Every time a block is broken in Minecraft versions Beta 1.8 through 1.12.2, the precise coordinates of the dropped item can reveal another player's location.
"Randar" is an exploit for Minecraft which uses LLL lattice reduction to crack the internal state of an incorrectly reused java.util.Random in the Minecraft server, then works backwards from that to locate other players currently loaded into the world.
Click here to learn about Randar in the form of a YouTube video instead.
Watch the timelapse:
timelapse_bw_trimmed_to_10mb_for_readme.mp4
See more timelapses here (as files) or here (as YouTube).
The goal is to determine the in-game locations (i.e. coordinates) of the other players in the world, no matter how far away they are. We're playing on 2b2t, which is the oldest and most famous "anarchy" Minecraft server (which means no rules, i.e. players aren't banned for any reason). Doing stuff like this is kind of "the point" on this server. On this server, the only thing keeping your stuff safe is that the map is huge (3.6 quadrillion square tiles) and no one else knows where you are. So it's a huge deal (a game-breaking deal) to have a coordinate exploit. (speaking of, before Randar we also had another coord exploit on 2b2t, Nocom, from 2018 to 2021; see that writeup here, HackerNews thread, YT)
The mistake in Minecraft's code is present from versions Beta 1.8 (released 2011) through 1.12.2 (released 2017, but 2b2t stayed on this version until August 14, 2023). The mistake is that various instances of the random number generator, java.util.Random, are reused sloppily in various parts of the code (and they're insecure to begin with). Specifically, there's reuse of RNG between generating terrain and in game actions such as mining blocks.
The exploit summarized:
- Some player on the server (our victim) walks around, causing a chunk (a 16x16 blocks section of the map, stretching to world height) to be loaded into memory server-side. This happens normally all the time.
- The server checks if certain structures are being generated in that chunk, and the last one to be checked is the Woodland Mansion. Due to sloppy code in Minecraft, the global
World.randhas its seed reset to a function of the chunk coordinates, in order to check where a nearby Woodland Mansion should be (and whether it's this chunk in particular). - One of our bot players, also on 2b2t but at an unrelated location, mines a block very soon after. The dropped item appears at a "random" coordinate within the mined block, determined by three consecutive
World.rand.nextFloat()calls to pick the X Y and Z coordinates between 0 and 1. The bot records the timestamp and the precise X Y Z values. - By using lattice reduction, we can determine the exact internal state of
World.randthat caused those three floats. Broadly speaking (more detail will come later), observing one output of the RNG could imply any one of about 16 million possible internal states of the RNG. However, we have sampled the output of the RNG not just once but three times in a row (the X, Y, and Z coordinates of the dropped item), and we know how the internal state is updated between each call (a simple multiply, add, then mod); therefore we can use lattice methods to essentially instantly narrow it down to the only possibility. - We step the RNG state backwards in time until we find one that could have been caused by a Woodland Mansion check. Again broadly speaking, the internal state of
java.util.Randomcan be stepped backwards just as easily as forwards, and by stepping backwards we can find it in just a few thousand steps (even on busy servers like 2b2t with many players and therefore heavy usage of RNG), which identifies the most recent time that the RNG's internal state was reset, and therefore the location of the most recent chunk that was loaded on the server. - A heatmap is built up over time from that database, and we pay some of the hotspots a visit in game and maybe steal their stuff or generally just cause chaos. To find a specific person, we can associate login times to hits, as logging in causes a lot of chunks to load immediately.
Even if you play on a server that has updated to a newer version of Minecraft, or has otherwise patched RNG manipulation, your coordinates are still at risk from Randar due to the ability to exploit RNG data retroactively. Some Minecraft players use mods like ReplayMod that log packets, and they might still have those log files sitting around. If anyone was using such a mod while you were at your base, they may have (unknowingly) recorded RNG data that could reveal your location, because breaking blocks is an extremely common action that's likely to have happened in such recordings, and every such block break reveals the server's RNG state and therefore the location of the most recently loaded chunk. This means Randar is a pretty big deal: due to this risk of exploiting retroactively, on every Minecraft server, every location that was active in versions Beta 1.8 through 1.12.2 should be considered compromised, even if the server has long since updated past 1.12.2 or patched RNG manipulation.
If you want to use the Randar exploit yourself, go here where rebane2001 has created a website where you can drag in your ReplayMod files from 1.12.2 and see the coordinates of other players. It runs client-side so your recordings will not leave your browser. Here's a video of what that website looks like in action, and you can run the example ReplayMod file from that video by downloading it here.
Randar was discovered by n0pf0x (pcm1k). This writeup was written by leijurv, with some additional commentary at the end written by n0pf0x. Exploiters were 0x22, Babbaj, TheLampGod, leijurv, Negative_Entropy and rebane2001. See TheLampGod's video here. See HermeticLock's 100% humorous 0% factual video here.
