Navigating Post-Quantum Blockchain: Resilient Cryptography in Quantum Threats

International Conference on Recent Developments in Cyber Security (ReDCySec2023)
30-31 May, 2024
Organized by Center for Cyber Security and Cryptology, Sharda University
Presenter:
Paper ID:
Navigating Post-Quantum Blockchain: Resilient
Cryptography in Quantum Threats
by
Dr Anupam Tiwari, Ph.D
#7
InternationalConference on Recent Developments in Cyber Security- ReDCySec-2024

— Problem Statement
— Introduction
— Cryptographic Primitives in Blockchain Technology
— Vulnerabilities of current cryptography to QC attacks in Blockchain Technology
— Foundations of PQC
— Literature Review
— Current State
— Challenges
— Conclusion
PRESENTATION LAYOUT

Navigating Post-Quantum Blockchain: Resilient
Cryptography in Quantum Threats
PROBLEM STATEMENT

INTRODUCTION
— Blockchain banks heavily on CRYPTOGRAPHY
— Blockchain imparts all it’s well known characteristics attributed to CRYPTOGRAPHY
• Transparency
• Redundancy
• Accountability
• Immutability
• Decentralization
• Consensus - Proof-of-work

Traditional CRYPTOGRAPHIC algorithms, which have effectively
demonstrated data integrity and privacy, now are confronted with
QUANTUM COMPUTERS
INTRODUCTION

WELL KNOWN ENCRYPTION & HASHING ALGORITHMS

RSA: Based on prime factorization
difficulty.
AES: Utilizes substitution-permutation
network.
DES: Employs Feistel network
structure.
ECC: Relies on elliptic curve
properties.
Diffie-Hellman: Solves discrete
logarithm problem.
SHA: Uses Merkle-Damgård construction
Blowfish: Variable key length Feistel
network.
Twofish: Variable key size substitution-
permutation network.
DSA: Modular exponentiation for
signatures.
RC4: Stream cipher for data encryption.
Well known Encryption and Hashing Algorithms

Where is Cryptography used in Blockchain Technology?
—Hash Functions
• Data Integrity
• Digital Signatures and Authenticity
—Public-Key Infrastructure (PKI) and Key Exchange
• Cryptographic Random Number Generators
• Merkle trees

VULNERABILITIES OF CURRENT CRYPTOGRAPHY TO QC ATTACKS
IN
BLOCKCHAIN TECHNOLOGY

Vulnerabilities of Current Cryptography to QC Attacks in BCT
—Shor's Algorithm
• Quantum algorithm for factoring large integers.
• Threatens security of RSA and other cryptographic schemes.
• Exponential speedup over classical factoring algorithms.
• Basis for potential quantum attacks on modern encryption.
• Discovered by Peter Shor in 1994.
—Grover's Algorithm
• Quantum search algorithm for unsorted databases.
• Quadratic speedup compared to classical search.
• Implications for breaking symmetric key cryptography.
• Discovered by Lov Grover in 1996.
Shor's algorithm threatens
Asymmetric Encryption by
efficiently factoring large
numbers, compromising
security.
Grover's algorithm poses a
threat to Symmetric Encryption
by speeding up brute-force
attacks, reducing its
effectiveness.

Asymmetric Encryption Algorithms
Symmetric Encryption Algorithms
CONTEXT PQC

Asymmetric Encryption Algorithms
• Generally more vulnerable to quantum threats compared to
symmetric encryption algorithms.
• Arises from the fact that many asymmetric encryption algorithms rely
on mathematical problems that can be efficiently solved by quantum
computers

Symmetric Encryption Algorithms
• Considered to be less vulnerable to quantum threats because they do
not rely on the same mathematical problems as asymmetric encryption.
• Typically based on operations such as Permutations, Substitutions,
and Bitwise operations rather than the mathematical problems that
asymmetric encryption algorithms rely on.

Thus
• Emergence of Quantum Computing raises concerns about the future
security of blockchain networks relying on traditional cryptographic methods.
• Transitioning to post-quantum cryptographic methods is imperative to
ensure the continued security of digital communication and asset protection

Foundations of Post
Quantum Cryptography
(PQC)

Foundations of Post
(PQC) • Quantum cryptography relies on the
principles of quantum mechanics to
secure communication channels.
• Unlike classical cryptography, quantum
cryptography utilizes the behavior of
particles like photons to create secure
communication protocols.

