Provably Secure Pseudorandom Number Generation via Hash Iteration
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Solution Overview
Problem
Existing cryptographic systems face challenges in generating pseudorandom numbers that are both provably secure and efficient, as secure methods are often inefficient, while efficient methods lack strong security analysis.
Innovation Solution
A computer-implemented method using a hardcore predicate and a collision-resistant hash function to iteratively generate pseudorandom numbers from a seed number, ensuring security by relying on the collision-resistance of the hash function and maintaining efficiency through the use of existing cryptographic hash functions like SHA-1 and SHA-2.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If provably secure pseudorandom number generation methods are used, then security is improved, but generation efficiency deteriorates
Solution Approach 1:
The patent changes the underlying cryptographic parameter from general hard problems to specifically collision-resistant hash functions, enabling both security proofs and practical efficiency. By parameterizing the security around hash function collision resistance rather than computational complexity assumptions, the system achieves provable security without the inefficiency of general-purpose secure generation methods
Solution Approach 2:
The patent replaces complex cryptographic primitives with simpler hash function-based mechanisms. Instead of using intricate secure generation protocols, it substitutes a streamlined process using only collision-resistant hash functions and hardcore predicates, maintaining security while dramatically improving generation speed and practical efficiency
2Productivity
If efficient pseudorandom number generation methods are used, then generation efficiency is improved, but security analysis strength deteriorates
Solution Approach 1:
The patent performs preliminary security analysis by establishing that collision-resistant hash functions provide both security and efficiency. By proving in advance that this specific cryptographic primitive satisfies both requirements, the system eliminates the need to choose between security and efficiency, as both are built into the foundation from the start
Data Source
AI summary
A pseudorandom number is generated from a random seed number using a collision-resistant hash function. A iteration input is extracted from the seed number. A hardcore predicate is applied to the iteration input to generate a pseudorandom bit. A pairwise-independent function is identified using a pairwise-independent function identifier extracted from the seed number and applied to the iteration input to produce a randomized iteration input. The collision-resistant hash function is applied to the randomized iteration input to produce a hash result and pad the output. The padded hash result is assigned as the iteration input for the next iteration. The process repeats iteratively and pseudorandom bits are generated using the hardcore predicate in each iteration until a predetermined number of pseudorandom bits are generated. The pseudorandom number is constructed using the generated pseudorandom bits.