Dr Petar Radanliev, PhD Thesis Department of Computer Sciences, University of Oxford

Dr Petar Radanliev, PhD Thesis
Department of Computer Sciences,
University of Oxford
Cryptography

Public Key Cryptography and
potential attacks to PK

1: Introduction to Cryptography
Cryptography from
Ancient Greek: kryptós
"hidden, secret"; and
γράφειν "to write", or -
λογία -logia, "study"
Cryptography
translated from its
original meaning in
Greek is ‘secret writing’

Cryptography vs
Cybersecurity – 3
key points
First point - good cryptography depends on the hardness of
the mathematical problem, in other words, the encryption is
only as strong as the mathematical problem of the specific
cryptographic algorithm
Second is the quality of implementation, because correct
implementation is fundamental in how secure the algorithm is
Third is the key secrecy, because secret keys need to be stored
somehow somewhere, usually by a centralised trusted authority
If you are a hacker and you are trying to hack a crypto system,
you will start with one of these three things, a hacker would try
to solve the math problem, look for vulnerabilities in the
implementation, or try to get access to the secret keys

2: Cryptography
and Romance
◦ Cryptography- the art of writing or solving
codes
◦ During the French revolution, the Queen of
France sent encrypted letter to her lover, and
encryption has been linked to love ever since
◦ Alice & Bob - The World’s Most Famous
Cryptographic Couple
◦ Alice and Bob are fictional characters originally
invented to make research in cryptology easier to
understand
◦ Eve, the passive and submissive eavesdropper

3: Romantic Cryptography
We show how Alice and Bob can
establish whether they love each
other, but without the
embarrassement of revealing that
they do if the other party does not
share their feelings
This is a “secure multiparty
computation” of the AND
function, where the participants
cooperate in producing the result
of the AND, but without learning
the input bit contributed by the
other party unless the result
implies it

3: Cultural Interpretations
of Alice and Bob
◦ In 2012, the computer scientist Srini
Parthasarathy wrote a document entitled “Alice
and Bob can go on a holiday!

4: Cryptography throughout the
History

Ancient Egypt
The oldest encryption
attempt known to
mankind dates back to the
kingdom of Egypt,
around two thousand
years before Christ
The first known evidence
of cryptography can be
traced to the use of
'hieroglyph' - a character
of the ancient Egyptian
writing system

Ancient Greece
◦ The ancient Greeks used a scytale, in which the
person sending a message wound a strip of cloth
around a stick

5: Cryptography throughout the
History

Ancient Rome
Julius Caesar used encryption in the days of the
Roman Empire to cipher letters and messages
Caesar Cipher: Named after Julius Caesar, who used
this method for secret military communications
Also known as a shift cipher, Caesar’s Code, or
Caesar Shift
Encipher- to convert a message or a piece of text
into coded form; encrypt
Decipher- To convert a text written in code, or a
coded signal, into normal language

USA
GEORGE WASHINGTON’S
ALPHABET CODE SHEET
PRESIDENT THOMAS JEFFERSON
DESIGNED A WHEEL-BASED
CIPHER MACHINE

6: Cryptography
throughout the History
◦ Enigma was a cipher device used by Nazi Germany's military
command to encode strategic messages before and during
World War II
◦ The most important codebreaking event of the war was the
successful decryption by the Allies of the German "Enigma"
Cipher
◦ Alan Turing credited as the father of computer science
◦ He was a British scientist and a pioneer in computer science
◦ During World War II, he developed a machine that helped break
the German Enigma code
◦ He also laid the groundwork for modern computing and
theorised about artificial intelligence
◦ After World War II, many of the first computers were created
to make or break codes

6:
Cryptography
throughout the
History
It is not true, as some books say, that NSA was a
“secret” organisation when it was established in
1952; however, there was little public awareness
of its work, and some people joked that the
initials stood for “No Such Agency
Cryptography + Cyber Security
Encryption Became Popular Long before the
Inception of the Internet

7: Symmetric vs Asymmetric
Cryptography

Symmetric
◦ Symmetric key cryptography is when one key is
used to encrypt and decrypt information and the
most well-known standard in this category is the
Advanced Encryption Standard , selected by the
U.S

Asymmetric
Asymmetric cryptography is also known as public-key cryptography,
uses two different keys, one is public key that is used for encryption
and is known to all, and second is the private key that is used for
decryption and is only known by one party
The most famous algorithm for public-key cryptography is the RSA
cryptosystem developed in 1977
The Digital Signature Algorithm
Diffie–Hellman key exchange over public channels
the Elliptic-curve cryptography