Table of contents: click here to learn about the exploitable code in more detail, here to learn about how lattice reduction was used, here to see how we protected our own stashes from Randar, here if you just want to see the complete exploit code, here if you run a server that's still on a version between Beta 1.8 and 1.12.2 and you want to patch Randar, or here for details on what n0pf0x did differently than us.
Diagram of the mistake (as PDF):
Diagram of the exploit (as PDF):
Diagram of a worked example of the exploit (as PDF):
Minecraft relies on random numbers throughout the game. Most of them we expect to be actually random, such as randomness used for mob spawning and weather, but some of them we expect to be predictable, for example we expect the same world seed at the same location to generate the same terrain. In 2011, when Notch first added structures to the game during Beta 1.8, he accidentally reused an RNG that's supposed to be unpredictable in order to place Villages in the world. Ever since then, until 1.13, this sloppy code has caused world generation to influence nearly all other supposedly random events in the game. It took until around May 2018, for Earthcomputer and friends to discover this mistake, realizing that chunk loads affect the game's RNG in an observable way, see this explanation. However, they did not realize, or just never revealed publicly, that you can also do this backwards, determining the most recent loaded chunk from observing the RNG. That discovery, Randar, was made by n0pf0x (aka pcm1k) on October 7, 2022. He posted a short, encrypted description of the exploit on Pastebin about two weeks after, to prove that he discovered it then. He used the exploit mostly on 9b9t, and only a relatively small amount on 2b2t and other servers. On 2b2t, n0p located and explored various locations, eventually coming to a Gringotts stash location. He was spotted by rebane2001, and initially silent about how he found the location. However, about a month later, he began a conversation with the SpawnMasons about it. n0p revealed he had used a powerful coordinate exploit and decided to share an explanation with us in April 2023, because the masons have past experience taking advantage of 2b2t exploits at larger scale, so it would be fun to see that happen again, and n0p was getting slightly bored with it anyway. We accepted and began recording item drop coordinates on several accounts that were already mining stone/cobblestone 24/7 for an unrelated project (so, there was no change in behavior). We reused the headless Minecraft system from nocom and added a Postgres database to record the measurements. As discussed later in this readme, we went through several iterations of software to crack the RNG measurements, eventually settling on an async Cuda batch job. As cracked measurements were added to the database, we also updated an analytics table with heatmap information that counted hits at each coordinate at intervals of all time, daily, and hourly. This allowed a simple Plotly Dash UI to select heatmap data from specific time ranges and granularities for display in a browser, and it let us remove all the Elytra stashhunting chunk load spam by only considering coordinates that were loaded in more than a few distinct hours. We added a simple shared annotation system to keep track of what we found at each hotspot on the map. Again reusing from Nocom, we have Baritone bots that automate the entire process of stealing item stashes and sorting the results, completely AFK. Many masons helped with this part, without knowing the exploit, using accounts such as munmap and 1248_test_user. All Gringotts stashes put together eventually grew to 1.3 billion items, of which about half is attributable to Nocom and half to Randar.
The full history is explained in the FitMC video.
Minecraft's map is procedurally generated and essentially deterministic based on the initial seed of the world. As players explore the map, new areas are generated on-demand as players get near. Since all the generation is meant to be repeatable (deterministic), it's perfectly reasonable for them to have used java.util.Random in a lot of places. They want it to be predictable. This is why java.util.Random is used, since it's a PRNG (not really a RNG). The P technically means "pseudo" but think of it as "predictable". Predictable RNG. It generates numbers that seem random, but they're actually repeatable given the same starting seed.
Minecraft has various structures that are generated in the world, such as villages, ocean monuments, strongholds, etc. These are part of the procedural generation, so they're also placed and generated deterministically.
There's only a dozen lines of Minecraft code needed to understand this, and I've simplified and commented it heavily:
// (chunkX,chunkZ) is being loaded, and this function checks if it should generate a Woodland Mansion
protected boolean canSpawnStructureAtCoords(int chunkX, int chunkZ) {
// divide by 80, rounding down, to determine which "Woodland region" (my made up term) we're considering
int woodlandRegionX = Math.floorDiv(chunkX, 80);
int woodlandRegionZ = Math.floorDiv(chunkZ, 80);
// seed the random number generator deterministically in a way that's unique to this Woodland region
Random random = this.world.setRandomSeed(woodlandRegionX, woodlandRegionZ, 10387319);
// pick which chunk within this region will get the Woodland Mansion
int woodlandChunkX = woodlandRegionX * 80 + (random.nextInt(60) + random.nextInt(60)) / 2;
int woodlandChunkZ = woodlandRegionZ * 80 + (random.nextInt(60) + random.nextInt(60)) / 2;
// but is it *this* chunk, that we're loading right now?
