Budget: 100 USD Deadline: 3 days
Good day.
I have over 20 years of experience in commercial projects. Interesting task, I am ready to complete it.
It is necessary to create a method for selecting seed, a, b mathematically without generators so that it takes milliseconds (maximum up to 1 minute) for 25 billion 4-digit numbers
Like 1234 3214 1122 1234 3412 1123 4234 4411...
Also, 100% recovery and maximum speed
The main description I made with chat gpt
Technical task (updated)
Goal
Implement a system consisting of two modules:
1. Selection (Recovery): find seed, a, b from a short fragment of the series.
2. Reproduction: generate a series of up to 25 billion numbers (1..4).
---
Data format
Base element: digit from the set {1,2,3,4}.
Packaging: 8 digits → 64 bits (2 bits per digit). This is one block.
Window for selection: W = 32..64 consecutive blocks.
---
MODULE A. SELECTION (Recovery)
A1. Input
y_window: array of W packed blocks (uint64) — consecutive.
seed_candidates: list of seed candidates (for example, [0..4095] or provided file with the list).
n0_local: known local index of the first block in the window (can be 0 if global is not needed).
A2. Output
seed: found seed.
a: difference (multiplier) modulo 2⁶⁴, odd.
b: offset modulo 2⁶⁴.
status: OK / FAIL (+ diagnostics).
A3. Model (for implementation)
x_n = (a*n + b) mod 2^64, where a is odd.
y_n = PRP_seed(x_n), where PRP_seed is the inverted permutation 64-bit (we provide implementation/interface).
A4. Selection algorithm (without brute force over the entire space)
For each seed in seed_candidates:
1. Calculate key PRP_seed^{-1}.
2. Invert the first 2 blocks:
x0 = PRP_inv(y0), x1 = PRP_inv(y1), set a = (x1 - x0) mod 2^64.
(If a is even — quick rejection.)
3. For i=2..W-1:
xi = PRP_inv(yi) and check (xi - x_{i-1}) == a.
If there is a mismatch — reject this seed.
4. If all differences are the same — seed found.
Calculate b = (x0 - a*n0_local) mod 2^64.
Return (seed,a,b) as the result.
> Computational complexity ~O(|seed_candidates| · W). For |seed_candidates|≤4096 and W≤64 — tens of ms.
A5. Pseudocode
for seed in seed_candidates:
key = PRP_make_key(seed)
x0 = PRP_inv(y[0], key)
x1 = PRP_inv(y[1], key)
a = (x1 - x0) mod 2^64
if (a % 2 == 0): continue
ok = True
prev = x1
for i in 2..W-1:
xi = PRP_inv(y[i], key)
if ((xi - prev) mod 2^64) != a: ok = False; break
prev = xi
if ok:
b = (x0 - a*n0_local) mod 2^64
return (OK, seed, a, b)
return (FAIL, -, -, -)
A6. Checks/validation
After finding (seed,a,b) check another 8–16 subsequent blocks (if any) for constant difference.
Optionally: generate 8–16 blocks ahead from n0_local and compare with provided ones.
---
MODULE B. OFFSET
B1. Input
y_obs: one observed block (uint64).
seed, a, b — obtained from Module A.
B2. Output
n: global index of the block (mod 2⁶⁴; if absolute is needed within the file — describe the range of pages/blocks).
B3. Formula
x = PRP_inv(y_obs, seed)
ainv = inverse_mod_2_64(a) // a is odd
n = (x - b) * ainv (mod 2^64)
B4. Time
O(1): one PRP inversion + one modular inversion (pre-prepared) + several 64-bit operations → microseconds.
---
MODULE C. REPRODUCTION OF THE SERIES
C1. Input
seed, a, b
start_n, count (range for generation)
C2. Output
Stream of blocks y_n in the specified range (packed 64-bit), or unpacked digits {1..4} (optional).
Support for streaming output to file in the format of 2 bits/digit.
C3. Algorithm
x = a*start_n + b
for i in 0..count-1:
y = PRP_seed(x)
output(y)
x += a
(Unpacking 8 digits from 64 bits — simple extraction of 2-bit fields +1.)
---
Performance requirements
Selection (W=64, |seed_candidates|≤4096): < 100 ms on a regular laptop.
Offset: ≈ microseconds.
Generation of 25 billion digits (with 2-bit packaging, 4 streams): ~2–6 minutes on Dell Latitude 5400 (benchmark).
---
Technical requirements for implementation
Language: C++17/20, compilation with -O3 -march=native.
Light PRP (inverted): 3–4 rounds of Feistel with 4×4 S-box, without heavy dependencies.
Modular inversion of a in mod 2⁶⁴ (Newton/Hensel).
Multithreading: OpenMP or std::thread (optional).
Output: buffered, in blocks of 8–32 MB; format—packed 2 bits/digit.
Code with comments, separate modules: prp.h/.cpp, recover.h/.cpp, regen.h/.cpp, pack.h/.cpp, cli.cpp.
---
CLI/API (minimum)
recover --window in.bin --seeds seeds.txt --n0 0 --out params.json
offset --block y.bin --params params.json --out n.txt
regen --params params.json --start 0 --count 100000000 --out stream.bin --packed
params.json:
{ "seed": 1234, "a": "0x1d3f5b7b9d", "b": "0xcafebabe12345678" }
---
Acceptance tests
1. Synthetic: generate a reference (known seed,a,b), cut 64 blocks, run recover → expect an exact match of seed,a,b.
2. Offset: for the first block from the reference — offset should equal its index.
3. Regen: with recovered parameters generate N blocks and byte-by-byte compare with the reference.
4. Perf: measure time recover (<100 ms) and speed regen (not worse than the specified threshold).
---
Additionally (options)
AVX2 vectorization (SIMD) for PRP.
Packager/unpackager {1..4}↔︎2 bits with streaming buffers.
Performance logs (--bench).
Library API (C-style/C++ class) for embedding.
Here is the link to the correspondence where you can read or ask questions
https://chatgpt.com/share/68b0912d-a1b0-8012-af8f-eb6049798075
Budget: 100 USD Deadline: 3 days
Good day.
I have over 20 years of experience in commercial projects. Interesting task, I am ready to complete it.
Budget: 100 USD Deadline: 1 day
Good afternoon, I'm curious, I can try to run all of this through my LLM and look at the result. If you're interested, write to me in a private message.
Budget: 99 USD Deadline: 1 day
Hello!
I am ready to complete your task! More details in private messages.
Budget: 2500 USD Deadline: 10 days
Hello Roman
I’ve reviewed your spec and can deliver both Selection (Recovery) and Reproduction modules exactly as described (mod
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∣seeds∣≤4096,W≤64 on a laptop.
Kindly inbox with answers to the following questions:
-Will you provide your PRP_seed / PRP_inv or should I ship mine (documented & tested)?
-Expected seed_candidates size upper bound? (Default ≤4096)
-Target OS/CPU (Linux vs Windows, AVX2 available?)
-Output file size/partitioning constraints for 25B digits? (packed ≈ 6.25 GB)
-Any requirement for portable bit-exactness across compilers/architectures?
Budget: 100 USD Deadline: 1 day
Good day!
I have experience in C++17/20, optimization (-O3, AVX2), multithreading, and modular arithmetic. I implement PRP (Feistel), fast selection of seed/a/b without brute force, recovery, and generation of 25 billion elements with bit packing.
I guarantee speed and 100% compliance with the technical specifications.
Budget $100 okay, ready to start now.
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