Quantum Meets Blockchain - Different Perspectives

Q U A N T U M M E E T S B L O C K C H A I N
A U T O N O M O U S N AT U R E I N C O N F L U E N C E W I T H A U T O N O M O U S N E T W O R K S

Q K D
C N O T G AT E
C C N O T G AT E
PA U L I G AT E
T O F F O L I G AT E
S WA P G AT E
H A D A M A R D T R A N S F O R M
K E Y W O R D S

Q U B I T
Q U D I T S
Q R N G
B E L L S TAT E
G H Z S TAT E
E N TA N G L E M E N T
S U P E R P O S I T I O N
S H O R A L G O R I T H M
G R O V E R A L G O R I T H M
K E Y W O R D S

Q U A N T U M M O N E Y
Q U A N T U M S E C U R E B L O C K C H A I N
Q U A N T U M A S S I S T E D B L O C K C H A I N
Q U A N T U M R E S I S TA N T B L O C K C H A I N
Q U A N T U M E N TA N G L E D B L O C K C H A I N
Q U A N T U M O P T I M I Z E D B L O C K C H A I N
P E R S P E C T I V E S

Q U A N T U M M O N E Y
• Design of bank notes making them
impossible to forge through quantum
mechanical techniques
• Stephen Wiesner, a graduate student
in Columbia University proposed the
idea in 1970. It remained
unpublished till 1983.
• Each bank note will have a unique
serial number connected to an
isolated two state quantum systems

S H O R ’ S A L G O R I T H M C I R C U I T M O D E L

Q U A N T U M S U B R O U T I N E S H O R A L G O R I T H M

Q U A N T U M C I R C U I T F O R S H O R ’ S A L G O R I T H M

G R O V E R ’ S A L G O R I T H M - O R A C L E C I R C U I T

G R O V E R ’ S A L G O R I T H M - P H A S E G AT E C I R C U I T

S T E P S I N G R O V E R ’ S
A L G O R I T H M
• Place a register in an equal
superposition of all states
• Selectively invert the phase of the
marked state
• Inversion about the mean operation
a number of times

Q U A N T U M
S E C U R I T Y
• Position based Quantum
Cryptography
• Device Independent Quantum
Cryptography
• Post Quantum Cryptography

P O S T Q U A N T U M C RY P T O G R A P H Y
A S U R V E Y O F E M E R G I N G A L G O R I T H M S A N D C O N C E P T S

P R O M I N E N T P Q C
S C H E M E S
• Lattice based cryptography
• Multivariate cryptography
• Hash based cryptography
• Code based cryptography
• Supersingular Elliptic Curve Isogeney
Cryptography
• Symmetric Key Quantum Resistance

Q U A N T U M R E S I S TA N T L E D G E R
A P O S T- Q U A N T U M S E C U R E B L O C K C H A I N F E AT U R I N G A S TAT E F U L S I G N AT U R E S C H E M E

Q U A N T U M
R E S I S TA N T L E D G E R
• Python based Blockchain Ledger
utilising hash based one-time Merkle
Tree signature scheme instead of
ECDSA.
• Proof of work selection via the
cryptonight algorithm
• Both PoW and PoW available on
TestNet
• Ephemeral Messaging and Smart
Contract Integration in the roadmap

Q R L B L O C K E X P L O R E R D E M O

Q R L R E C E N T T R A N S A C T I O N S

Q U A N T U M AT TA C K S O N B I T C O I N
D I V E S H A G G A R WA L , 1 , 2 G AV I N K . B R E N N E N , 3 T R O Y L E E , 4 , 2 M I K L O S S A N T H A , 5 , 2 A N D M A R C O
T O M A M I C H E L : N U S , C Q T, N T U , U N I V E R S I T Y O F S Y D N E Y

By most optimistic estimates, as early as 2027, a quantum computer
could exist that can break elliptic curve signature scheme in less than
10 minutes, the block time used in Bitcoin

Q U A N T U M C H A L L E N G E S
T O B L O C K C H A I N
T E C H N O L O G Y
• Digital Signature
• Cryptographic Hash Functions

B I T C O I N
E S S E N T I A L S
• In Bitcoin, the hash function chosen for the
proof of work is two sequential applications of
SHA 256.
• As the size of the range of h is 2^256, the
expected number of hashes that need to be
tried to accomplish the hashcash proof of work
with parameter t is 2^256/t.
• In Bitcoin proof of work, it is specified in terms
of the difficulty D where D = 2 ^ 224 / t.
• This is the expected number of hashes needed
to complete the proof of work divided by 2 ^
32, the number of available nonces.