if (chunkX == woodlandChunkX && chunkZ == woodlandChunkZ) {
// and, is this chunk in a biome that allows Woodland Mansions? (e.g. roofed forest)
if (this.world.getBiomeProvider().areBiomesViable(chunkX * 16 + 8, chunkZ * 16 + 8, 32, ALLOWED_BIOMES)) {
return true;
}
}
return false;
}
// and here's what it calls in World.java:
public Random setRandomSeed(int seedX, int seedY, int seedZ) {
this.rand.setSeed(seedX * 341873128712L + seedY * 132897987541L + seedZ + this.getWorldInfo().getSeed());
return this.rand; // this.getWorldInfo().getSeed() is the overall seed of the entire map, which has been cracked long ago for 2b2t (it's -4172144997902289642)
}The above is commented and slightly modified for clarity, but it's functionally accurate to the real code.
So the idea is to decide where the Woodland Mansion should go in this Woodland region (which is 80 by 80 chunks), check if that place is right here, and if so, generate a Woodland Mansion starting right here.
This code might look a little silly, you might be thinking "it's absurd to do all these checks on every chunk, just pick where Woodland Mansions should go once per region and be done with it". The reason is that Minecraft chunks are generated independently of each other, and in unknown order, yet we still want to generate a deterministic world from a given seed. We don't know in what order the player is going to walk around the world, and it's nice to be able to generate any chunk on-demand in a stateless manner. It's a good game experience. Thus, weird-looking code like this.
Anyway, that code gets called on every chunk load, for every chunk in a large square around the one being loaded. It's a bit complicated to explain why so I'll mostly skip it (the basic idea is that these structures are (much) larger than one chunk in size, so we need to check for a structure origin in many nearby chunks in order to generate this current one correctly).
Note that this only affects the Overworld. The Nether is safe, as all of its structure generation has always used safe RNG. Loading chunks in The End is affected due to end cities, but only on their initial generation, not every subsequent time they're loaded, thus The End is relatively safe because each chunk at your base only affects the RNG once ever when you first load it. However, this is not totally foolproof, as players commonly generate new chunks each time while travelling to their base, and occasionally generate new chunks while already at their base.
The problem is that it modifies the seed of the global World.rand. This is just lazy coding. All they're doing is calling nextInt four times to pick the X and Z coordinate. They could have replaced Random random = this.world.setRandomSeed(... with Random random = new Random(the same stuff) (in other words, make a new Random here rather than messing with the existing one that's used by everything else???).
Crucially, the setRandomSeed is called in order to check where the Woodland Mansion should go. It happens no matter what, on every chunk load, everywhere. You don't have to be standing in/near the Woodland Mansion or anything like that.
Well, turns out World.rand is used in literally hundreds of places, and many of those places can be easily observed by playing the game normally. For example, when you mine a block:
/**
* Spawns the given ItemStack as an EntityItem into the World at the given position
*/
public static void spawnAsEntity(World world, BlockPos pos, ItemStack stack) {
double xWithinBlock = world.rand.nextFloat() * 0.5F + 0.25D;
double yWithinBlock = world.rand.nextFloat() * 0.5F + 0.25D;
double zWithinBlock = world.rand.nextFloat() * 0.5F + 0.25D;
EntityItem entityitem = new EntityItem(world, pos.getX() + xWithinBlock, pos.getY() + yWithinBlock, pos.getZ() + zWithinBlock, stack);
world.spawnEntity(entityitem);
}Again, slightly modified, but functionally accurate for the stuff we're talking about.
The idea here is that in Minecraft when you mine a block, it drops an item. The item is dropped at a random position within the block. For example, if the block was at (10, 20, 30), the item will appear somewhere between (10.25, 20.25, 30.25) and (10.75, 20.75, 30.75).
And the exact location of that item is chosen by calling world.rand.nextFloat() three times in a row, for the X, the Y, and the Z.
That's all the Minecraft code needed!
Now, I said that we can do something with these nextFloat calls. First, let's see if we can "work backward" to see what the nextFloat calls are. It's pretty lucky, but we actually can. Note in the above code: the random float is multiplied by 0.5, then added to 0.25. The idea is to move from a random number between 0 and 1 to a random number between 0.25 and 0.75. You might be worried, because if you were to divide an integer by two, you'd lose a bit of information since the result is rounded down. Thankfully, multiplying a float by 0.5 is totally reversible, since it just decrements the exponent while leaving the mantissa untouched. Then, the float is casted to a double, which has way more precision. 0.25 is added, then the block coordinate is added. Then, it's sent to the client over the network in full precision. The upshot: this whole process is reversible so we can get the exact three floats that World.rand.nextFloat() produced.
