1. Cybersecurity:
Aspects of Cryptography from a Classical and Quantum Perspective (An Ongoing Review)
Joseph Spring
University of Hertfordshire
British Council India Tour January 2017 – Pune and Chennai

2. Cyber Security

3. Cyber security
“the protection of information systems from theft or damage to the hardware, the software, and to the information on them, as well as from disruption or misdirection of the services they provide”
M. Gasser, 1988, Building a secure computer system, van Nostrand Reinhold.
Information security – “the practice of preventing unauthorized access, use, disclosure, disruption, modification, inspection, recording or destruction of information”

4. Cyber security
Following the statements above we note the following concepts:
Authentication
Establishing for example that I am who I say that I am and that I am entitled to gain access to some entity such as my computer
Confidentiality
Any data sent between two parties is not seen by unauthorised observers
Integrity
Establishing that the message sent is the same as the message received
Non repudiation
Ensuring that the sender of some information cannot deny that they sent the information
Accessibility
If I am entitled for example to use a service then I want to be able to do so
Anonymity
In for example voting schemes where one might also like confidentiality
A long standing tool in maintaining a degree of control and defence of information systems is cryptography

5. Threat Models

6. Standard Threat Model Encrypt Decrypt Plaintext Ciphertext Ciphertext
Alice
Bob K1
Eve K2
Trusted Key Source

7. Classical Cipher Schemes

8. Classical Cryptography
Symmetric Systems
K1 = K2
Vernam (One Time Pad), Data Encryption Standard, Blowfish, Twofish, Serpent …
Rijndael, Advanced Encryption Standard
Asymmetric Systems
K2 = (K1)-1
Based on what are perceived to be hard problems
Integer Factorisation Problem (IFP) and the Discrete Logarithm Problem (DLP, ECDLP)
RSA for the IFP
Diffie – Hellman (DLP based Key Agreement Protocol)
El Gamal (Number Fields, Algebraic Number Fields, Points on an Elliptic Curve)

9. Quantum cryptography

10. Cryptography Quantum Information Theory Postulates 1 Postulate 2
cbits - binary bits 0 or 1
Qubits - vectors in a 2 dimensional vector space, a Hilbert Space
Postulate 2
Analogues of processing information using classical AND, OR, NAND, NOR logic gates
Not all reversible
Operators/Gates: Hadamard, Pauli Operators, CNOT, swap, phase gate, ….
Unitary operators, all are reversible
Postulate 3
After processing information in a quantum setting we measure using Hermitian operators which give us real/classical values
Postulate 4
Using tensor products to represent multiple qubits similar to how we use bytes to represent bits

11. Resources Key Quantum Resources include Entanglement Teleportation
4 Bell entangled states
Generated by two qubits, a Hadamard and a CNOT gate
Teleportation
Involves an unknown state that we wish to send (Teleport) to a particular receiver
CNOT, Hadamard, measurement and being able to communicate classically with a receiver
Both concepts have been experimentally verified
Both concepts are being used in the construction of quantum networks
Entanglement, Entanglement swapping and Teleportation

12. Quantum Cryptography Key Agreement Protocols
The Diffie Hellman Key Agreement Protocol is a classical based protocol
Uses a multiplicative cyclic group, a primitive and the DLP to agree a symmetric key, the same key for sender and receiver
BB84, B92 and E91 are quantum based key agreement protocols
They employ:
No cloning Theorem (Quantum Property)
Information gain implies disturbance (Quantum Property)
Information Reconciliation (Classical Technique)
Privacy amplification (Classical Technique)

13. Shors Algorithm
In the mid 1990’s Peter Shor published a paper in which he established that given a quantum computer of sufficient processing power his algorithm would break any scheme based on either the IFP or the DLP
It broke the following algorithms in a very efficient manner
Diffie Hellman
RSA
El Gamal – all three forms
And led to the problem of what to replace these algorithms with. These were/are very efficient in comparison to current alternatives.

14. Post Quantum Cryptography
The PQC cryptographers and designers have been looking at
Hash Based Cryptography
Code Based Cryptography
Lattice Based Cryptography
Multivariate Quadratic Equation Based Cryptography
Symmetric Key Based Cryptography

15. Cyber Related Issues

16. Cyber Related Issues We are now in an age in which:
Quantum information
Quantum technology
are going to increasingly pervade our everyday experience
Likewise:
Cybersecurity, cyberwarfare and cybercrime
Pervasive computing,
Distributed systems
The cloud
Internet of things

17. Thank You