La criptografía cuántica es una de las joyas de la corona del cómputo cuántico. Además de conocerse a detalle el fundamento teórico de los protocolos de esta disciplina, se ha hecho investigación experimental por más de dos décadas y, como resultado, existen ya equipos de criptografía cuántica que se pueden comprar e instalar bajo la lógica de cualquier producto comercial. En esta plática, titulada “Criptografía cuántica - fundamentos, productos y empresas”, el Dr Venegas Andraca dará una introducción concisa a los protocolos de criptografía cuántica BB84 y EK91, describirá las ventajas que estos protocolos tienen respecto de protocolos populares de criptografía convencional, expondrá las restricciones tecnológicas de BB84 y EK91, presentará los equipos de criptografía cuántica disponibles en el mercado y dará un análisis sucinto de las estimaciones de crecimiento comercial de esta disciplina.

2. Quantum Cryptography:
Quantum cryptography: foundations,
products and companies
Salvador E. Venegas-Andraca
Tecnol´ogico de Monterrey, Escuela de Ingenier´ıa y Ciencias
Qualtop, SA de CV
Software Gur´u Virtual Conference 2017
24 May 2017

3. Quantum Cryptography:
Thanks
Table of Contents
1 Thanks
2 Quantum Computation and Quantum Information
3 Mathematics for quantum cryptography
4 Cryptography
5 Business

4. Quantum Cryptography:
Thanks
My warmest thanks to
Software Gur´u
CONACyT - Fronteras de la Ciencia and SNI
Tecnol´ogico de Monterrey
Qualtop

5. Quantum Cryptography:
Quantum Computation and Quantum Information
Table of Contents
1 Thanks
2 Quantum Computation and Quantum Information
3 Mathematics for quantum cryptography
4 Cryptography
5 Business

6. Quantum Cryptography:
Quantum Computation and Quantum Information
Quantum computation and quantum information
Quantum computation and quantum information are scientific
and engineering disciplines devoted to the development of
i) Quantum algorithms.
ii) Quantum information processing protocols and devices.

7. Quantum Cryptography:
Quantum Computation and Quantum Information
Quantum computation and quantum information
Some key results in quantum computation and quantum infor-
mation include the discovery of
Quantum teleportation, which consists of transmitting
quantum information (originally contained in a qubit) via a
quantum channel.
Quantum dense coding, which allows sending two
classical bits using only one qubit.
quantum cryptography, which allows coding using
quantum systems.

8. Quantum Cryptography:
Quantum Computation and Quantum Information
Quantum Cryptography
Quantum cryptography is a robust field of science and engineer-
ing that has evolved in an emergent high-tech market with com-
panies capable of delivering off-the-shelf products. Quantum
cryptography protocols can be categorized into
Quantum key distribution protocols (QKD).
Quantum secret sharing protocols (QSS).
Quantum secure direct communication protocols
(QSDC).
Deterministic secure quantum communication
protocols (DSQC).

9. Quantum Cryptography:
Quantum Computation and Quantum Information
Quantum Cryptography
Let us now provide a succinct introduction to some fundamental
concepts of quantum computation needed to formally describe
quantum cryptography protocols.

10. Quantum Cryptography:
Mathematics for quantum cryptography
Table of Contents
1 Thanks
2 Quantum Computation and Quantum Information
3 Mathematics for quantum cryptography
4 Cryptography
5 Business

11. Quantum Cryptography:
Mathematics for quantum cryptography
A question: what is quantum computation?
Quantum Computation
=
Quantum Mechanics + Computer Science
Quantum Mechanics: a set of physical laws that describe the
behaviour of atomic and subatomic phenomena.
Computer science: branch of mathematics divided into
automata theory, computability theory and complexity theory.

12. Quantum Cryptography:
Mathematics for quantum cryptography
A question: what is quantum computation?
Quantum computation, one of the most recent joint ventures be-
tween physics and computer science, may be defined as follows:
Quantum Computation is a multidisciplinary field focused on
the development of computers and algorithms, i.e. hardware
and software, based on the quantum mechanical properties of
Nature.

13. Quantum Cryptography:
Mathematics for quantum cryptography
Bits and Qubits
In classical computation, information is stored and manipulated
in the form of bits.
The mathematical structure of a classical bit is rather simple:
it suffices to define two logical values, traditionally labelled as
{0, 1} (i.e. a classical bit lives in a scalar space) and to relate
those values to two different and mutually exclusive outcomes
of a classical measurement.

14. Quantum Cryptography:
Mathematics for quantum cryptography
Bits and Qubits
In quantum computation, information is stored, manipulated and
measured in the form of qubits (= quantum bit). A qubit is a
physical entity described by the laws of quantum mechanics.