How does java.util.Random generate floats? Well actually it's quite simple. It generates an integer between 0 and 2^24, then divides it by 2^24 (resulting in a number between 0 and 1).
How does it get that random integer? Also pretty simple! It's a linear congruential generator (LCG). That means that the next seed is the previous seed times something, plus something else, modulo something else.
public float nextFloat() {
this.seed = (this.seed * multiplier + addend) % modulus; // update the seed
int randomInteger = (int) (this.seed >> 24); // take the top 24 bits of the seed
return randomInteger / ((float) (1 << 24)); // divide it by 2^24 to get a number between 0 and 1
}In this case, the multiplier is 25214903917, the addend is 11, and the modulus is 2^48.
With the float that came out of this, we can multiply it by 2^24 to get back the randomInteger, and therefore get the "top half" (the most significant 24 bits) of the 48 bit seed.
In short, from our measurement, we learn that the seed is between measuredRandomInteger * 2^24 and (measuredRandomInteger + 1) * 2^24.
And we can do this three times in a row, for the X, the Y, and the Z.
And we know that between the X and the Y, and between the Y and the Z, the seed was updated according to newSeed = (oldSeed * 25214903917 + 11) mod 2^48
I must mention that one valid option is a for-loop that tries all 2^24 possible lower bits. For the programmers reading this, I hope this makes clear what the problem is:
for (long seed = firstMeasurement << 24; seed < (firstMeasurement + 1) << 24; seed++) {
// all these seeds will match the first measurement
if (nextSeed(seed) >> 24 == secondMeasurement && nextSeed(nextSeed(seed)) >> 24 == thirdMeasurement) {
// if nextSeed(seed) matches secondMeasurement, and nextSeed(nextSeed(seed)) matches thirdMeasurement
// then we found a seed that matches all three measurements! yay!
return seed;
}
}This would work, and does work, but it's not that fast and not that fun. So we use lattices instead!
However, I feel like I have to go a bit out of order. The lattice reduction part does come in right here but it's really complicated and I bet it would have low reader retention and I don't want to lose you. So I'll just give you that for-loop solution (which DOES work), and continue to the next step of the exploit. The explanation of the lattice reduction method will come right after :)
What do we do with this seed once we have it?
First, note that we can step the LCG backwards. Obviously, adding eleven is reversible, but is multiplying by that big number reversible? Our multiplier 25214903917 is an odd number, meaning it isn't divisible by two, and therefore it doesn't share any factors with our modulus 2^48 (since 2^48 is literally just a bunch of twos). Since it's relatively prime to the modulus, we can invert it, which means to find another number x that satisfies x * 25214903917 - 1 is divisible by 2^48. Or in other words, 25214903917 * x mod 2^48 = 1. That number is 246154705703781. This helps invert the multiplication because if we have, for example, secret * 25214903917 and we want to figure out secret, we can just compute secret * 25214903917 * 246154705703781 mod 2^48 = secret * 1 mod 2^48 = secret.
Ok, so we can step the internal seed of java.util.Random both forwards and backwards. Forwards is newSeed = (oldSeed * 25214903917 + 11) mod 2^48 and backwards is oldSeed = ((newSeed - 11) * 246154705703781) mod 2^48. And this works because those numbers 25214903917 and 246154705703781, when multiplied together, come out to 1 when you take it mod 2^48.
Now, as we step backwards, we would like to check at each step whether this seed could mean that a Woodland Mansion check was recently performed somewhere in the world (the whole point of the exploit). How do we do that?
The Minecraft world ranges from -30 million to +30 million blocks. Each "Woodland region" (an area of the world where a single Woodland Mansion is placed at random, as per the code shown previously) is 80 by 80 chunks, which is 1280 by 1280 blocks. This is 23437.5 Woodland regions, but for all of our code we just rounded up to 23440 because it's a round number and even though your player can't travel beyond 30 million, you load chunks beyond it just by standing near it, and we just didn't want to have to worry about all that.
So, -23440 to +23440 on both X and Z axes. That's (23440*2+1)^2 (aka 2197828161) possible Woodland regions, each of which generates a unique "mansion seed" (defined as a seed that reveals that someone just loaded a chunk at a certain Woodland region). We need to be able to check if something is a mansion seed. Could we iterate over all 2.2 billion mansion seeds to check each one? Would be too slow. Could make a HashSet<Long> with 2.2 billion entries? Would take up too much RAM even using chronicle map like we did in nocom, and even in C++ using abseil-cpp it used like 50gb ram. And that's not to mention the other part: we actually want to learn where they are in the world (that's the whole point). So it's not good enough to learn this is a mansion seed, we also want to (efficiently) learn which Woodland region caused it.
