MemComputing, a creator of advanced computing architectures, has released results from a study on computing prime factorization. The study was part of a contract with the US Air Force and assessed the potential to factorize large numbers using MemComputing’s patented circuit architecture. The team developed an approach based on a congruence model, which uses the electronic circuit’s dynamical behaviour to identify congruences among integers with unique properties that are used to factorize efficiently.
“This latest development not only showcases the raw power and versatility of our technology but also paves the way for significant advancements in fields that rely heavily on prime factorization, such as computer science and cryptography.”
John Beane, CEO of MemComputing, Inc.
The circuit design was customized with Self-Organizing Gates (SOGs) to address the model effectively. Results showed that the circuit generated the appropriate congruences for benchmark problems up to 300 bits. The next step is to extend the effective range beyond 300 bits, which requires customizing the SOG design to even larger factorization problems. The company forecasts that solutions for problems at the scale of 2048 bits could be achieved with either emulation or ASICs and that the latter could be in real-time. This development paves the way for significant advancements in fields that rely heavily on prime factorization, such as computer science and cryptography.
MemComputing’s Study on Prime Factorization
MemComputing has shared the results of a study on prime factorization. The study was part of a Small Business Innovation Research contract with the US Air Force. The research aimed to assess the potential of factorising large numbers using MemComputing’s patented circuit architecture to solve prime factorization on a large scale.
The research team developed an approach based on a congruence model. This model utilises the dynamical behaviour of the electronic circuit to identify congruences among integers with unique properties, which are then used to factorise efficiently. The team tailored the circuit design, composed of Self-Organizing Gates (SOGs), to effectively address the model. They focused on test problems ranging from 30 to 150 bits.
Software emulations of the circuit were used to measure the time taken to produce congruences. The results indicated that the circuit generated the appropriate congruences for benchmark problems up to 300 bits. The time required to factorise followed a 2nd-degree polynomial in the number of bits.
Extending the Range of Prime Factorization
The project’s next phase is to extend the effective range beyond 300 bits. This will involve tailoring the SOG design to larger factorization problems. The ultimate aim is to realise this capability in an Application Specific Integrated Circuit (ASIC).
The company predicts that solutions for problems at the scale of 2048 bits could be achieved with either emulation or ASIC. They also suggest that the latter could potentially be performed in real time.
The results of this study have significant implications for fields that rely heavily on prime factorization, such as computer science and cryptography. The advancements made in this study demonstrate the power and versatility of MemComputing’s technology and pave the way for significant improvements in these fields.
MemComputing, Inc. is a deep tech company specialising in solving complex optimisation problems using its cloud-based MEMCPU™ Platform. Its proprietary circuit design, rooted in physics, harnesses the power of computational memory to overcome the limitations of traditional computing methods. MemComputing is developing various hardware solutions for numerous edge-processing applications for industries such as energy, transportation, logistics, and the DoD.
Access to the Study and Demonstration
The manuscript detailing the study and the results can be accessed online. A video presentation and demonstration of the prime factorization process can also be found on the company’s website. A recent paper has been published on ArXiv.
“With this latest achievement, MemComputing reaffirms its unwavering commitment to spearheading innovation in the computational domain,”
John Beane, CEO of MemComputing, Inc.
Quick Summary
MemComputing, a computing architecture firm, has developed a method for prime factorisation using a congruence model and their patented circuit design, demonstrating the potential for large-scale solutions. The study showed that the time needed to factorise followed a 2nd-degree polynomial in the number of bits, with plans to extend the effective range beyond 300 bits.”
- MemComputing, Inc., a computing architecture company, has released results from a study on computing prime factorization conducted under a Small Business Innovation Research contract with the US Air Force.
- The study explored the potential to factorize large numbers using MemComputing’s patented circuit architecture, demonstrating the feasibility of solving prime factorization at scale.
- The team developed an approach based on a congruence model, which uses the electronic circuit’s dynamical behaviour to identify congruences among integers with unique properties for efficient factorization.
- The circuit design was customized with Self-Organizing Gates (SOGs) to address the model, focusing on test problems from 30 to 150 bits.
- The circuit generated the appropriate congruences for benchmark problems up to 300 bits, and the time needed to factorize followed a 2nd-degree polynomial in the number of bits.
- The next step is to extend the effective range beyond 300 bits, which requires customizing the SOG design for larger factorization problems. The goal is to realise the capability in an Application Specific Integrated Circuit (ASIC).
- The company forecasts that solutions for problems at the scale of 2048 bits could be achieved with either emulation or ASIC and that the latter could be in real-time.
- CEO John Beane stated that this development showcases the power and versatility of their technology and paves the way for advancements in fields that rely heavily on prime factorization, such as computer science and cryptography.