15. Quantum Cryptography:
Mathematics for quantum cryptography
Bits and Qubits
Remember:
– R2, the two-dimensional space studied in elementary
school. Elements of R2, denoted by ˛x, are vectors.
– Any vector ˛x = (a, b) can be written as a linear combination
of a basis, e.g.
˛x = (a, b) = ˛x = (a, b) = aˆı + bˆä

16. Quantum Cryptography:
Mathematics for quantum cryptography
Bits and Qubits
In quantum computation, we use the following notation for
denoting vectors:
˛x = |xÍ
So,
˛x = aˆı + bˆä … |xÍ = a|iÍ + b|jÍ

17. Quantum Cryptography:
Mathematics for quantum cryptography
Bits and Qubits
A qubit is a unit vector in a two-dimensional complex space
|ÂÍ œ C2

18. Quantum Cryptography:
Mathematics for quantum cryptography
Bits and Qubits
A qubit |ÂÍ may be written in general form as
|ÂÍ = –|pÍ + —|qÍ
where –, — œ C, |–|2 +|—|2 = 1 and {|pÍ, |qÍ} is an arbitrary basis
spanning C2.
Note that a most important consequence of the vectorial nature
of a qubit is the possibility of writing it as a linear combination of
elements of any basis.

19. Quantum Cryptography:
Mathematics for quantum cryptography
The choice of {|pÍ, |qÍ} is often the orthonormal basis
{|0Í, |1Í}
known as the computational basis.

20. Quantum Cryptography:
Mathematics for quantum cryptography
In addition to the computational basis {|0Í, |1Í}, it is customary
in quantum cryptography protocols to use the diagonal basis
{|+Í, |≠Í}

21. Quantum Cryptography:
Cryptography
Table of Contents
1 Thanks
2 Quantum Computation and Quantum Information
3 Mathematics for quantum cryptography
4 Cryptography
5 Business

22. Quantum Cryptography:
Cryptography
Intro to cryptography
Cryptography is the branch of science and engineering devoted
to the design and implementation of techniques for secure com-
munication, under the assumption that a third party is interested
in reading our messages.

23. Quantum Cryptography:
Cryptography
Symmetric/Asymmetric key cryptosystems
Modern cryptography has two types of encryption: symmetric
key and asymmetric key cryptosystems. Let us briefly describe
each type.

24. Quantum Cryptography:
Cryptography
Symmetric key cryptosystems
Symmetric key cryptosystems, also known as private key
cryptosystems, are encryption algorithms that use a single
key for both encryption and decryption of the ciphertext. In
this field, algorithms for encryption and decryption are
known while the key must remain private, i.e. secret.

25. Quantum Cryptography:
Cryptography
Asymmetric key cryptosystems
Asymmetric key cryptosystems use two keys: a public key
and a private key, the public key is used for encryption and
the private key for decryption. These cryptosystems work
under the rationale of a safe with two keys: the key to lock
the safe is known by everybody but the key for opening is
available to only one person.

26. Quantum Cryptography:
Cryptography
Private key cryptosystems
Private key cryptosystems can be very powerful. For example,
The cryptosystem known as the one-time pad can be proved
to be perfectly secured as long as the key is truly random,
the length of the key is equal to the size of the message and
the key is only used once.
Other private key cryptosystems include the Data Encryp-
tion Standard (DES) and the Advanced Encryption Stan-
dard.

27. Quantum Cryptography:
Cryptography
Key distribution
One of the most sensible issues with private key cryptosystems
is safe key distribution, i.e., the process of establishing a private
key between two users who cannot use a perfectly secure
communication channel.
The issue is the fact that, if the channel used to distribute a
private key is governed by the laws of classical physics, then
in principle any (classical) key can be passively eavesdropped,
i.e. without users becoming aware of this vulnerability.

28. Quantum Cryptography:
Cryptography
BB84 - Quantum Key distribution
In 1984, Charles Bennett and Gilles Brassard proposed a quan-
tum key distribution protocol known as BB84. The key idea of
BB84 is to produce a key by encoding bits in qubits that are
taken from a set composed by the union of the computational
and diagonal bases, i.e., a set of four non-orthogonal quantum
states.

29. Quantum Cryptography:
Cryptography
BB84 Quantum Key distribution
Let us suppose the following setting:
- Alice and Bob want to create a key for encoding a message.
- The key, to be shared by Alice and Bob, must be random and
secret.
- There is a third character: Eve, an eavesdropper.
- The conflict in this story is: Alice and Bob’s key need their key
to be secret and Eve will do anything in her power to reveal at
least some portions of the key.

