Assessment Item A1 – Understanding and analysis of the operations underlying the
RSA encryption algorithm - CS321
Skill being assessed: Ability of student to identify concepts involved in the RSA
algorithm, apply those concepts in a computation for a small example, and explain
the complications that arise when this computation is scaled up to a realistically
large example.
Program outcome to which this skill is mapped: (a) An ability to apply knowledge
of computing and mathematics appropriate to the discipline
Performance Assessment Abstract: You are given the following computational
facts:
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
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You get an encrypted message in the form of one number whose value is 85.
It was encrypted using the public key (23, 143). (Aside not told to students
doing exercise: Two small primes – 13 and 11 – are the prime factors of 143)
When you execute the ExtendedEuclid algorithm with 23 and 143, it returns
the triple (56, −9, 1)
When you execute the ExtendedEuclid algorithm with 23 and 120, it returns
the triple (47, −9, 1)
(Aside – in the future, it would be good to have an online app for the ExtendedEuclid
algorithm, so they would actually have to use this to determine the critical
information for the mod inverse. That way we would not have to tell them possible
return values they might or might not need.)
Given this information:
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
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What is private key for RSA decryption? Explain how you used the
computational facts you were given in determining this key.
What is the value of the decrypted message using the private key that you
determined in the preceding question? (Leave your answer in factored form.)
When you worked from the computational facts that you were given to get
the private key, there was one additional fact that you had to discover above
and beyond those given facts to fathom the private key. What was this
additional fact? Explain why, in practice, this additional fact would not be
easy to discover and consequently why RSA encryption safeguards encrypted
data from being easily decrypted by those who might surreptitiously
intercept a message that was not intended for them.
Rubric for Evaluation
Criteria
Determination of
private key.
Exemplary
The student
knows the
computations
that apply – in
particular the
role of the
ExtendedEuclid
algorithm – and
carries them out
correctly for this
example to get
the right value
for the private
key.
Decryption of data
using a private key
in computationally
simple example.
The student
demonstrates
precise
knowledge of
computations
that apply and is
able to correctly
use them in
determining the
formula that
should be
applied to get the
correct
decrypted value
for this example.
Explanation of
what computation
typically cannot be
determined in the
RSA method of
encryption and
how the difficulty
of this
computation
prevents data
encrypted by RSA
from being
decrypted by
those who should
not have access to
it.
The student
correctly
identifies that
determining the
prime factors of
N is the
computation that
cannot be
determined in a
reasonable time
and gives a
precise
explanation of
how our inability
to perform this
computation
protects the
security of the
encrypted
Satisfactory
The student
knows the
computations
that apply. In
carrying them out
for this example,
they demonstrate
knowledge of
how the
computations
should be applied
but make an error
in doing
arithmetic and
hence get an
incorrect answer.
The student
knows the
computations
that apply in a
general fashion.
However, in
carrying them out
for this particular
example, they
make a minor
error in actually
applying the
appropriate
formula to the
specific numbers
involved.
The student
correctly
identifies that
determining the
prime factors of N
is the
computation that
cannot be done
but is not precise
in explaining
what keeps this
computation from
being practical
and thereby how
RSA encryption is
safeguarded.
Marginal
The student
knows the
computations
that apply but is
confused about
how to apply
them to get an
actual answer for
this example.
Deficient
The student is not
even aware of the
computations that
apply.
The student
knows the
computations
that apply but is
confused about
how to apply
them to get an
actual answer for
this example.
The student is not
even aware of the
computations that
apply.
The student
correctly
identifies that
determining the
prime factors of N
is the
computation that
cannot be done
but offers no
explanation of
why this
computation is
impractical and
thereby protects
RSA-encrypted
data.
The student is not
able to correctly
identify the
computation.
message.