Recall the function that goes from Woodland Region to mansion seed (note: I've now combined some constants since the code above for simplicity, this equation is now specialized to 2b2t's seed):
seed = x * 341873128712 + z * 132897987541 - 4172144997891902323 mod 2^48
(the -4172144997891902323 number comes from the -4172144997902289642 + 10387319, which is the 2b2t world seed + the magic value used for seeding the Woodland region (as shown earlier). For any other world you would just put your own seed instead into this equation.)
Not much we can do with the x coordinate, since it's being multiplied by an even number. But what's that coefficient on the z coordinate? It looks like an odd number!!! Let's use the same trick as before to invert it again, and we get 211541297333629.
Let's imagine we have a given seed. What if we could just iterate through all possible X coordinates from -23440 to +23440, and for each one, compute what the Woodland region's Z coordinate WOULD be, IF it had this mansion seed. In other words, the above equation gives us seed if we know x and z, but can we make an equation that gives us z if we know seed and x? Answer: yes. We just rearrange the above equation, and use the fact that the coefficient of Z is invertible mod 2^48 since it's an odd number.
The equation is:
z = (seed + 4172144997891902323 - x * 341873128712) * 211541297333629 mod 2^48
So this is a pretty good solution because instead of two nested loops (one for X and one for Z) that do a total of 2.2 billion iterations, we can have a single for-loop for X that just does 46,881 iterations. Here it is in Java:
private static WoodlandRegionCoord woodlandValid(long internalSeed) {
long seed = 25214903917 ^ internalSeed; // java.util.Random XORs in the multiplier while doing setSeed, so XOR that back out to go from a "this.seed" to what the input to setSeed() would be
for (int x = -23440; x <= 23440; x++) {
long z = ((seed + 4172144997891902323L - x * 341873128712L) * 211541297333629L) << 16 >> 16;
if (z >= -23440 && z <= 23440) {
return new WoodlandRegionCoord(x, z);
}
}
return null;
}(note: the weird << 16 >> 16 is doing mod 2^48, but we actually want to do it using signed types so that we still get the correct answer when z is between -23440 and 0, this is a way to sign-extend the 48-bit number to 64 bits, filling the upper 16 bits with the correct sign bit for two's complement)
So this does work and it's reasonably fast.... for a single seed. But remember that we're stepping back the RNG for potentially thousands of steps, and running this check at each step until we find a match. At the time, we were using a shitty DigitalOcean droplet on their lowest tier, and this was actually lagging everything out and couldn't keep up with real time (bots mining many blocks per second, each block taking thousands of rng steps to crack, and each rng step taking 23440*2+1 operations to check, multiply those together and you get well into the hundreds of millions of operations per second, so you see why that had trouble on a crappy VPS, especially when that VPS is also trying to run multiple headless instances of Minecraft).
Anyway so we switched to a lookup table approach and rewrote it in Cuda to run on my desktop as a batch job every few minutes. It can do literally millions per second because each of the thousands of cuda cores can work on their own seed in parallel. Here's the idea: the lookup table's key is the lower 32 bits of the mansion seed, and the value is the X coordinate of the Woodland region. This lookup table works with no collisions because each mansion seed has a unique lower 32 bits, somehow. I don't understand why that's true, it's fascinating. You'd think it wouldn't work. But I think the coefficients 341873128712 and 132897987541 may have been specially chosen to make this work? Like, if you have 2.2 billion marbles, and 4.3 billion buckets, and you independently put each marble in a random bucket, what are the odds that each marble gets its own bucket? Essentially zero. Nearing the end, each new marble has a more than 50% chance of hitting a bucket that's already filled. Yet, clearly, these are not independently random, so somehow it works. Unironically if you're reading this and understand how this works or why those two specific coefficients make this work, please let me know. Anyway, it works. The lookup table has 2^32 entries, and each entry is 2 bytes (since it's just a number between -23440 and +23440), so this needs about 9 gigabytes of VRAM on your GPU.