8: Quantum Cryptography
Unlike cryptography, which relies on mathematical algorithms and computational complexity to secure
information, quantum cryptography is based on the laws of physics and the behaviour of quantum
particles
When we have a large-scale quantum computer built, it would break all public-key cryptography that is
widely used today
The most well-known quantum cryptography protocol "quantum key distribution" , involves the
transmission of a random sequence of quantum bits or "qubits" between two parties
The best known "quantum key distribution" is the BB84 protocol published by Bennett and Brassard
in
Quantum cryptography is unhackable

4: Introduction to
Public Key Cryptography

Definition of Public Key cryptography
Also known as
asymmetric cryptography
uses a pair of
mathematically related
keys: a public key and a
private key
Different than symmetric
cryptography, which uses
a single key for both
encryption and decryption

Importance of PK cryptography in
secure communications
◦ Secure communication and various
cryptographic functionalities, such as secure key
exchange, digital signatures, and encryption of
data
◦ Use cases include secure email, secure web
browsing , secure file transfer , and secure
messaging platforms
◦ Provides a mechanism for secure and
confidential communication between parties
without the need for a shared secret key

Explanation of key pair generation
The public and private keys are
mathematically linked in such a
way that the public key can be
derived from the private key,
but it is computationally
infeasible to determine the
private key from the public key
This property ensures the
security of the communication
and prevents unauthorized
access to the encrypted
information

Mathematical relationship between the two keys
The relationship between the
two keys is typically based on
mathematical operations that
are computationally easy in
one direction but
computationally difficult in the
reverse direction
This property ensures that
while the public key can be
easily derived from the private
key, it is practically impossible
to calculate the private key
from the public key

Encryption and
Decryption

How encryption
with the public
key works
The sender prepares the message
they want to send to the
recipient
Using the recipient's public key,
the sender applies an encryption
algorithm to the message

How decryption with the private key works
Upon receiving the
encrypted message, the
recipient uses their private
key, which is kept secret,
to perform the decryption
process
The result of the
decryption process is the
original message, restored
to its original form

Use of PK cryptography for digital signatures
Document
Hashing
Hash
Encryption
Digital
Signature
Creation
Signature
Verification
Document
Hash
Calculation
Comparing
Hashes

Importance of
digital signatures
in authentication
and integrity
Authentication
Integrity
Non-Repudiation

Explanation of key exchange using PK cryptography
Key
Generation
Public Key
Exchange
Key
Encryption
Key
Decryption
Shared
Secret Key

Benefits of secure key exchange
Key exchange using PK
cryptography provides a secure
method for establishing a shared
secret key, enabling secure
communication and encryption of
sensitive information
It is widely used in various
protocols, such as Secure Sockets
Layer/Transport Layer Security for
secure web browsing, Secure Shell
for secure remote access, and
Virtual Private Networks for
secure communication over public
networks

Overview of the
RSA algorithm
In RSA, the mathematical relationship
is based on the difficulty of factoring
large numbers into their prime factors
The public key consists of a modulus
and an exponent
The decryption process, on the other
hand, involves raising the ciphertext to
the power of the private exponent and
taking the modulus

Elliptic Curve Cryptography

Introduction to
ECC and its
advantages over
RSA
Elliptic Curve Cryptography uses the
mathematical properties of elliptic
curves to establish the relationship
between the public and private keys
The public key is derived from a point
on the elliptic curve, while the private
key is a randomly chosen scalar value
The operations involved in ECC
ensure that it is extremely difficult to
calculate the private key from the
public key

Diffie-Hellman Key Exchange

Explanation of
the Diffie-
Hellman key
exchange
algorithm
The Diffie-Hellman key exchange
algorithm is a cryptographic protocol
developed by Whitfield Diffie and Martin
Hellman in 1976 and is widely used in
modern encryption systems
The goal of the Diffie-Hellman key
exchange is to enable secure
communication between two entities
without needing to pre-share a secret key
Instead, the parties can generate a shared
secret key by performing mathematical
operations on publicly exchanged
information

How it enables secure key exchange over an insecure
channel
The security of the Diffie-
Hellman key exchange relies on
the computational difficulty of the
discrete logarithm problem
While an eavesdropper can
intercept the public keys
exchanged between Alice and Bob,
it is computationally infeasible to
derive the secret numbers "a" and
"b" or the shared secret key "s"
from this information alone

Potential Attacks on
PK Cryptography

Brute-force attack: Explaining the concept and
its limitations

Man-in-the-middle attack: How it
compromises PK cryptography

Side-channel attacks: Exploiting information
leakage

Quantum computing attacks: Impact on PK
cryptography

Brute-force attack on PK cryptography
In a brute-force attack, an
attacker systematically tries
all possible private keys to
decrypt an encrypted
message
The strength of the PK
cryptography lies in the large
key space, which makes this
attack computationally
infeasible for sufficiently long
key sizes

