chapter08 - copiecrypto.cs.mcgill.ca/~crepeau/COMP251/chapter08.pdf · Chapter 8. Copyright © The...
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Chapter 8
Transcript of chapter08 - copiecrypto.cs.mcgill.ca/~crepeau/COMP251/chapter08.pdf · Chapter 8. Copyright © The...
Chapter 8
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⟨a1,a2,a3⟩
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⟨a1,a2,a3⟩ ⟨a1,a3,a2⟩
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⟨a2,a1,a3⟩⟨a1,a2,a3⟩ ⟨a1,a3,a2⟩
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⟨a2,a1,a3⟩⟨a1,a2,a3⟩
⟨a2,a3,a1⟩⟨a1,a3,a2⟩
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⟨a3,a1,a2⟩⟨a2,a1,a3⟩⟨a1,a2,a3⟩
⟨a2,a3,a1⟩⟨a1,a3,a2⟩
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⟨a3,a1,a2⟩⟨a2,a1,a3⟩⟨a1,a2,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩⟨a1,a3,a2⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a2,a1,a3⟩⟨a1,a2,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩⟨a1,a3,a2⟩
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⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a2,a1,a3⟩⟨a1,a2,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩⟨a1,a3,a2⟩
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⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a2,a1,a3⟩⟨a1,a2,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩⟨a1,a3,a2⟩
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⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a2,a1,a3⟩⟨a1,a2,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
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⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a2,a1,a3⟩⟨a1,a2,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩⟨a2,a3,a1⟩
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⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a2,a1,a3⟩⟨a1,a2,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a3,a1,a2⟩ ⟨a3,a2,a1⟩⟨a2,a3,a1⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a3,a1,a2⟩ ⟨a3,a2,a1⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a3,a2,a1⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩ ⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩ ⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
⟨a2,a1,a3⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
⟨a2,a1,a3⟩
⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a3,a2,a1⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a1,a3,a2⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a1,a3,a2⟩ ⟨a3,a1,a2⟩
⟨a3,a1,a2⟩⟨a1,a3,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a1,a3,a2⟩ ⟨a3,a1,a2⟩
⟨a3,a1,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a1,a3,a2⟩ ⟨a3,a1,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a1,a3,a2⟩ ⟨a3,a1,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
⟨a2,a3,a1⟩
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⟨a1,a2,a3⟩
⟨a1,a3,a2⟩ ⟨a3,a1,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩⟨a2,a3,a1⟩
⟨a2,a3,a1⟩ ⟨a3,a2,a1⟩
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⟨a1,a2,a3⟩
⟨a1,a3,a2⟩ ⟨a3,a1,a2⟩
⟨a2,a1,a3⟩
⟨a3,a2,a1⟩
⟨a2,a3,a1⟩ ⟨a3,a2,a1⟩
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⟨a1,a2,a3⟩
⟨a1,a3,a2⟩ ⟨a3,a1,a2⟩
⟨a2,a1,a3⟩
⟨a2,a3,a1⟩ ⟨a3,a2,a1⟩
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N!
N!/2 N!/2
N!/4 N!/4 N!/4 N!/4
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
log N! ∈ 𝜽(N log N)
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩ ⟨a1,a2,a3⟩⟨a1,a2,a3⟩
⟨a1,a2,a3⟩ ⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
⟨a1,a2,a3⟩⟨a1,a2,a3⟩
⟨a1,a2,a3⟩
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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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Uses 65536 memory cells, however...
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Uses 65536 memory cells, however...
