A Summary of the FV Homomorphic Encryption Scheme and the Average-Case Noise Growth

Homomorphic encryption is a method of encryption that allows for secure computation of data. Many industries are moving away from owning expensive high-powered computers and instead delegating costly computations to the cloud. In an age of data breaches, there is an inherent risk when putting sensitive data on the cloud. Homomorphic encryption allows one to securely perform computations on the cloud without allowing the host or any other party access to the raw data itself. One application being explored is encrypting health data on low-powered embedded devices, uploading it to a cloud application, performing computations to assess health risks, and send the results back to the user’s device for decryption and interpretation. Another application being explored is digital voting. This thesis aims to provide a summary of the current state-of-the-art of homomorphic encryption. We will begin by providing the reader with sources for the current main im- plementations and schemes they are based on. We will then present the mathematical background used in existing schemes. This includes a background on lattices, cyclotomic fields, rings of integers, and the underlying believed-to-be-hard problems existing schemes take advantage of. We will then shift our attention to the FV scheme which is based on the ring-LWE problem and is one of the main schemes used today. We will then briefly discuss some optimizations used in FV implementations. Finally, we will look at some probabilistic experiments which suggest the noise growth in FV is significantly lower than the theoretical maximum in the average case, and will explore some of the benefits that can be gained

Secure Outsourced Computation on Encrypted Data

Homomorphic encryption (HE) is a promising cryptographic technique that supports computations on encrypted data without requiring decryption first. This ability allows sensitive data, such as genomic, financial, or location data, to be outsourced for evaluation in a resourceful third-party such as the cloud without compromising data privacy. Basic homomorphic primitives support addition and multiplication on ciphertexts. These primitives can be utilized to represent essential computations, such as logic gates, which subsequently can support more complex functions. We propose the construction of efficient cryptographic protocols as building blocks (e.g., equality, comparison, and counting) that are commonly used in data analytics and machine learning. We explore the use of these building blocks in two privacy-preserving applications. One application leverages our secure prefix matching algorithm, which builds on top of the equality operation, to process geospatial queries on encrypted locations. The other applies our secure comparison protocol to perform conditional branching in private evaluation of decision trees. There are many outsourced computations that require joint evaluation on private data owned by multiple parties. For example, Genome-Wide Association Study (GWAS) is becoming feasible because of the recent advances of genome sequencing technology. Due to the sensitivity of genomic data, this data is encrypted using different keys possessed by different data owners. Computing on ciphertexts encrypted with multiple keys is a non-trivial task. Current solutions often require a joint key setup before any computation such as in threshold HE or incur large ciphertext size (at best, grows linearly in the number of involved keys) such as in multi-key HE. We propose a hybrid approach that combines the advantages of threshold and multi-key HE to support computations on ciphertexts encrypted with different keys while vastly reducing ciphertext size. Moreover, we propose the SparkFHE framework to support large-scale secure data analytics in the Cloud. SparkFHE integrates Apache Spark with Fully HE to support secure distributed data analytics and machine learning and make two novel contributions: (1) enabling Spark to perform efficient computation on large datasets while preserving user privacy, and (2) accelerating intensive homomorphic computation through parallelization of tasks across clusters of computing nodes. To our best knowledge, SparkFHE is the first addressing these two needs simultaneously

Side-Channel Analysis on Post-Quantum Cryptography Algorithms

The advancements of quantum computers brings us closer to the threat of our current asymmetric cryptography algorithms being broken by Shor\u27s Algorithm. NIST proposed a standardization effort in creating a new class of asymmetric cryptography named Post-Quantum Cryptography (PQC). These new algorithms will be resistant against both classical computers and sufficiently powerful quantum computers. Although the new algorithms seem mathematically secure, they can possibly be broken by a class of attacks known as side-channels attacks (SCA). Side-channel attacks involve exploiting the hardware that the algorithm runs on to figure out secret values that could break the security of the system. The third round of the PQC standardization put some emphasis on the algorithm\u27s ability to mitigate side-channel attacks. In this work, two candidate KEM algorithms Kyber and Saber are analyzed through a multi-platform setup. Both unprotected and protected implementations on Cortex-M4 microcontrollers through masking are analyzed using the test vector leakage assessment with an oscilloscope and a ChipWhisperer too

A practical key-recovery attack on LWE-based key-encapsulation mechanism schemes using Rowhammer

Physical attacks are serious threats to cryptosystems deployed in the real world. In this work, we propose a microarchitectural end-to-end attack methodology on generic lattice-based post-quantum key encapsulation mechanisms to recover the long-term secret key. Our attack targets a critical component of a Fujisaki-Okamoto transform that is used in the construction of almost all lattice-based key encapsulation mechanisms. We demonstrate our attack model on practical schemes such as Kyber and Saber by using Rowhammer. We show that our attack is highly practical and imposes little preconditions on the attacker to succeed. As an additional contribution, we propose an improved version of the plaintext checking oracle, which is used by almost all physical attack strategies on lattice-based key-encapsulation mechanisms. Our improvement reduces the number of queries to the plaintext checking oracle by as much as $39\%$ for Saber and approximately $23\%$ for Kyber768. This can be of independent interest and can also be used to reduce the complexity of other attacks