• Qubits
• Superposition
• Entanglement
• Quantum Gates
• Quantum Algorithms
• De-coherence & Error Correction
• Quantum Measurement
Foundations of Post
(PQC)

• Qubits: Quantum computing's core, like classical bits
• Superposition: Qubits can represent 0 and 1 simultaneously, boosting computational power.
• Entanglement: Qubits can be correlated regardless of distance, enhancing computational capabilities.
• Quantum Gates: Manipulate qubits to perform operations like classical logic gates.
• Quantum Algorithms: Leverage qubits to solve problems exponentially faster than classical methods.
• De-coherence & Error Correction: Techniques counteract errors caused by environmental factors.
• Quantum Measurement: Process collapses qubit states, providing classical output from quantum
computations.
Foundations of PQC

• In the world of computers, information is built on bits, tiny switches that are either on (1) or off (0).
• Quantum computers take things a step further with qubits. These are like bits, but weirder.
• A qubit can be 1, 0, or both at the same time (superposition), thanks to the strangeness of quantum
mechanics. Imagine a coin spinning – it's both heads and tails until you stop it and look.
• This lets qubits explore many possibilities simultaneously, making them supercharged for tackling
problems that would take regular computers forever.
• Here's the catch: qubits are delicate. Measuring them forces them to be a 1 or 0, collapsing their
superposition. But if we can harness them, they hold immense potential for revolutionizing fields like
medicine, materials science, and cryptography. Think of it as unlocking a whole new way of processing
information, with qubits as the key.
QUBITS

• Qubits vs Bits: Qubits, the building blocks of quantum computers, differ from classical bits. While bits
are restricted to 0 or 1, qubits can be in a superposition of both states at once.
• Superposition Explained: This "both-at-once" state arises from quantum mechanics. Mathematically, a
qubit's state is a combination of |0> and |1> with probabilities encoded by complex numbers (amplitudes).
• Basis States: The |0> and |1> states are the foundation for qubits. They act as reference points for
describing more complex quantum states.
• Bloch Sphere Visualization: This mathematical tool depicts a qubit's state as a point on a sphere. The
position depends on the amplitudes associated with the basis states.
• Parallel Processing Power: Superposition allows multiple qubits to explore numerous possibilities
simultaneously. This unlocks the ability to tackle problems that would overwhelm classical computers.
• Fragile Nature: Measuring a qubit forces it to collapse into a definite state (0 or 1), destroying the
superposition. Careful control is needed to harness its potential.
SUPERPOSITION

• Twin Qubits: Imagine two qubits linked like twins. This is entanglement, where their fates are
connected.
• Instantaneous Connection: A change in one entangled qubit instantly affects the other, no matter the
distance. (Think: Separated coins flipping the same way every time!)
• Not Teleportation: Entanglement doesn't transmit information faster than light, but allows for powerful
correlations in quantum algorithms.
• Beyond Bits: Unlike classical bits, entangled qubits share a single quantum state, defying classical
physics.
• Unlocking Potential: Entanglement holds promise for secure communication and solving complex
problems in various fields.
ENTANGLEMENT: SPOOKY ACTION AT A DISTANCE

• The Tools of the Trade: Quantum gates are like logic gates in classical computers, but for qubits. They
manipulate the superposition and entanglement of qubits.
• Flipping and Combining: Common gates like Hadamard and CNOT can flip a qubit's state (0 to 1 or
vice versa) or combine the states of two entangled qubits.
• Building Quantum Circuits: By combining different gates in specific sequences, we create quantum
circuits to perform complex calculations.
• Unlocking Potential: Quantum gates allow us to control and orchestrate the unique properties of
qubits, paving the way for solving problems intractable for classical computers.
• Precision is Key: Quantum gates are delicate, requiring precise control to maintain the fragile quantum
states of qubits.
QUANTUM GATES: THE ARCHITECTS OF QUBIT MAGIC

• Beyond Classical Limits: Unlike classical algorithms designed for bits, quantum algorithms leverage
the power of superposition and entanglement.
• Tackling the Intractable: These algorithms can solve certain problems exponentially faster than
classical computers, especially those involving complex optimization or large simulations.
• Famous Examples: Shor's Algorithm could break many encryption standards, while Grover's Algorithm
can speed up search tasks.
• Still Under Development: Quantum algorithms are a young field, constantly evolving and being
optimized for specific tasks.
• The Future is Quantum: Mastering these algorithms will unlock breakthroughs in fields like drug
discovery, materials science, and financial modeling.
QUANTUM ALGORITHMS

• Decoherence is the enemy of qubits. It's the loss of their delicate quantum states due to interactions
with the environment, making them behave classically (0 or 1).
• Keeping it Quantum: Quantum error correction fights back. These techniques use multiple qubits to
encode information redundantly, detecting and correcting errors caused by decoherence.
• Like Fort Knox for Qubits: Error correction codes act like shields, protecting the fragile superposition
of qubits during computations.
• The Challenge Remains: Implementing effective error correction requires many extra qubits, making it
a hurdle for large-scale quantum computers.
• The Race is On: Researchers are constantly developing new error correction methods to pave the way
for robust and reliable quantum computations.
DE-COHERENCE & ERROR CORRECTION

