Final answer:
Quantum Cryptography is the field that applies highly parallel algorithms using quantum mechanics principles to achieve secure communication faster than traditional computing methods.
Step-by-step explanation:
The approach to cryptography that uses highly parallel algorithms capable of solving problems significantly faster than conventional computers is a) Quantum Cryptography. Quantum cryptography leverages the principles of quantum mechanics to encrypt and decrypt data in a way that is inherently secure against many forms of eavesdropping. Unlike classical computing which relies on bits to process information sequentially, quantum computing uses quantum bits, or qubits, which can exist in multiple states simultaneously, allowing for parallel processing on a scale not possible with traditional computers.