The woodland check function now looks like (again, this is the actual code but simplified, all helpers and constants inlined etc):
__global__ void computeSteps(const int16_t* mansionTable, const int64_t* seedsArr, Result* resultArr, size_t numData) {
auto tid = blockIdx.x * blockDim.x + threadIdx.x;
[[unlikely]] if (tid >= numData) {
return;
}
auto seed = seedsArr[tid];
int steps = 0;
while (true) {
auto externalSeed = seed ^ 25214903917;
const auto x = mansionTable[externalSeed & ((1LL << 32) - 1)];
const auto z = ((externalSeed + 4172144997891902323LL - (int64_t) x * 341873128712LL) * 211541297333629LL) << 16 >> 16;
if (z >= -23440 & z <= 23440) {
resultArr[tid] = {.startSeed = seedsArr[tid], .x = (int16_t) x, .z = (int16_t) z, .steps = steps};
return;
}
seed = ((seed - 0xBLL) * 0xdfe05bcb1365LL) & ((1LL << 48) - 1); // prevSeed(seed)
steps++;
}
}
// and that mansionTable was generated like this
// note: mansionTable must be calloc'd before this function because not every entry will be written to, and an x value outside -23440 to 23440 bounds could create a false positive later on while using the table
__global__ void writeToSeedTable(int16_t* mansionTable) {
auto tid = blockIdx.x * blockDim.x + threadIdx.x;
if (tid >= (23440 * 2 + 1) * (23440 * 2 + 1)) return;
auto x = tid / (23440 * 2 + 1) - 23440;
auto z = tid % (23440 * 2 + 1) - 23440;
auto seed = ((int64_t) x * 341873128712LL + (int64_t) z * 132897987541LL - 4172144997891902323LL) & ((1LL << 48) - 1);
mansionTable[seed & ((1LL << 32) - 1)] = (int16_t) x;
}This works great in giant batches and can crack on the order of ten million seeds per second on a 3090. Turns out to not be too big of a deal when some of the threads in a warp terminate early, and we couldn't really make it any faster than this. (the reason is that we fundamentally can't know beforehand which seeds will take more/less steps).
Well that's about it. Given the seed, that's how we get the Woodland region in the world where the most recent chunk load happened. In other words, we just learned that the most recent time that someone walked around on 2b2t and loaded a new area of the world, was somewhere within this 1280 by 1280 block Woodland region that we just identified. (that's precise enough that locating them takes just a few minutes of searching)
In practice, how many RNG steps were needed? On the low end, reliable measurements start at 4 RNG steps, everything below that is measurement error / random noise, which we know because the Woodland Mansion code immediately calls rand.nextInt four times before it's possible for us to measure it. On average, there are about 128,000 steps between each Woodland seed, but in practice, the vast majority of the time on 2b2t, we found a Woodland seed within a few dozen steps. This is due to the particulars of what happens in what order in a Minecraft tick. Our measurement technically happens at the very beginning of the tick, since that's where the packets for breaking blocks are processed. Generally, a chunk has been loaded in the very recent history during the previous tick. However, sometimes, an event can cause a bunch of RNG steps in between. We believe that this event is explosions, such as someone blowing up an end crystal by punching it, or possibly wither skulls. End crystal explosions would also occur during packet processing from the player punch packet, and the number of RNG steps also lines up at 1354 steps (1352 from calculating the block damage in a cuboid
And zoomed in to the first 2000 steps, here you can see smaller spikes that are presumably caused by other intermittent in-game events that use about forty RNG steps each time:
Here's a fun thought: What if we looked at what fraction of our measurements indicated a crystal had blown up since the most recent chunk load? It would be noisy, and could be confused by other explosions, but it should approximate a metric of how much crystal PvP is going on in the overworld.
select avg(case when steps_back > 1357 then 1 else 0 end) as crystal_frac, received_at / 86400000::bigint as day from rng_seeds where steps_back < 5000 group by day order by day
One more thing: is it possible for this whole process to misidentify the most recently loaded chunk? Sure, it'll be wrong if you have the wrong server-side world seed, but let's assume that everything is working properly, and let's assume that it's a fairly busy server that has chunk loads practically every single tick. Is Randar guaranteed to produce the correct chunk? Well, as we just covered, the RNG can take thousands of steps between when the chunk is loaded and when we measure it, even in the best possible case of measuring the next tick. What if the RNG stepped into a different Woodland region? Then, an exploiter who steps backwards and simply returns the first match would hit that decoy, and get a false positive. It could be difficult to detect such a scenario too, even if you knew it was possible. How would you tell which was the real hit? Perhaps you could have heuristics such as "is it nearby or equivalent to a recent hit", but there is no way to know with total certainty.
Now, recall that it is impossible to measure the RNG with less than 4 steps of lag, and if you're using a Fortune enchanted pickaxe to mine (which is plausible because of how duped Eff V picks on 2b2t are basically all fortune or silk), your minimum will be 5 because of the fortune item drop check. Recall this code:
// seed the random number generator deterministically in a way that's unique to this Woodland region
Random random = this.world.setRandomSeed(woodlandRegionX, woodlandRegionZ, 10387319);
// pick which chunk within this region will get the Woodland Mansion
int woodlandChunkX = woodlandRegionX * 80 + (random.nextInt(60) + random.nextInt(60)) / 2;
int woodlandChunkZ = woodlandRegionZ * 80 + (random.nextInt(60) + random.nextInt(60)) / 2;In order to pick the location of the Woodland Mansion structure, random.nextInt is called four times, guaranteed, before anything else can observe any randomness.
