters would contribute to each dot product? _.Schedule change: skip Playfair cipher, start ch 3 tomorrow.

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