30. Quantum Cryptography:
Cryptography
BB84 - Quantum Key distribution
- The purpose of BB84 is to produce a key, i.e. actual encoded
data transmission is not part of the BB84.
- Hereinafter, we assume that:
a) Alice has access to a source of individual photons, the exper-
imental equipment and expertise to manipulate the polarization
of her photons, and a source of random bits.
b) There is a channel available to Alice and Bob that they can
use to send quantum states (e.g. an optical fiber.)
c) Bob has the experimental facilities and expertise required to
measure quantum states using different bases.
d) Alice and Bob have a classical channel (e.g. a telephone line)
that may or may not be a secure line, it doesn’t matter.

31. Quantum Cryptography:
Cryptography
BB84 - Quantum Key distribution
The BB84 protocol is composed of the following steps: 1. Alice
starts by generating two sets of random bits A = {a1, a2, . . . an}
and B = {b1, b2, . . . bn}

32. Quantum Cryptography:
Cryptography
BB84 - Quantum Key distribution
2. Alice uses the set of random bits A to select the vector basis
with which she will prepare the initial polarization state of her
photons, according to the following criterion: Alice will read one
bit at a time from set A and, depending on her reading (either 0
or 1), she will choose the computational basis (+) or the diagonal
basis (◊) to prepare her photons. In computational terms, this
step would be more or less equivalent to variable initialization.

33. Quantum Cryptography:
Cryptography
BB84 - Quantum Key distribution
For instance, let us suppose that A = {0, 1, 0, 0, 1, 0, 1, 1, 1, 0}
and that Alice has chosen the following criterion: if 0 then use
the computational basis; if 1 then use the diagonal basis. Then,
Alice would initialize her qubits using the following list: (+, ◊, +,
+, ◊, +, ◊, ◊, ◊, +).

34. Quantum Cryptography:
Cryptography
BB84 - Quantum Key distribution
3. Now, Alice must randomly choose one vector from each basis
to prepare the polarization initial state of each photon. To do so,
Alice will use the elements of set B according to the following
function:
initial polarization state =
Y
_____]
_____[
|0Í (or |1Í) if (+,0)
|1Í( or |0Í) if (+,1)
|+Í( or |≠Í) if (◊,0)
|≠Í( or |+Í) if (◊,1)

35. Quantum Cryptography:
Cryptography
BB84 - Quantum Key distribution
4. Alice sends her qubit sequence to Bob via the quantum chan-
nel they both have access to. This step is Eve’s chance to extract
information from the quantum channel.

36. Quantum Cryptography:
Cryptography
BB84 - Quantum Key distribution
The KEY point to remember here is the following:
– Extracting information from a quantum system (e.g. a pho-
ton) makes irreversible changes in the actual information
contained in the quantum system.
– This is due to a truly exotic property of quantum mechan-
ics: measuring a quantum system is a probabilistic process
that changes the state of the quantum system.

37. Quantum Cryptography:
Cryptography
BB84 - Quantum Key distribution
Measuring a quantum system is equivalent to projecting (as in
analytical geometry) a vector onto a vector basis.

38. Quantum Cryptography:
Cryptography
BB84 - Quantum Key distribution
So, if Eve is eavesdropping, she will change the contents of any
qubits and that is the footprint that we need in order to detect
her presence!

39. Quantum Cryptography:
Cryptography
BB84 - Quantum Key distribution
Table: Example of the BB84 protocol in action
Alice’s bits 1 1 0 1 0 0 1 1 1 0 0 1
Alice’s bases + + ◊ + ◊ + ◊ + ◊ + ◊ ◊
Alice’s qubits |0Í |0Í |+Í |0Í |+Í |1Í |≠Í |0Í |≠Í |1Í |+Í |≠Í
Eve’s bases + ◊ + + ◊ ◊ + ◊ + + + +
Eve’s measurements |0Í |+Í |1Í |0Í |+Í |0Í |0Í |+Í |1Í |1Í |1Í |0Í
Bob’s bases ◊ + + + ◊ ◊ ◊ + + + + ◊
Bob’s measurements |+Í |0Í |1Í |0Í |+Í |≠Í |+Í |1Í |1Í |1Í |1Í |+Í
Bob’s bits 1 1 0 1 0 1 0 0 0 0 0 0
Selection • • • • • • •

40. Quantum Cryptography:
Business
Table of Contents
1 Thanks
2 Quantum Computation and Quantum Information
3 Mathematics for quantum cryptography
4 Cryptography
5 Business

41. Quantum Cryptography:
Business
IDQuantique
IDQuantique
http://www.idquantique.com/
Quantum Key Distribution Servers
Random Number Generators

42. Quantum Cryptography:
Business
Thanks again!
Thank you very much!
Questions?