So, this raises the question. For a given server's world seed (2b2t's in our case), could we compute how big the gaps between Woodland regions are? There are about 2 billion Woodland regions, and 280 trillion possible states for java.util.Random. So, about one out of every ~130,000 RNG seeds is a woodland seed. In other words, the gap between Woodland regions is ~130,000 steps on average. But that's just on average, this is a random distribution and there totally could be outliers! We ran a scan through the entire space to get a complete picture of the distribution, and to my surprise, there are tens of thousands of Woodland regions that are only one step apart from each other! If the distribution was truly independently random, the odds of the next seed also being a Woodland region would be simply one out of ~130,000, which is the rate overall. I suspected there might be some, but I didn't ever run the math for how many to expect, so this was a fascinating surprise.
It turns out that one out of every ~20k Woodland regions on 2b2t has this special hiding property, in that there is another Woodland region within the next four RNG steps! That means that if someone was running the Randar exploit and assuming that the most recent Woodland hit is genuine (which is reasonable! and we did ourselves!), they would never observe this region correctly, and every time they would think that the hit was at that second decoy Woodland region, no matter how good their heuristics are.
On 2b2t while Randar was active, we wanted at least some level of safety, so we decided to build several stashes at regions such as this, carefully built so that the entire structure was compact enough that your render distance would never cause a chunk outside of this Woodland region to be loaded (because, such a chunk load would show up unprotected to a Randar exploiter!). We also stationed an AFK account and built a small base at the decoy location, so that if someone else discovered Randar, they'd see that decoy location light up brightly due to our stash activities, and they'd travel there and see a tiny base and no stash, and they'd maybe grief it but we wouldn't care because that base doesn't matter because the stash itself was protected.
According to our own Randar logs, these stashes remained "clean" the entire time, in that we never accidentally loaded an adjacent Woodland region. As far as we know no one else used Randar, but if they had, this would have given our stashes an extra layer of protection.
(obviously we have moved these stashes by now, otherwise this information would cause them to stick out like a sore thumb if anyone decided to run Randar against any ReplayMod recording from 2b2t from mid 2023)
Now back to the fun part, lattices!
We'll reframe the problem as finding a point in a 3d lattice. To reiterate, we have made three consecutive measurements of the most significant 24 bits of the internal seed of java.util.Random. Additionally, we know exactly how the seed was updated between our measurements (it's just nextSeed(seed) = (seed * 25214903917 + 11) mod 2^48). We want to determine the entire 48-bit seed (aka: figure out what the lower 24 bits are).
In more formal terms, seed is a secret number between 0 and 2^48 that we want to figure out. We know that seed is between m1*2^24 and (m1+1)*2^24, nextSeed(seed) is between m2*2^24 and (m2+1)*2^24, and nextSeed(nextSeed(seed)) is between m3*2^24 and (m3+1)*2^24 (where m1, m2, and m3 are shorthand for our three measurements).
This can be done faster than brute force because the nextSeed function is not really all that random.
Let's rewrite nextSeed(seed) = (25214903917*seed+11) mod 2^48 as nextSeed(seed) = (seed * a + b) mod c, just so that I'm not spamming long numbers everywhere.
Let's visualize the problem with these kind of linear congruential generators (any generator of that ^ form, seed*a+b mod c).
What if we were to plot seed on the X axis, and nextSeed(seed) on the Y axis? It would look something like this to start:
(note: I'm using fake numbers: a=7, b=5, and c=64, so that the plot is readable and has a manageable number of points (less than a trillion))
This should look familiar as a y=mx+b plot (except, it's nextSeed(seed) = a*seed+b). Very clearly not random, very clearly predictable.
Then, it approaches the modulus, and wraps around back to zero each time that happens:
So, you can visually see that this has a predictable structure, although it isn't quite a straight line anymore. This structure is called a lattice.
A lattice is a set of points in space that are all integer multiples of some vectors that form a basis for the lattice. Lattices have the property that you can add together any of its points, and get to another point in the lattice (e.g. if (1,2) and (500, 700) are points in the lattice, then (501, 702) must also be a point in the lattice). These plots are (almost) lattices (you just have to shift all the points by a bit, because lattices technically have to include the (0,0) point, we'll do this later). The intuition for lattices is that they're conceptually a grid, but, squish squashed in some way. If you sorta tilt your head, you can see how you could take a grid of points, squish/tilt them, and get this plot.
In our case, we get three measurements (not just two), so we'll actually be using a 3D plot where the Z axis is nextSeed(nextSeed(seed)) (but the X and Y axes are still the same). Here's what that looks like:
The lattice pattern in 2d as lines is even more apparent in 3d as planes. (aside: this is actually a test for PRNGs, whether or not it makes planes like this, and if so, how far apart they are).
