Using Virus Machines to Compute Pairing Functions.

Area of Science:

• Theoretical Computer Science
• Computational Biology
• Cryptography

Background:

• Virus machines are a computational model inspired by viral behavior, capable of replication and host resource utilization.
• This model has been proven computationally equivalent to Turing machines through various methods.
• Investigating practical applications and efficiency of virus machines is crucial for their development.

Purpose of the Study:

• To explore the practical applications of virus machines in computation.
• To develop basic modules for constructing an arithmetic calculator using virus machines.
• To implement and calculate two key pairing functions for cryptographic use.

Main Methods:

• Designing virus machine modules for arithmetic operations.
• Implementing two distinct virus machines to compute pairing functions.
• Utilizing graph-based instruction systems to control virus machine behavior.

Main Results:

• Successfully constructed the fundamental components for an arithmetic calculator.
• Demonstrated the computation of the Cantor pairing function using a virus machine.
• Successfully computed the Gödel pairing function via a separate virus machine implementation.

Conclusions:

• Virus machines offer a viable and powerful model for practical computation, including arithmetic.
• The implemented virus machines effectively calculate essential cryptographic pairing functions.
• This research highlights the potential of virus machines in applied computational tasks and cryptography.