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3 1 This problem concerns encoding phrases using numbers using the e

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3.1 This problem concerns encoding phrases using
numbers using the encoding of Section 3.3.2. What is the
longest that an arbitrary sequence of letters (no spaces)
can be if it must fit in a number that is less than 10^20? In
order to use the RSA cryptosystem to encrypt messages, it
is necessary to encode them as a sequence of numbers of
size less than n = pq. We now describe a simple way to do
this. Note that in any actual deployed implementation, it is
crucial that you add extra random characters (\"salt\") at
the beginning of each block of the message, so that the
same plain text encodes differently each time. This helps
thwart chosen plain text attacks. Suppose s is a sequence
of capital letters and spaces, and that .s does not begin
with a space. We encode s as a number in base 27 as
follows: a single space corresponds to 0, the letter A to 1,
B to 2, ..., Z to 26. Thus \"RUN NIKITA\" is a number
written in base 27. RUN NIKITA doubleheadarrow 27^9
middot 18 + 27^8 middot 21 + 27^7 middot 14 + 27^6
middot 0 + 27^5 middot 14 + 27^4 middot 9 + 27^3 middot
11 + 27^2 middot 9 + 27 middot 20 + 1 =
143338425831991 (in decimal). To recover the letters
from the decimal number, repeatedly divide by 27 and read
off the letter corresponding to each remainder.
Solution
The best case is that take each letter as A.The question is
that to find largest n such that
1+27+.............+27k<=1020

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3.1 This problem concerns encoding phrases using numbers using the encoding of Section 3.3.2. What is the longest that an arbitrary sequence of letters (no spaces) can be if it must fit in a number that is less than 10^20? In order to use the RSA cryptosystem to encrypt messages, it is necessary to encode them as a sequence of numbers of size less than n = pq. We now describe a simple way to do this. Note that in any actual deployed implementation, it is crucial that you add extra random characters (\"salt\") at the beginning of each block of the message, so that the same plain text encodes di ...
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