• Extracting the Unknown: Unlike classical bits, qubits hold probabilistic information. Measurement
aims to extract this information from a qubit (or entangled qubits) existing in superposition (both 0 and 1).
• Superposition Collapse: Measurement forces the "both-at-once" state to collapse. The qubit is forced
into a definite state (0 or 1) – a one-way trip.
• Probabilistic Outcomes: Forget certainties! We only get the probability of finding the qubit in a specific
state (0 or 1) after measurement, based on its wavefunction before.
• The Observer Effect: Measurement requires interaction with a device, disrupting the qubit and forcing
collapse. This interaction highlights how the act of measurement itself influences the system.
• Bridging Two Worlds: Quantum measurement connects the probabilistic world of qubits with the
classical world of definite states. It provides information, but fundamentally alters the measured system.
QUANTUM MEASUREMENT

LITERATURE REVIEW

Hash Function(s) Used Blockchain Platforms
SHA-256
Bitcoin, Ripple (XRP), Bitcoin Cash, TRON, VeChain,
Stellar, Algorand, NEM, Hedera Hashgraph
Keccak-256 (SHA-3)
Ethereum, Binance Smart Chain, Cardano, Polkadot,
Solana, EOS
Blake2b Binance Smart Chain, Cardano
Scrypt Litecoin, Multichain
CryptoNight Monero
Kerl (Custom Hash Function) IOTA
X11 (Combination of Hash Functions) Dash
Equihash (Memory-Bound Proof-of-Work) Zcash
RIPEMD-160 Bitcoin, Tezos, NEO

Navigating Post-Quantum Blockchain: Resilient Cryptography in Quantum Threats

[8]: System design has been proposed that schemes a voting system on the
blockchain, incorporating PQC offering a systematic and critical view towards laying
down a quantum-resistant blockchain for near future online voting systems in the
PQC era ahead.
[9] addresses the challenge of collaborating network services with heterogeneous
devices from various vendors by leveraging blockchain technology.
Research also explores the integration of PQC algorithms to safeguard against
future threats and demonstrates superior write performance of Quorum Blockchain
by exploiting PQC algorithm shortest vector problem (SVP) in a lattice.

[12]: Employs Grobner basis algorithms over finite fields, bidding better security
against possible quantum attacks
Grobner basis algorithms
Special kind of set of polynomials that captures the
essence of a larger set. Like having a bunch of complex
polynomial equations & a Grobner basis renders a
simplified set that holds all the essential
information about the original equations, making it
easier to analyze.

[12]: Employs Grobner basis algorithms over finite fields, bidding better security
against possible quantum attacks
[13]: Concentrating specifically on Bitcoin & Ethereum, the authors demonstrate how
these platforms enable primitives to ensure data integrity, authenticity, and non-
repudiation and then they acknowledge the potential threat posed by emergent QC
advancements. The authors foresee a future where BCT networks employ NIST-
recommended PQC primitives, ascertaining their continued practicality in the QC era.

Primitive Name Vulnerability Quantum Attack Impact on Blockchain Security
Elliptic Curve
Cryptography
Shor's Algorithm
Breaks ECC algorithms used for digital
signatures and key exchange
Loss of transaction integrity, unauthorized access to
funds, and potential manipulation of the ledger
RSA Shor's Algorithm
Breaks RSA algorithms used for digital
signatures and key exchange
Similar impact as ECC
SHA-256 Grover's Algorithm
Enables finding collisions with
considerably less effort
Potential for forging transactions and compromising
data integrity
ECDSA Signatures Shor's Algorithm Breaks ECDSA signature scheme Loss of transaction authenticity and non-repudiation
Merkle Trees Grover's Algorithm
Speeds up finding preimages and
second preimages
Potential for forging transactions and compromising
data integrity
Proof-of-Work Grover's Algorithm
Enables finding solutions to PoW
puzzles with reduced computational
effort
Potential for mining dominance and centralization of
the network

Most PQC algorithms base
their security on one or
more of the mathematical
problems
PQC methods with
different mathematical
foundations
Lattice Based
Code Based
Multivariate
Polynomial
Hash Based
Isogeny Based
Post-Quantum
Key Exchange
Hybrid
Cryptographic
Schemes
Super-Singular
Elliptic Curve

Most PQC algorithms base
their security on one or
more of the mathematical
problems
Lattice Based
Code Based
Multivariate
Polynomial
Hash Based
Isogeny Based
Post-Quantum
Key Exchange
Hybrid
Cryptographic
Schemes
Super-Singular
Elliptic Curve
PQC methods that are to be
taken seriously belong to 5
families that differ in
mathematical foundations

