#1 Added improvements: Implemented Pollard's Rho for large keys, para… #5
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…s, parallel processing, and adaptive NN training
- The original script failed for moduli above 300 bits due to naive search failures. Here, we resort to Pollard's Rho, a probabilistic method based on cycle detection that is more effective for semiprimes, preserving the NN for quick gains on small keys.
- Now, the load_data_and_model function will load factor pairs stored in JSON (n {p, q}), falling back to the default sequential model if .h5 is missing. The update_model_and_data function will add new data only for n < 2^53 (avoiding loss of floating-point precision); it retrains on subsets with 50 epochs. Batch_size=min(32,data_len) saves the model after fitting.
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The original script failed for moduli above 300 bits due to naive search failures. Here, we resort to Pollard's Rho, a probabilistic method based on cycle detection that is more effective for semiprimes, preserving the NN for quick gains on small keys.
Now, the load_data_and_model function will load factor pairs stored in JSON (n {p, q}), falling back to the default sequential model if .h5 is missing. The update_model_and_data function will add new data only for n < 2^53 (avoiding loss of floating-point precision); it retrains on subsets with 50 epochs. Batch_size=min(32,data_len) saves the model after fitting.
Another improvement implements the Brent variant of Pollard's Rho with cycle detection via the tortoise-hare (x, y advances). This limits iterations to 1M per attempt to avoid crashes, and uses math.gcd for divisor checks. The factor_with_rho function will orchestrate the trial division up to 10K for small factors and then execute Rho in parallel. Returning ordered (p, q) only after the Miller-Rabin primality check.
512-bit semiprimes are expected to be successfully factored in <10s on average (tested using synthetic keys, e.g., p=next_prime(2^256), q=next_prime(2^256 + 2^100)). It also returns errors in primes or failures, which will increase reliability.