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Secure data processing using homomorphism in cryptography - applications in multi-party search, signatures, neural networks and e-voting
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Date
2025
Authors
Ganesh, Buvana
Journal Title
Journal ISSN
Volume Title
Publisher
University College Cork
Published Version
Abstract
Homomorphism is a fascinating property in Mathematics that has found its way into the field of cryptography. This property allows for the preservation of the structure of a system during an operation, enabling the manipulation of encrypted data that was previously incomprehensible. As the field of Homomor phic Encryption (HE) matures toward fruition, this thesis not only offers new functionalities for HE, but also investigates their real-world applications, for when it gets standardized. The constructions in the chapters of the thesis contribute to the development of data processing architectures that address security concerns through this property while adhering to the triad of confidentiality, integrity, and availability. This thesis delves into the concept of homomorphism and its impact on modern cryptography, with a particular focus on its use in lattice-based cryptosystems. Every chapter introduces novel schemes and architectures with different security primitives and guarantees.
The primary contributions in the different chapters revolve around the cryptographic constructions supporting various functionalities of the homomorphic
property including a novel architecture for secure homomorphic search among multiple parties, two novel homomorphic signature schemes, a novel methodology for efficient secure recurrent neural networks using linearized activation
functions, and novel electronic voting using group identity-based identification and the partially homomorphic distributed ElGamal encryption scheme. The practicality of homomorphism is demonstrated by combining these components to construct an end-to-end data processing framework. Through these efforts and contributions, this thesis would facilitate the widespread adoption and integration of HE in various domains, enabling secure and privacy-preserving data processing. The use of lattice-based hardness assumptions assures that the frameworks are quantum-safe, as a bonus.
Through the exploration of homomorphic cryptography, this thesis showcases how its use can increase security and unlock new capabilities for handling the vast amounts of data. The proposed solutions contribute to advancing the field of secure data processing and showcase the potential of HE through integration into various cryptographic primitives.
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Keywords
Homomorphic encryption , Cryptography , Digital signatures , Post-quantum cryptography
Citation
Ganesh, B. 2025. Secure data processing using homomorphism in cryptography - applications in multi-party search, signatures, neural networks and e-voting. PhD Thesis, University College Cork.