Exercise 4.6 
************

The first plaintext is from page 357 of "The Papers of Samuel Marchbanks", by
Robertson Davies, Clarke Irwin, 1947. 

      I became involved in an argument about modern painting, a subject upon which I am spectacularly
      ill-informed. However, many of my friends can become heated and even violent on the subject, and I
      enjoy their wrangles in a modest way. I am an artist myself and I have some sympathy with the
      abstractionists, although I have gone beyond them in my own approach to art. I am a lumpist. Two or three
      decades ago it was quite fashionable to be a cubist and to draw everything in cubes. Then there was a
      revolt by the vorticists who drew everything in whirls. We now have the abstractionists who paint
      everything in a very abstracted manner, but my own small works done on my telephone pad are composed
      of carefully shaded, strangely shaped lumps with traces of cubism, vorticism, and abstractionism in them.
      For those who possess the seeing eye, as a lumpist, I stand alone. 

The second plaintext is from page 17 of "Lake Wobegon Days", by Garrison
Keillor, Penguin Viking, Inc., 1985. 

      Lake Wobegon is mostly poor sandy soil, and every spring the earth heaves up a new crop of rocks. Piles
      of rocks ten feet high in the corners of fields, picked by generations of us, monuments to our industry. Our
      ancestors chose the place, tired from their long journey, sad for having left the motherland behind, and this
      place reminded them of there, so they settled here, forgetting that they had left there because the land
      wasn't so good. So the new life turned out to be a lot like the old, except the winters are worse.

Exercise 5.4 
************

The plaintext is from page 1 of "The English Patient", by M. Ondaatje, Alfred
A. Knoph, Inc., 1992. 

      She stands up in the garden where she has been working and looks into the distance. She has sensed a
      change in the weather. There is another gust of wind, a buckle of noise in the air, and the tall cypresses
      sway. She turns and moves uphill towards the house. Climbing over a low wall, feeling the first drops of
      rain on her bare arms, she crosses the loggia and quickly enters the house.


Exercise 8.3 
************

U computes alpha ^{a_U} = 7580 and
V computes alpha ^{a_V} = 22181.
U computes 22181 ^{a_U} = 10141 and
V computes 7580 ^{a_V} = 10141. 

Exercise 8.5 
************

MTI:
I= p,alpha,beta,gamma,delta,epsilon.

DH:
I= p,alpha,u=alpha^a,v=alpha^b

Solving DH given MTI.
--------------------

Construct an MTI instance from the DH instance:
set p=p,alpha=alpha,beta=u,gamma=v,delta=1,epsilon=1
and solve using algorithm for MTI.

the answer to DH instance is the asnwer to MTI instance.

Solving MTI given DH.
--------------------

Construct a DH instance from the MTI instance:
set p=p,alpha=alpha,u=beta,v=gamma
and solve using algorithm for DH; let z be the answer.

Construct another DH instance from the MTI instance:
set p=p,alpha=alpha,u=delta,v=epsilon
and solve using algorithm for DH; let z' be the answer.

the answer to MTI instance is z*z' mod p.

Exercise 12.6 
*************

The plaintext is from page 129 of "Under the Hammer", by J. Mortimer, Penguin
Books, 1994. 

      It was a fine spring morning in Wedensbury Park, Somerset. The dawn chorus was over, but the early
      sunshine still sparkled on the dew. The daffodils were in bud and the azaleas looked promising, when Lady
      Pamela Wedensbury threw the entire contents of her husband's wine cellar into the lake.