IMPORTANCE OF KEY SIZE
IN PREVENTING
SUCCESSFUL BRUTE-FORCE
ATTACKS
Search Space Security Margins

Man-in-the-Middle
Attack

Man-in-the-
middle attack on
PK cryptography
In a man-in-the-middle attack, an
attacker intercepts the
communication between two parties
and poses as each party to the other
The attacker can intercept the public
keys exchanged during the key
exchange process and replace them
with their own
MITM attacks can be mitigated by
using trusted public key
infrastructure and digital certificates

HOW ATTACKERS INTERCEPT
AND MANIPULATE
COMMUNICATION
Intercepting Communication

Side-Channel
Attacks

Side-channel attacks and their
impact on PK cryptography
◦ Side-channel attacks exploit information leaked
during the execution of a cryptographic
algorithm, such as timing information, power
consumption, or electromagnetic radiation
◦ By analysing these side-channel information, an
attacker can potentially extract the private key
◦ Countermeasures like constant-time
implementations and hardware protections can
be employed to mitigate side-channel attacks

Common types of side-channel
attacks

Quantum
Computing Attacks

Quantum
computing on PK
cryptography
Quantum computers have the potential to
break many of the currently used public
key algorithms, such as RSA and ECC
Shor's algorithm, for example, can
efficiently factor large numbers, which
breaks RSA
To mitigate quantum computing attacks,
post-quantum cryptography algorithms are
being developed and standardised, which
are resistant to attacks by quantum
computers

Shor's algorithm
and its impact on
RSA and ECC
Shor's algorithm is a quantum
algorithm developed by
mathematician Peter Shor in
ECC is also vulnerable to
attacks using Shor's algorithm

Importance of
protecting private
keys
PK cryptography relies on the secrecy of
the private key
If the private key is compromised, either
through theft or unauthorized access, an
attacker can decrypt any messages
encrypted with the corresponding public
key
It is crucial to protect private keys with
strong encryption and proper access
controls

Consequences of key compromise in PK
cryptography

Blockchain
Technologies

Smart contracts and their applications
Smart contracts are self-
executing contracts with the
terms of the agreement
directly written into code
They run on blockchain
platforms, such as Ethereum,
and automatically execute
actions based on predefined
conditions without the need
for intermediaries

Blockchain in
supply chain
management
Smart contracts can enhance supply chain
management by automating and
streamlining processes
They enable transparent and efficient
tracking of goods, automatic verification
of transactions, and secure transfer of
ownership or payments based on
predefined conditions
Smart contracts can increase transparency,
reduce fraud, and improve overall supply
chain efficiency

Blockchain's potential for transparent governance and
voting systems
The examples listed are just a
few examples of how smart
contracts are being applied
across various industries
The versatility and automation
capabilities of smart contracts
make them a powerful tool for
creating trust, efficiency, and
transparency in a wide range
of applications

Cybersecurity and
Quantum Computing Integration

Quantum-safe cryptography and its
importance in cybersecurity
◦ Quantum Computers' Threat to Classical
Cryptography

Quantum-
resistant
algorithms and
post-quantum
cryptography
The development and standardisation of
quantum-resistant algorithms are ongoing
Organisations such as the National
Institute of Standards and Technology in
the United States have initiated efforts to
evaluate and standardise post-quantum
cryptographic algorithms
This process involves rigorous analysis,
testing, and evaluation of various candidate
algorithms to determine their security,
efficiency, and suitability for different
applications

Preparing for the cybersecurity challenges posed
by quantum computing

Recap of the important
concepts in PK cryptography

AWARENESS OF
POTENTIAL ATTACKS AND
THE NEED FOR SECURE
PRACTICES
Evolving Threat Landscape

Additional
Resources

RECOMMENDATIONS FOR
FURTHER READING AND
RESEARCH ON PK
CRYPTOGRAPHY
National Institute of Standards and Technology

Sources of information
used in the presentation
◦ National Institute of Standards and Technology
: Post-Quantum Cryptography: Matt Scholl:
https://www.nist.gov/blogs/taking-
measure/post-quantum-cryptography-qa-nists-
matt-scholl NIST Announces First Four
Quantum-Resistant Cryptographic Algorithms:
https://www.nist.gov/news-
events/news/2022/07/nist-announces-first-
four-quantum-resistant-cryptographic-
algorithms Post-Quantum Cryptography:
https://csrc.nist.gov/Projects/post-quantum-
cryptography/selected-algorithms-2022

2: Additional References

Questions and
Discussion

Dr Petar Radanliev, PhD Thesis Department of Computer Sciences, University of Oxford

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