Cryptography - Sage

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This work is licensed under aCreative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.See http://creativecommons.org for details.c○David R. Kohel
Page 1: Author (David R. Kohel) /Title (Cry
Page 5 and 6: 6.2 Properties of Stream Ciphers .
Page 8: CHAPTERONEIntroduction to Cryptogra
Page 11 and 12: The string monoids A ∗ form a ver
Page 13 and 14: To recover to our original notion,
Page 15 and 16: SUPPOSETHATWEFIRSTENCODEAMESSAGEBYP
Page 17 and 18: This gives the encoded plaintext:HU
Page 19 and 20: ZYXWVUT T T TSRQPONNMLKJIIH H HGFEE
Page 21 and 22: IIHDYOOWSAEONUAPVCNTGSIEKDHHREYSEES
Page 24 and 25: CHAPTERTHREEElementary Cryptanalysi
Page 26 and 27: Examples of CryptanalysisLet’s be
Page 28 and 29: Exercise. Explain why ciphertext fo
Page 30 and 31: # 1 2 3 4 5 6 7 8 9 10 113 Z A Z K2
Page 33 and 34: Exercise 3.3 For each of the crypto
Page 35 and 36: Two statistical measures that we ca
Page 37 and 38: What is the maximum value of x log
Page 39 and 40: 4.4 Conditional EntropyWe can now d
Page 41 and 42: Exercise 4.2 Show that the rate of
Page 43 and 44: involving the repetition of an inte
Page 45 and 46: 5.2 Digital Encryption Standard Ove
Page 47 and 48: 5.4.1 Electronic Codebook Mode (ECB
Page 49 and 50: the deciphered plaintext block M
Page 51 and 52: 3. Error propagation. An error in a
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CHAPTERSIXStream CiphersA stream ci
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Before discussing the mathematical
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Periods of LFSR’sWe begin with so
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Linear feedback shift registers (LF
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LFSR Cryptosystems We introduce new
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CHAPTERSEVENElementary Number Theor
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we find similarly that x 7 = (x 5 +
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Theorem 7.8 The cyclotomic polynomi
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If a, b, and c are as above, then f
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Symmetric Cryptography ProtocolInit
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on the difficulty of factoring n, o
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and similarlym 2 = c d 2mod 23 ≡
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aise both sides to the power m, the
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andom prime, gcd, xgcd, and inverse
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CHAPTERNINEDigital SignaturesA digi
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3. The spender remains anonymous un
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Shamir’s scheme is defined for a
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APPENDIXASAGE ConstructionsSAGE is
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sage: x = 2sage: type(x)sage: y = 2
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at the command line:sage: x = 2sage
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A set in SAGE (i.e. Python) represe
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sage: S = ’This\n is\n a \n strin
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APPENDIXBSAGE CryptosystemsString m
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CryptosystemsSpecific cryptosystem
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Solution.The inverse of the above s
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APPENDIXCSolutions to ExercisesIntr
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sage: (r,s) = (7,5)sage: G = Symmet
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1 : 0.04128012438455552 : 0.0424744
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sage: X = pt.frequency_distribution
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where N is the total number of char
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Solution.By rearranging the sum∑
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where X = K ⊕ M = (X 1 , X 2 , X
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Solution. The data of a LFSR diagra
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Unlike the encoding function strip
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Exercise 6.11 Since the LFSR is the
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is 624499148328708779 — pretty mu
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We would like to compute the value
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With a value of 128, the modulus is
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1. Fermat’s little theorem tells
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Then verify that c n 5= a 129n 5and
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APPENDIXDRevision ExercisesLet A be
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4. (∗) The polynomial g(x) = x 6
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2. We find log 7 (2) = 48 in F 89 a
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Cryptography - Sage

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