Cryptography Reference
In-Depth Information
App.31. Verify the four properties of Blum Integers given on page 508.
Use the continued fraction algorithm, described on pages 512 and 513 to
factor the integer
n
given in Exercises App.32-App.36.
App.32.
n
= 6457.
App.33.
n
= 75433.
App.34.
n
= 387181.
App.35.
n
= 98759.
App.36.
n
= 689863.
App.37.
1 algorithm to factor the integers in Exercises
App.32-App.36. (See pages 514 and 515.)
Use Pollard's
p
−
App.38. Use Pollard's Rho-Method to factor the integers in Exercises App.32-
App.36. (See pages 515-517.)
App.39. Use the QS method to factor the integers in Exercises App.32-App.36.
(See pages 517-519.)
App.40. Use the MPQS method to factor the integers in Exercises App.32-
App.36. (See pages 519-522.)
App.41. Use the ECM method to factor the integers in Exercises App.32-
App.36. (See pages 522-524.)
App.42. Compare the factoring methods used in Exercises App.37-App.41.
In Exercises App.43-App.46, use the Silver-Pohlig-Hellman algorithm pre-
sented on pages 530-532, to find the value of
log
α
β
from the given param-
eters.
App.43.
p
= 73,
α
=5,
β
=8.
App.44.
p
= 1637,
α
=2,
β
= 15.
App.45.
p
= 2689,
α
= 19,
β
= 27.
App.46.
p
= 2999,
α
= 17,
β
= 38.
App.47. Use the baby-step giant-step algorithm described on pages 533 and
534, to calculate the values in Exercises App.43-App.46.
App.48. Use the index-calculus method, delineated on pages 534-536, to cal-
culate the values in Exercises App.43-App.46.
In Exercises App.49-App.52, use radix-
64
encoding via the description on
pages 541 and 542, to encode the given three-byte segments.
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