• Building with Lattices: This approach leverages mathematical structures called lattices – grids of
points formed by integer combinations of vectors.
• Hard Problems, Secure Keys: The security of lattice-based PQC relies on the difficulty of solving
specific lattice problems in polynomial time, even for quantum computers. Think complex mazes with no
easy escape!
• Encryption & Signatures: Lattice-based schemes offer both encryption and digital signature
functionalities, crucial for secure communication and data integrity in the quantum age.
• Standardization on the Horizon: Promising lattice-based PQC algorithms like CRYSTALS-KYBER and
CRYSTALS-Dilithium are undergoing standardization, paving the way for real-world adoption.
LATTICE IS SPECIAL TODAY

Approaches of Post Quantum Cryptography
Based on Description TRL
Lattice Based Mathematical structures based on grids of points and Defined by basis
vectors
4
Code Based Relies on error-correcting codes for its security 3
Multivariate Polynomial Employs systems of polynomial equations for cryptographic security. 2
Hash Based Leverages the collision resistance 4
Isogeny Based Involves the complexity of computing isogenies between elliptic curves. 5

Primitive Name Potential Post-Quantum Replacement Algorithm
Elliptic Curve Cryptography
Lattice-based cryptography, multivariate cryptography, Supersingular
Isogeny Diffie-Hellman (SIDH)
RSA
Lattice-based cryptography, multivariate cryptography, post-quantum RSA
(PQ-RSA)
SHA-256 Quantum-resistant Merkle trees
ECDSA Signatures Lattice-based signatures, multivariate signatures, XMSS
Merkle Trees
Quantum-resistant Merkle trees with alternative collision-resistant hash
functions
Proof-of-Work
Quantum-resistant PoW algorithms, post-quantum consensus
mechanisms
Potential Post-Quantum Replacement Algorithm

Mechanism Name Latency Throughput
Energy
Consumption
Scalability
Suitability for Different Blockchain Use
Cases
Lattice-based Moderate Moderate High Good
Suitable for public and permissioned
blockchains
Multivariate BFT Low Moderate Low Good
Suitable for resource-constrained private
blockchains
Isogeny Moderate High Moderate Good
Suitable for high-throughput applications
and public blockchains
Hash-based Low Moderate Low Good
Suitable for private blockchains requiring
fast consensus
Quantum-resistant
Proof of Work (PoW)
High Low High Moderate
Suitable for public blockchains requiring
high security and decentralization
Quantum-resistant
Proof of Stake (PoS)
Moderate Moderate Low Good
Suitable for public and permissioned
blockchains
PQC MECHANISMS: PERFORMANCE & SUITABILITY FOR BLOCKCHAIN

CURRENT STATE

NIST chose four finalist algorithms in July 2022 for post-quantum cryptography.
The fourth standard (FALCON) will release its draft for comments in 2024.
CRYSTALS-Kyber : Lattice method for asymmetric encryption.
CRYSTALS-Dilithium : Lattice method, it is used for digital signature.
FALCON : Signature method is also based on lattices.
SPHINCS+ : Hash-based SPHINCS+ is another signature method
NIST also identified many additional candidates to be evaluated which also include non-lattice-based
choices.

In addition to NIST, German federal office BSI recommends two PQC models
• Classic McEliece
• FrodoKEM
IETF has proposed two hash based models
• XMSS (RFC 8391)
• Leighton-Micali (RFC 8554)

Literature Review Summary
- 15 Papers explored with Lattice based PQC in maximum
- Voting enabled on blockchain applications
- Max demonstrations limited to Ethereum blockchain and few on Quoram
- QKD for Quantum-Safe Smart Contracts
- Mostly Theoretical frameworks
- Lack of Quantum research resources
- Promising and Definite association of Blockchain and PQC
- Threats and repercussions to Smart Contracts
- Existing Governance Mechanisms in place

CHALLENGES OF IMPLEMENTING PQC IN BLOCKCHAIN

Challenges of Implementing PQC in Blockchain
— Performance and Efficiency
• PQC algorithms demand more computation, potentially slowing down blockchain platforms.
— Interoperability and Compatibility
• Integrating PQC requires major updates to blockchain protocols for compatibility with existing systems.
• Lack of standardized PQC algorithms can lead to compatibility issues across blockchain platforms.
— Security Considerations in Transitioning to PQC
• PQC implementations are vulnerable to side-channel attacks.
— Migration
• Likewise for any migration in PQC by NIST, there exists a number of challenges
—Current Chip Architectures
• Current card chip architectures are designed for RSA or Diffie-Hellman keys and have a corresponding coprocessor.
• In contrast, they are not designed to perform lattice or, code operations, certainly not with the necessary key lengths.
• Revision of current chip architectures is therefore an important challenge for the coming years

Conclusion
• Solution without a problem
• Cryptoagility
• Ability of a cryptographic system to rapidly adapt and evolve in response to new
threats, vulnerabilities, or technological advancements
• Realisation of threat by state
• Harvest now Decrypt Later
• Blockchain future readiness imminent
• AI arrival spoils the scenario further

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