PIE and Mercury: Enabling Secure and Efficient Computation of Fractional Data in Privacy-Enhancing Technologies

Enabling Secure and Efficient Computation of Fractional Data


This white paper introduces two groundbreaking innovations by Algemetric: PIE (P-adIc Encoder) and Mercury, which enable efficient and accurate computation over fractional data in Privacy-Enhancing Technologies (PETs). Traditional PETs, such as Homomorphic Encryption (HE) and Multiparty Computation (MPC), have faced challenges in efficiently handling fractional data, particularly regarding operations like division. Algemetric’s PIE and Mercury protocols address these challenges by allowing computations over rational numbers as if they were integers, revolutionizing the landscape of secure and private data analytics, machine learning, finance, artificial intelligence, and more. This paper delves into the technical details and implications of these innovative solutions.


1. Introduction

In the era of data-driven decision-making, ensuring the privacy and security of sensitive data is paramount. Traditional PETs, while powerful, have limitations when dealing with fractional data and complex mathematical operations, particularly division. These limitations have hindered the broad application of PETs in fields where fractional data is ubiquitous.


2. PIE: A Rational Encoder for Integer-Based Computations

PIE is the cornerstone of Algemetric’s approach to efficient fractional data computation. It transforms computations involving rational numbers into operations on integers. PIE enables the four fundamental mathematical operations (addition, subtraction, multiplication, and division) on rational numbers to be encoded as integer operations, thus significantly improving computational efficiency.


2.1. Homomorphic Computation


PIE plays a pivotal role in enhancing homomorphic computations’ efficiency, enabling the addition, subtraction, multiplication, and division of rationals encoded as integers. This opens up new possibilities for implementing a wide range of advanced functions and algorithms in privacy-preserving environments.


3. Mercury: Empowering MPC with Efficient Division

Mercury, Algemetric’s MPC protocol, builds upon Shamir’s Secret Sharing (SSS) principles while incorporating PIE to efficiently handle all four basic mathematical operations. Before Mercury’s introduction, division in MPC protocols was arduous and inefficient, characterized by numerous communication rounds and bit-wise computations. With Mercury, division becomes practical for real-world solutions, eliminating a significant bottleneck in MPC-based computations.


3.1. Protocols for Equality and Comparators


Mercury extends its capabilities to include protocols for equality (A == B) and comparators (A < B, A > B, A >= B, A <= B). These operations are performed efficiently, moving away from impractical bit-wise computations and binary circuits that were previously the norm.


4. Prisma: Fully Encrypted SQL Query Interface

Algemetric’s ultimate goal, fully realized in Prisma, is to create the world’s first fully encrypted SQL query interface. With the ability to compute all basic mathematical operations, equality, and comparators using the Mercury MPC protocol, users can securely query their encrypted data without needing expertise in encrypted data operations. A translator seamlessly converts SQL queries into MPC commands, making it possible for anyone familiar with standard SQL to work with Prisma over encrypted data.


5. AI-Assisted Natural Language Processing

Prisma incorporates AI-assisted Natural Language Processing to simplify data interaction further. It enables users to convert natural language queries into SQL commands, subsequently translated into MPC instructions, expanding the horizons of secure and private data processing.


6. Obscura: A Robust Data Processing Platform

Powered by Mercury, Obscura offers a comprehensive data processing platform. In addition to Mercury’s capabilities, it features a low-level flagging system designed to identify and block the reconstruction of confidential and sensitive data, reinforcing the security and privacy compliance aspects of Algemetric’s offerings.


7. Business Opportunities Enabled by Algemetric’s Solutions

The limitations of traditional Privacy-Enhancing Technologies (PETs) in handling fractional data, as previously discussed, have profound implications for business opportunities across many industries. Algemetric’s innovative solutions, PIE and Mercury, can unlock a vast array of possibilities by bridging the gap hindering the utility and applicability of HE-based and MPC-based solutions.


7.1. Data Analytics


The ability to efficiently compute advanced mathematical operations on fractional data is a game-changer in data analytics. With PIE and Mercury, businesses can perform intricate analyses, derive valuable insights, and make data-driven decisions without compromising data privacy. This opens the door to myriad applications, from market research and customer behavior analysis to predictive modeling and anomaly detection, all of which depend on the manipulation of fractional data.


7.2. Machine Learning and Artificial Intelligence


Machine learning and artificial intelligence (AI) rely heavily on complex algorithms and models, often involving fractional data. Algemetric’s solutions pave the way for fully secure and private machine learning and AI applications. The opportunities and innovation potential are boundless, from training models on encrypted data to developing AI-driven solutions for personalized recommendations and natural language processing.


7.3. Finance and Banking


In the financial sector, the need for secure data processing is non-negotiable. With Algemetric’s technology, financial institutions can perform risk assessments, portfolio management, and fraud detection while preserving the confidentiality of sensitive financial data. Algemetric’s solutions enable banks to harness the power of PETs without sacrificing computational efficiency, ultimately safeguarding both their bottom line and the trust of their customers.


7.4. Data Science


Data science encompasses various applications, from predictive modeling and clustering to data mining and optimization. All of these areas leverage fractional data and advanced mathematical operations. Algemetric’s solutions ensure that data scientists can perform these operations securely and privately, expanding the possibilities in research, product development, and problem-solving across various domains.


7.5. Privacy-Enhancing Technologies as a Competitive Advantage


Algemetric’s offerings bring to light a pivotal competitive advantage. The ability to securely and privately perform operations on fractional data sets businesses apart in a world where data privacy is of paramount concern. Companies can develop innovative solutions that meet the growing demand for secure data handling and earn the trust of their customers.


7.6. Market Expansion


The utility of HE and MPC in industries where fractional data is a cornerstone, such as healthcare, pharmaceuticals, and scientific research, is undeniable. Algemetric’s solutions open doors to previously unexplored markets by removing the limitations that once hindered their application. Businesses can expand their reach and explore new avenues for growth by offering secure, privacy-preserving solutions in these domains.


7.7. Compliance and Regulatory Alignment


Algemetric’s solutions are well-positioned to meet stringent data protection regulations and compliance standards. This helps businesses avoid costly fines and enhances their reputation as trustworthy stewards of sensitive information.


The utility of HE-based and MPC-based solutions has significantly been restricted by their limitations in dealing with fractional data and complex mathematical operations. Algemetric’s PIE and Mercury address these limitations and create a fertile ground for businesses to explore new horizons, leverage data securely, and capitalize on the ever-increasing demand for privacy-enhancing technologies. The possibilities are boundless, and the business opportunities are limitless.


8. Conclusion


Algemetric’s PIE and Mercury have ushered in a new era of secure and efficient computation over fractional data within Privacy-Enhancing Technologies. These innovations enable the safe use of data in numerous fields while maintaining privacy and confidentiality. With Prisma and Obscura, Algemetric provides a holistic solution that empowers organizations to unlock the full potential of their data securely and privately.