Table 1.

Notations used in the QuantumShield-BC framework for quantum-secure blockchain operations.

Notation	Definition
	Transaction initiated by the user in the blockchain network
	A post-quantum digital signature is generated using a private key
	Cryptographic hash of the transaction
	Transaction validity function, verifying if the transaction is authentic using post-quantum cryptography
	Newly created blockchain block containing validated transactions
	Cryptographic hash of the newly created block using quantum-resistant hashing
	The previous block’s hash is used to ensure blockchain immutability
	Post-quantum public key of validator ii
	Individual transactions in a block
	Validator authentication status using post-quantum signatures
	Consensus validation result ensures all transactions in a block are validated
	The secret key is established using Quantum Key Distribution (QKD)
	The quantum state is transmitted from the sender node (Alice) in QKD
	Quantum state received by receiver node (Bob) in QKD
	A hybrid encryption key is generated from QKD, and a post-quantum key encapsulation mechanism (PQC-KEM) is used
	Quantum consensus threshold, ensuring that a predefined fraction of validators reach agreement
	An individual validator’s vote contributes to the consensus process
	A minimum threshold is required to achieve consensus in Q-BFT
	Quantum entropy value generated by the Quantum Random Number Generator (QRNG)
	Sequence of quantum bits used for entropy generation in QRNG
	Probability distribution of quantum states in QRNG
	The leader node is selected for block finalization in the consensus process
	Block confirmation time measures the total time to validate and finalize a block
	Computational complexity of breaking a cryptographic key using Shor’s Algorithm
	Computational complexity of searching for a cryptographic hash using Grover’s Algorithm
	Network overhead factor introduced by QKD encryption
	Bandwidth consumed during QKD-based encryption
	Bandwidth consumed using classical encryption methods
	Multi-party consensus verification function using quantum-secure cryptography