Modular Exponentiation Lookup Table for Untrusted Platforms
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Solution Overview
Problem
Existing digital signature schemes, such as RSA, require access to the secret exponent for modular exponentiation, which can be insecure in untrusted platforms, and existing solutions like white-box cryptography are resource-intensive and require large lookup tables.
Innovation Solution
A method and device for performing modular exponentiation using a lookup table with pre-computed values based on a cryptographic key modulus, allowing digital signatures to be generated without access to the secret exponent, and optimizing the size and resources required for the lookup table.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional modular exponentiation is used in RSA digital signatures, then security is maintained through secret exponent, but resource consumption increases and security is compromised on untrusted platforms
Solution Approach 1:
The patent pre-computes modular exponentiations for all possible encoded values and stores them in a lookup table before execution. This preliminary action eliminates the need for real-time secret exponent usage, reducing resource consumption during actual signature operations while maintaining security on untrusted platforms.
Solution Approach 2:
The patent creates a lookup table that contains copies of pre-computed modular exponentiation results. Instead of performing complex calculations with the secret exponent during runtime, the system retrieves pre-computed values from the lookup table, significantly reducing computational resources and enhancing security on untrusted platforms.
2Reliability
If white-box cryptography is used to protect secret exponent on untrusted platforms, then security is improved, but lookup table size and resource requirements increase significantly
Solution Approach 1:
The patent applies local quality by optimizing the lookup table to store only the specific pre-computed values needed for the particular RSA implementation. Instead of storing all possible modular exponentiations, the table is tailored to contain only the necessary entries for the given key and encoding scheme, reducing overall table size while maintaining security.
Solution Approach 2:
The patent changes parameters by optimizing the encoding scheme and factor set used to generate the lookup table. By carefully selecting the encoding method and factorization approach, the patent reduces the number of entries required in the lookup table while still providing adequate security coverage for the untrusted platform.
3Productivity
If lookup table is used for modular exponentiation without secret exponent, then resource consumption is reduced, but computation accuracy may be affected
Solution Approach 1:
The patent performs preliminary computation of modular exponentiations with high precision and stores the exact results in the lookup table. This preliminary action ensures that when values are retrieved during runtime, they maintain computational accuracy while the system benefits from reduced resource consumption during actual operations.
Data Source
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AI summary
Various embodiments relate to a method of encoding data and a related device and non-transitory machine readable storage medium, including: determining a plurality of factors of a value, b, to be exponentiated; retrieving, from a lookup table, a plurality of lookup table entries associated with the plurality of factors; calculating a product of the plurality of lookup table entries; and calculating a residue of the product using a cryptographic key modulus, N, to produce an exponentiated value, s.