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Quantum Meets Blockchain - Different Perspectives

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Gokul Alex

The document explores the intersection of quantum computing with blockchain technology, highlighting advancements like quantum money, quantum-resistant blockchains, and post-quantum cryptography. It discusses potential threats posed by quantum attacks on traditional cryptographic methods used in blockchain and illustrates solutions like quantum key distribution and quantum ledger systems. Additionally, it outlines algorithms such as Grover's and Shor's, which influence mining processes and the security of blockchain systems.

Technology
Related topics:
Quantum Computing • Quantum Cryptography
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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 It remained unpublished till 1983.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
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
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
Quantum Meets Blockchain - Different Perspectives
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
Quantum Meets Blockchain - Different Perspectives
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
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
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
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
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
Quantum Meets Blockchain - Different Perspectives
Quantum Meets Blockchain - Different Perspectives
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 R L WA L L E T
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
G R O V E R ’ S A L G O R I T H M 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 G R O V E R ’ S A L G O R I T H M 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
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 • Two optimisation problems are presented for POW • Quadratic Unconstrained Binary Optimisation ( QUBO ) • Quadratic Continuous Optimisation ( QCO )
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 • 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.”

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Quantum Meets Blockchain - Different Perspectives

  • 1. 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
  • 2. 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
  • 3. 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
  • 4. 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
  • 5. 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
  • 14. 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
  • 16. 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
  • 18. 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
  • 21. 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
  • 22. 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
  • 23. 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
  • 28. 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
  • 29. 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
  • 30. 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
  • 33. 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
  • 34. 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
  • 35. Q R L B L O C K E X P L O R E R D E M O
  • 36. Q R L R E C E N T T R A N S A C T I O N S
  • 37. Q R L WA L L E T
  • 38. 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
  • 39. 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
  • 40. 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
  • 41. 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.
  • 42. 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
  • 43. 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
  • 44. 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
  • 45. 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
  • 46. 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
  • 47. 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.
  • 48. 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 )
  • 49. 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
  • 50. 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
  • 51. 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.
  • 52. 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.
  • 53. 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
  • 54. 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.
  • 55. 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
  • 56. 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
  • 57. 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
  • 58. 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
  • 59. G R O V E R ’ S A L G O R I T H M 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
  • 60. 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
  • 61. 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 >
  • 62. 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
  • 63. P R O B L E M S O F U S I N G G R O V E R ’ S A L G O R I T H M 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
  • 64. 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
  • 65. 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
  • 66. 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
  • 67. 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
  • 68. 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
  • 69. 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
  • 70. 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
  • 71. 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
  • 72. 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
  • 73. 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
  • 74. 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
  • 75. 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
  • 76. 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 • Two optimisation problems are presented for POW • Quadratic Unconstrained Binary Optimisation ( QUBO ) • Quadratic Continuous Optimisation ( QCO )
  • 77. 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 • 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
  • 78. – 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.”