RSA Key Generation Using Pre-computed Byte Tables
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for generating RSA keys that satisfy the German Digital Signature Law are inefficient, requiring numerous random number attempts, scarce resource usage, and complex software, making them unsuitable for restricted environments like smart cards.
Innovation Solution
A pre-computed table of bytes is used to start the prime searching process, ensuring primes satisfy digital signature law requirements without additional random numbers, resulting in a faster, simpler, and less biased key generation algorithm.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If random numbers are generated and checked to satisfy digital signature law requirements, then key generation reliability is improved, but key generation time and resource consumption increase
Solution Approach 1:
The patent pre-computes and stores valid starting bytes in a lookup table during an offline phase. During online key generation, these pre-computed starting bytes are retrieved and used to generate random numbers that are guaranteed to satisfy the digital signature law requirements, eliminating the need for time-consuming validation checks.
Solution Approach 2:
The patent divides the key generation process into two distinct phases: an offline phase where valid starting bytes are pre-computed and stored in a lookup table, and an online phase where these pre-computed values are retrieved and used for actual key generation. This segmentation allows the computationally intensive pre-computation to be done separately from the time-critical online operation.
2Reliability
If multiple random numbers are generated to satisfy digital signature law requirements, then key generation reliability is improved, but resource consumption increases
Solution Approach 1:
The patent pre-computes and stores valid starting bytes in a lookup table during an offline phase. During online key generation, these pre-computed starting bytes are retrieved and used to generate random numbers that are guaranteed to satisfy the digital signature law requirements, eliminating the need for multiple validation attempts and reducing overall random number consumption.
3Reliability
If complex software algorithms are used to generate primes satisfying digital signature law, then key generation reliability is improved, but device complexity increases
Solution Approach 1:
The patent pre-computes and stores valid starting bytes in a lookup table during an offline phase. During online key generation, these pre-computed starting bytes are retrieved and used to generate random numbers that are guaranteed to satisfy the digital signature law requirements, eliminating the need for complex validation software algorithms.
Solution Approach 2:
The patent uses a lookup table that stores pre-computed valid starting bytes as copies of successfully generated starting values. During online operation, these copied values are retrieved and used directly, replacing the need for complex software algorithms to validate each generated number.
4Adaptability or versatility
If random numbers are generated without pre-computed starting bytes, then flexibility is maintained, but key generation speed decreases
Solution Approach 1:
The patent pre-computes and stores valid starting bytes in a lookup table during an offline phase. During online key generation, these pre-computed starting bytes are retrieved in constant time and used to generate random numbers, providing both speed and flexibility since the lookup table can be indexed to retrieve appropriate starting bytes for different key generation requirements.
Data Source
AI summary
In order to further develop a circuit arrangement for as well as a method of performing at least one operation, in particular at least one cryptographic calculation, wherein the problem of creating at least one key, in particular the R[ivest-]S[hamir-]A[dleman] key, satisfying at least one defined digital signature laws, in particular satisfying the German Digital Signature Law, is solved it is proposed that at least one, preferably two, prime numbers (p; q) for key generation, in particular for R[ivest-]S[hamir-]A[dleman] key generation, are searched in compliance with at least one defined digital signature law, in particular with the German Digital Signature Law.