T H E D I F F I C U LT Y I S T H E E X P E C T E D N U M B E R O F VA R I AT I O N S O F
T R A N S A C T I O N S A N D T I M E S TA M P S T H AT N E E D T O B E T R I E D
W H E N H A S H I N G B L O C K H E A D E R S , W H E N F O R E A C H F I X I N G O F
T H E T R A N S A C T I O N S A N D T I M E S TA M P S A L L N O N C E S A R E T R I E D
D E F I N I N G D I F F I C U LT Y

G R O V E R A L G O R I T H M
A N D P R O O F O F W O R K
• Using Grover’s search, a quantum computer can
perform the hashcash POW by performing
quadratically fewer hashes than is needed by a
classical computer.
• However, the extreme speed of current ASIC
hardware for performing the hashcash POW,
coupled with much slower projected gate
speeds of current quantum architectures
negates this quadratic speedup
• Quantum gate speeding upto 100 GHZ could
allow quantum computers to solve the POW
about 100 times faster than the current
technology

Q U A N T U M S E C U R E D
B L O C K C H A I N T E C H N O L O G Y
E . O . K I K T E N K O , 1 , 2 N . O . P O Z H A R , 1 M . N . A N U F R I E V, 1 A . S . T R U S H E C H K I N , 1 , 2 R . R . Y U N U S O V, 1 Y. V. K U R O C H K I N , 1
A . I . LV O V S K Y, 1 , 3 , ∗ A N D A . K . F E D O R O V 1 - R U S S I A N Q U A N T U M C E N T E R , U N I V E R S I T Y O F C A L G A RY

B L O C K C H A I N A N D
C RY P T O G R A P H Y
• Blockchain relies on two one way
computational methods
• Cryptographic Hash Functions
• Digital Signatures
• Most Blockchain platforms rely on
ECDSA or RSA to generate the
digital signature

S H O R ’ S A N D G R O V E R ’ S
A L G O R I T H M S
• Shor’s quantum algorithm solves
factorisation of large numbers and
discrete logarithms in polynomial time
• Grover’s search algorithm allows a
quadratic speedup in calculating the
inverse hash functions
• This will enable the 51% attack in which a
syndicate of malicious parties controlling
a majority of the network’s computing
power to monopolise mining of new
blocks

B L O C K C H A I N
S E C U R I T Y A N D P Q C
• Security of blockchains can be
enhanced by using post quantum
digital signature schemes for signing
transactions
• However post quantum signatures
are computationally intensive and
not helpful against attacks that utilise
the quantum computer to dominate
the netowks mining hash rate.

Q U A N T U M K E Y
D I S T R I B U T I O N
• Quantum Key Distribution for
Authentication
• QKD is able to generate a secret key
between two parties connected by a
quantum channel ( for transmitting
quantum states ) and a public classic
channel ( for post processing
procedures )

Q K D B A S E D D I G I TA L
S I G N AT U R E G E N E R AT I O N
• QKD requires an authenticated
classical channel for operation
• Each QKD session generates a large
amount of shard secret data, part of
which can be used for authentication
in subsequent sessions
• Small amount of seed secret data that
parties share before the first QKD
session ensures secret authentication
for all future communications

Q U A N T U M S E C U R E
B L O C K C H A I N
A R C H I T E C T U R E
• Blockchain Protocol with a two layer
network with n-nodes
• First layer is a QKD network with
pairwise communication channel
• Second layer is used for transmitting
messages with authentication tags
based on Toeplitz hashing that are
created using the private keys
procured in the first layer

U N I Q U E
T E C H N I Q U E S
• Block proposal by miners are not
required as it is vulnerable to quantum
computer attacks
• Transactions are not rigged with digital
signatures. Miners have complete
freedom to fabricate aribitrarily,
apparently valid
• Nodes equipped with Quantum
Computer is able to mine new blocks
dramatically faster than any non-quantum
node.

B R O A D C A S T
P R O T O C O L
• Proposed by Shostak, Lamport and Pease
• Able to achieve Byzantine Final Agreement in any
network with pairwise authentication
communication provided that the number of
dishonest parties is less than n/3
• Each node forms a block out of all admissible
transactions sorted according to their timestamps
• Broadcast protocol is relatively data intensive, the
data need not be transmitted through quantum
channels.
• Quantum channels are only required to generate
Private Keys.

