Int generateRandomPrivateKey(Int minKey, Int maxKey, Xoshiro256plus &rng) {
    // Validate inputs
    if (intGreater(minKey, maxKey)) {
        throw std::invalid_argument("minKey must be <= maxKey");
    }

    // Calculate range = maxKey - minKey + 1 (inclusive)
    Int rangeSize;
    rangeSize.Set(&maxKey);
    rangeSize.Sub(&minKey);
    Int one;
    one.SetBase16("1");
    rangeSize.Add(&one);  // rangeSize = maxKey - minKey + 1

    if (rangeSize.IsZero()) {
        return minKey;  // Edge case: minKey == maxKey
    }

    // (4x 64-bit numbers at once)
    __m256i rand_vec;
    {
        uint64_t rand_vals[4] = {
            rng.next(),
            rng.next(),
            rng.next(),
            rng.next()
        };
        rand_vec = _mm256_loadu_si256((__m256i*)rand_vals);
    }

    // Convert to Int (using the first random number)
    Int randomPrivateKey;
    randomPrivateKey.SetInt32(0);

    // Extract the first 64-bit random value
    uint64_t rand_val = _mm256_extract_epi64(rand_vec, 0);

    // Split into 64-bit chunks for Int
    for (int i = 0; i < NB64BLOCK; i++) {
        randomPrivateKey.ShiftL(64);
        randomPrivateKey.Add(rand_val);
        rand_val = rng.next();  // Get next random number if needed
    }

    // Ensure within range: randomPrivateKey % rangeSize + minKey
    randomPrivateKey.Mod(&rangeSize);
    randomPrivateKey.Add(&minKey);

    return randomPrivateKey;
}