Cryptology - Unofficial St. Mary's College of California Web Site

Chapter 11
Knapsack Ciphers
Merkle had great confidence in even the single
iteration knapsack system and posted a note on
his office offering a $100 reward to anyone who
could break it. ...[After Shamir broke it,] Merkle,
always one to put his money where his mouth
was ... paid Shamir the $100 is prize money.
... Merkle’s enthusiasm [wasn’t] dampened. He
promptly raised his bet and offered $1000 to anyone
who could break a multiple iteration knapsack.
It took two years, but in the end, Merkle
had to pay.
Whitfield Diffie
The First Ten Years of
Public-Key Cryptography
In cryptography one takes plaintext (that is easy to read) and attempts turn it
into ciphertext (that is apparently hard to read). In other words, cryptography
involves an easy and hard version of the same problem. There are several
mathematical problems that also have both an easy version and a hard version.
Can the parallel between an easy/hard math problem and the easy/hard to read
text be made useful As it will turn out, yes.
11.1 The Knapsack Problem
One day, whilst out hiking, you discover a cave containing many gold bars.
Being ethically challenged, you wish to carry out as much gold as possible.
Unfortunately the owner of the gold, a dragon, will probably return soon and
your backpack (knapsack) can only carry so much weight without breaking.
How can you decide which gold bars to take This is the Knapsack problem.
(To fit the knapsack problem into the cave-gold-dragon analogy, you can carry
however much your knapsack can hold, you have time to make one trip, and,
since the dragon will not the mistake of leaving his/her cave unguarded again,
one trip only.)
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