G R O V E R S A L G O R I T H M
AT TA C K O N B L O C K C H A I N
• Malicious party equipped with a quantum
computer can work offline to forge the
database
• They can change one of the past transaction
record and performs a Grover search for a
variant of other transactions with the same
block such that its hash remains the same, to
make the forged version appear legitimate.
• Once the search is successful, it hacks into all
or some of the network nodes and
substitutes the legitimate database by its
forged version

G R O V E R S A L G O R I T H M
AT TA C K O N B L O C K C H A I N
• Potential of this attack to cause serious
damage appears low, because the attacker
would need to simultaneously hack into one
third of the nodes to alter the consensus.
• Grover’s algorithm offers only a quadratic
speedup with respect to classical search
algorithms
• Hence this attack can be prevented by
increasing the convention on the block hash
to about a square of its safe non-quantum
value.

Q U A N T U M A S S I S T E D
B L O C K C H A I N T E C H N O L O G Y
D . S A PA E V 1 , 3 , D . B U LY C H K O V 2 , 3 , F. A B L AY E V 3 , A . VA S I L I E V 3 , M . Z I AT D I N O V 3

G R O V E R ’ S A L G O R I T H M
A N D P R O O F O F W O R K
• Quantum Computers can perform an
exhaustive search quadratically faster
than classical computers
• We can use modified Grovers
Algorithm to perform mining on
Quantum Computers
• If we can consider all the values of
nonce at once, then we can speedup
the search for the right one

Q U A N T U M R E G I S T E R
D E S I G N O V E R V I E W
• Dividing a Quantum Register
• Applying Hadamard Transform to the
Qubits
• Considering all values at once
• Functional Qubit for Grovers
Algorithm

Q U A N T U M R E G I S T E R
C O M P U TAT I O N
• Applying Hadamard Transform to the
nonce quibits. Calculate the Hash Values
for all the nonce values at once
• For each incoming block header, mix it
with the hash state and then compute
the hash function
• We get a register that contains all values
of nonce, hash values for each nonce, a
number of service quibits that are
needed to store the intermediate
computations and a functional quibit

A N D N O N C E VA L U E
• We use the Oracle function to
calculate the hash value that is below
a certain threshold.
• This function is a NOT operation
controlled by those qubits whose
value is intended to be zero in the
desired hash value
• Apply Grover’s algorithm to find
desired hash value and nonce

C L A S S I C A L H A S H I N G
A L G O R I T H M S O N
Q U A N T U M C O M P U T E R S
• We need the following set of
primitives - XOR, AND, NOT and
bitwise shift
• XOR is implemented using CNOT
gate
• We need to write the result of an
XOR operation into separate Qubit

X O R O P E R AT I O N O N
T H E S E R V I C E Q U B I T
• Initialize the service qubit in the state | 0 >
• Perform a CNOT gate, in which the first
operand is the controlling one and the
service qubit is the target
• Perform the same transformation, but with
the second operand as the controlling
one
• Service Qubit will be in the state | 1 > if
and only if exactly one of the operand is 1,
otherwise it will be | 0 >

Q U A N T U M G AT E
I M P L E M E N TAT I O N
• AND is implemented using three bit
gate CCNOT - it inverts the target
qubit only when the first two are in
state | 1>
• NOT is implemented by a simple
Pauli Gate X
• Bit shift can be implemented using a
series of swap transformations

P R O B L E M S O F U S I N G
F O R M I N I N G
• Too low value for the average
• Grovers algorithm works efficiently
only if we have a uniform
superposition of all qubits
participating in it

Q U A N T U M B L O C K C H A I N U S I N G
E N TA N G L E M E N T I N T I M E
D E L R A J A N A N D M AT V I S S E R , V I C T O R I A U N I V E R S I T Y O F W E L L I N G T O N

C R U X
• Encoding Blockchain into a temporal
GHZ ( Greenberger - Home -
Zellinger ) state of photons that do
not simultaneously co-exist
• Entanglement involves nonclassical
correlations, usually between
spatially separated quantum systems

G H Z , B E L L S TAT E S A N D
S U P E R D E N S E C O D I N G
• Multipartite GHZ states are ones in
which all subsystems contribute to
the shared entangled property.
• Superdense Coding helps us to
convert classical information into
spatially entangled Bell states
• Bell States are orthonormal and
hence they can be distinguished by
quantum measurements

