# The Bridge - February 2018 - 21

```Quantum Cryptography and Side Channel Attacks

Suppose we have two individuals who wish to
establish secure communication, Alice and Bob.
While Alice and Bob are physically separated, they
are connected by a single optical fiber cable. They
also have access to ordinary, unsecured classical
communication channels (such as the Internet).
1. Alice creates randomly polarized photons
and sends them to Bob
As the first step, Alice creates a long sequence of
qubits in the form of randomly polarized photons.
When modeled as a two-state quantum system,
photon polarization consists of two quantum states
that form a complete orthogonal basis spanning
the two-dimensional Hilbert space. A common pair
of basis states is horizontal (|Hi = |0i) and vertical
(|V i = |1i). Through superposition, two additional
orthogonal states can be created (non-orthogonal to
H and V ): the diagonal (|Di) and antidiagonal (|Ai).
Those states are defined as:

(1)

(2)

So, prior to creating each photon qubit, Alice
chooses a random polarization basis (HV or AD).
She records this information. Then, she creates the
photon with a random polarization state within that
basis. She also records this polarization state and its
associated bit value. Note that upon measurement
|Hi and |Di correspond to bit 0 and |V i and |Ai
correspond to bit 1. Thus, each photon that Alice
creates has a random polarization state with a
25% probability of being |Hi, |V i, |Ai, or |Di.
She then transmits the qubit to Bob via their
optical fiber cable.
2. Bob receives the qubits from Alice
and measures them
Upon receiving the photons from Alice, Bob
measures their polarization states to begin the
process of creating a secret key. As follows from the
basic principles of quantum mechanics, the basis
that Bob uses for his measurements will affect their

outcome. For each photon that Bob receives, he
randomly chooses either the HV or AD basis, and
performs the measurement. He records his basis
choices and measurement results in the form of
random bits.
3. Alice and Bob compare results
As the final step in the BB84 protocol, Alice and
Bob indirectly compare their random bits to obtain a
sifted key. Alice announces to Bob over an insecure
classical channel her random basis choices while
keeping secret her state choices. Bob looks at
his basis choices, and tells Alice which photons
had Alice and Bob choosing the same basis, and
which had a basis mismatch. Bob communicates
this information to Alice over the insecure classical
channel, keeping secret his measurement outcomes.
Alice and Bob then agree to keeping measurements
when their measurement basis matched, and
discarding all other measurements.
This step is significant because in keeping only the
photons for which Bob knows he used the same
basis as Alice, he can be certain that the random
bit resulting from his measurement is exactly
the same random bit that Alice obtained when
randomly choosing a polarization state prior to
photon transmission, due to the nature of quantum
measurement. So the BB84 protocol allows Alice
and Bob to create two sets of sifted keys of random
bits that they know are identical just by comparing
basis choices so that their actual random bits
remain secret.
As a result, Alice and Bob now share a string of
random bits that they can use as their secret key
for the proved-secure one-time pad procedure as
discussed earlier. Note that the one-time pad also
works with strings of random bits [9, 12]. Suppose
Alice uses an encoding system to convert her
secret alphanumerical message to the binary string
"10111001." The secret key that she shares with
Bob might be "11001101." She performs bitwise
modulo-2 sum (XOR) with her message and the

HKN.ORG

21

```
http://www.HKN.ORG

# Table of Contents for the Digital Edition of The Bridge - February 2018

Contents
The Bridge - February 2018 - Cover1
The Bridge - February 2018 - Cover2
The Bridge - February 2018 - Contents
The Bridge - February 2018 - 4
The Bridge - February 2018 - 5
The Bridge - February 2018 - 6
The Bridge - February 2018 - 7
The Bridge - February 2018 - 8
The Bridge - February 2018 - 9
The Bridge - February 2018 - 10
The Bridge - February 2018 - 11
The Bridge - February 2018 - 12
The Bridge - February 2018 - 13
The Bridge - February 2018 - 14
The Bridge - February 2018 - 15
The Bridge - February 2018 - 16
The Bridge - February 2018 - 17
The Bridge - February 2018 - 18
The Bridge - February 2018 - 19
The Bridge - February 2018 - 20
The Bridge - February 2018 - 21
The Bridge - February 2018 - 22
The Bridge - February 2018 - 23
The Bridge - February 2018 - 24
The Bridge - February 2018 - 25
The Bridge - February 2018 - 26
The Bridge - February 2018 - 27
The Bridge - February 2018 - 28
The Bridge - February 2018 - 29
The Bridge - February 2018 - 30
The Bridge - February 2018 - 31
The Bridge - February 2018 - 32
The Bridge - February 2018 - 33
The Bridge - February 2018 - 34
The Bridge - February 2018 - 35
The Bridge - February 2018 - 36
The Bridge - February 2018 - 37
The Bridge - February 2018 - 38
The Bridge - February 2018 - 39
The Bridge - February 2018 - 40
The Bridge - February 2018 - 41
The Bridge - February 2018 - 42
The Bridge - February 2018 - 43
The Bridge - February 2018 - 44
The Bridge - February 2018 - 45
The Bridge - February 2018 - 46
The Bridge - February 2018 - 47
The Bridge - February 2018 - 48
The Bridge - February 2018 - 49
The Bridge - February 2018 - 50
The Bridge - February 2018 - 51
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