Server-Assisted Homomorphic Exponentiation for Secure Elements
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Solution Overview
Problem
Current cryptographic protocols face challenges in performing secure exponentiation operations, particularly modular exponentiation, which are computationally demanding for secure elements with limited power, such as low-cost SIMs or smart cards, and require large numbers of multiplications, making them inefficient.
Innovation Solution
The method employs polynomial homomorphic encryption to delegate the exponentiation task to a computationally powerful but untrusted server, using encryption parameters to perform homomorphic exponentiation without decrypting the secret value, thereby reducing computational load and time while maintaining security.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If modular exponentiation is performed locally on secure elements (SIMs, smart cards), then security is maintained, but computational time and energy consumption increase significantly
Solution Approach 1:
The patent introduces a server as an intermediary that performs the computationally intensive modular exponentiation operation. The secure element generates cryptographic parameters and sends them to the server, which then computes the exponentiation result and returns it. This mediator approach allows the secure element to maintain security while offloading time-consuming computations to the server.
Solution Approach 2:
The cryptographic operation is segmented into distinct phases: parameter generation by the secure element, exponentiation computation by the server, and result processing by the secure element. This segmentation allows each component to perform only the operations it is best suited for, maintaining security while improving overall computational efficiency.
2Reliability
If modular exponentiation is performed locally on secure elements, then security is maintained, but computational load and energy consumption increase
Solution Approach 1:
The server acts as an intermediary that consumes the energy for heavy computation instead of the secure element. The secure element performs only lightweight operations (parameter generation and result processing) while the server handles the energy-intensive modular exponentiation, significantly reducing the energy consumption of the secure element.
Solution Approach 2:
The patent replaces the mechanical computation process in the secure element with a remote computational process on the server. The secure element substitutes its local exponentiation capability with a remote service, replacing high-energy mechanical operations with low-energy communication and parameter generation tasks.
3Reliability
If modular exponentiation is performed locally on secure elements, then security is maintained, but the number of multiplications required increases computational complexity
Solution Approach 1:
The server as an intermediary takes on the complexity of performing numerous multiplications required for modular exponentiation. The secure element's complexity is reduced to generating parameters and processing results, while the server handles the computationally complex exponentiation operation using its greater processing power.
Solution Approach 2:
The computational complexity is segmented between the secure element and the server. The secure element performs simple parameter generation with minimal multiplications, while the server performs the complex modular exponentiation requiring many multiplications. This segmentation distributes computational complexity according to each component's capabilities.
Data Source
AI summary
In one embodiment, a method for secure computation, includes receiving in a server, over a communication channel from a device external to the server a request to perform a modular exponentiation operation in which an exponent of the operation comprises a secret value, wherein the secret value is not provided to the server, and at least two parameters that encode the secret value in accordance with a polynomial or matrix homomorphic encryption of the secret value computed by the device, and performing in the server, in response to the request, a homomorphic exponentiation using the at least two parameters received from the device without decrypting the secret value in the server, so as to generate an output that is indicative of a result of the modular exponentiation operation.