T E M P O R A L B E L L S TAT E S
A N D T I M E S TA M P I N G
• As records as generated, the system
encodes them as blocks into
temporal Bell states
• These photons are then created and
absorbed at their respective times
• To create the desired quantum
design, the system should chain the
bit strings of the Bell states together
in chronological order, through
entanglement in time

M A P P I N G B E L L S TAT E S
I N T O G H Z S TAT E
• Through a fusion process, temporal
Bell States are recursively projected
into a growing temporal GHZ state
• The time stamps allow each block’s
bit string to be differentiated from
the binary representation of the
temporal GHZ basis state
• Decoding process extracts the
classical information from the state

Q U A N T U M N E T W O R K
U S I N G R A N D O M I S E D
C O N S E N S U S
• Random Node selection using Quantum Random Number
Generator
• The untrusted source shares a possible valid block, an n-
qubit state.
• Since it knows the state, it can share as many copies of the
block as is needed without violating no-cloning theorem
• The verifying nodes generate random angles such that it is
a multiple of pi
• The classical angles are distributed to each node,
including the verifier
• If the n-qubit state was a valid block, i.e, a spatial GHZ
state, the necessary condition is satisfied with probability 1

Q U A N T U M B L O C K C H A I N W I T H P R O O F O F W O R K
B A S E D O N A N A L O G H A M I LT O N I A N O P T I M I S E R S
K I R I L L P. K A L I N I N 1
A N D N ATA L I A G . B E R L O F F, U N I V E R S I T Y O F C A M B R I D G E &
S K O L K O V O I N S T I T U T E O F S C I E N C E A N D T E C H N O L O G Y

P O W A N D H A S H
F U N C T I O N S
• Usually POW problems are based on a
function H, called hash function
• Hash y can be easily computed from the initial
data x by calculating y = H(x), but finding x
given a y is computationally hard
• The inversion of a hash function requires an
exponentially growing computational time or
an order of O(2^n) where n is the hash size.
• Every transaction in the block has a Hash
associated with it and each block in the
Blockchain is identified by its block header
hash

M I N I N G D I F F I C U LT Y
• The mining difficulty is represented by
the difficulty target value and dynamically
controlled and regularly adjusted by a
moving average giving an average
number of blocks per hour fixed in order
to compensate the increasing
computational power and varying interest
in running nodes involved in mining
• In bitcoin, the difficulty target is updated
every 2016 blocks in order to target the
desired block interval accurately

Q U A N T U M
S I M U L AT O R S
• Quantum simulator is an approach of using
one well tunable quantum system to
simulate another quantum system
• To design such a quantum simulator, one
needs to map the variables of the desired
Hamiltonian of the system into the
elements ( spins, currents, photons etc. ) of
the simulator, tune the interactions between
them, prepare the simulator in a state that
is relevant to the physical problem of
interest and perform measurements on the
simulator with the required precision

P H Y S I C A L S Y S T E M S F O R
Q U A N T U M S I M U L AT O R S
• Systems that use quantum processes for their operation
• Trapped Ions
• Superconducting Qubits
• Systems for which quantum processes are crucial in forming the
state of the system
• Bose Einstein Condensates
• Ultra cold atoms in optical lattices
• Network of optical parametric oscillators
• Coupled Lasers
• Polarisation Condensates
• Multimode Cavity QED
• Photon Condensates

Q U A N T U M O P T I M I S AT I O N
P R O B L E M S A N D P O W
• Universal Hamiltonians are NP-Hard
problems for a general matrix of couplings
• Number of operations grows as an
exponential function with the matrix size
• Hence we can formulate a spin
Hamiltonian for which the global minimum
can be found by a simulator
• Finding the optimal solution of the general
n vector model for a sufficiently large size
may be suitable for a POW protocol

• Two optimisation problems are
presented for POW
• Quadratic Unconstrained Binary
Optimisation ( QUBO )
• Quadratic Continuous
Optimisation ( QCO )

• Two optimisation problems are
presented for POW
• Quadratic Unconstrained Binary
Optimisation ( QUBO )
• Quadratic Continuous Optimisation
( QCO )
• QUBO is a discrete version of QCO for
which the decision variables are
constrained to lie on the unit circle with
is a continuous domain

– D AV I D D E U T S C H
“Quantum computation is … nothing less than a distinctly new way
of harnessing nature … It will be the first technology that allows
useful tasks to be performed in collaboration between parallel
universes, and then sharing the results.”

Quantum Meets Blockchain - Different Perspectives

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