Now, recall that our measurements give us three different bounds for each of seed, nextSeed(seed), and nextSeed(nextSeed(seed)). Visually, our measurements form a cubic constraint in this space. Our overall plot is 2^48 on each side, and our three measurements define a cube of side length 2^24 (recall how our three measurements were imprecise, only narrowing down the seed to a range of 2^24 values, since we only saw the most significant 24 bits of a truly 48 bit seed). Simply put, if you know the X coordinate is in some range, Y is in some range, and Z is in some range, this constraint can be visualized as a cube. Our goal is to recover the original value of this.seed. Crucial point, make sure you understand this: If we can identify a lattice point within that cube, we'll have solved the problem. Our lattice points are of the form (seed, nextSeed(seed), nextSeed(nextSeed(seed))), and our cube represents the constraints we've measured on those three things (the seed, the next seed, and the one after that). If we find an exact lattice point within that cube, it'll mean we've identified a seed that would have produced the measurements that we took (aka: java.util.Random has been successfully cracked). If we could identify such a point, its first coordinate will be the this.seed before the first nextFloat call, which is what we're trying to find with all this.
Here's a visualization of the problem: we have our lattice, and our measurements tell us the coordinates of the cube we need to search in (shown in red), now the problem is efficiently identifying a lattice point within that cube. And still keep in mind that while this GIF may make the problem look easy, this is NOT the real 3d plot, it's just a simplification, the real 3d plot has nearly 300 trillion points.
So, we have a 3d scatter plot of points, with one point for each possible seed. For every integer seed value from 0 to 2^48, we have plotted a point at (seed, nextSeed(seed), nextSeed(nextSeed(seed))). In other words, (seed, seed*a+b mod c, (seed*a+b)*a+b mod c).
This 3d scatter plot looks like a lattice, but if we want to apply helpful mathematical tools from integer linear programing, we need to describe this lattice formally in mathematical terms that can be plugged into those tools. We do this by coming up with basis vectors that define the lattice. First, we've plotted all possible seed values, so let's formalize that by defining what happens as you increment the seed value by 1. That will fill out our lattice nicely starting from 0 and including every value by induction. When you add 1 to the seed, it adds a to the next seed, and a^2 to the one after that (because nextSeed(seed) = seed*a+b). In other words, the plot is defined by a basis vector of (1, a, a^2). You can add this to any lattice point and still be at a valid lattice point. Great, that's one basis vector done! What else defines this lattice? Well, you may notice that I neglected the mod 2^48 (aka mod c). That modulo happens to both the second and third components (because, we have nextSeed(seed) and nextSeed(nextSeed(seed)))). When computing a modulo, keep in mind that it can be expressed as just subtracting c some number of times. Therefore, we'll also treat (0, -c, 0) and (0, 0, -c) as basis vectors. The reason is that as the multiplication goes above 2^48, it "wraps around" back down to zero, which is the exact same as subtracting 2^48 an integer number of times. Note that lattices are infinite by construction, but we'll only need to consider the points that are between 0 and 2^48 on all three axes. Those points between 0 and 2^48 are exactly the points that we want to care about, and they'll match up with our original 3d scatter plot.
Our three basis vectors are (1, a, a^2), (0, c, 0), and (0, 0, c). (peeking back into reality, the actual numbers are (1, 25214903917, 635791379543541942889), (0, 281474976710656, 0), and (0, 0, 281474976710656). Now you can see how that would be nasty and incomprehensible if I'd been using those all along!) (mirroring these vectors around zero doesn't affect anything, so I'll do c instead of -c)
Any point representing (seed, nextSeed(seed), nextSeed(nextSeed(seed))) is represented by some combination of adding and subtracting (1, a, a^2), (0, c, 0), and (0, 0, c). That first vector will be added seed times, the second one will be subtracted however many times the modulo wraps around back to zero on the first nextSeed call, and the third one is the same but for the second nextSeed call.
(note that this technically isn't a lattice yet because it doesn't technically include (0, 0, 0), it starts at (0, nextSeed(0), nextSeed(nextSeed(0))), in other words (0, b, a*b+b). That has to be subtracted from all our points first. I've been glossing over this because it would be confusing to mention in every sentence, and because it's really easy to account for; we'll just shift our measurements later on to subtract that out. Trust me, it's fine.)
We have plotted one point in 3d for every possible internal state of java.util.Random, and recall that our measurements form a cube in that space. We need to find which of the points we plotted is inside that cube.
Given the lattice structure, and a cubic constraint, we want to find any lattice point in that cube. We've successfully converted our problem into a standard mathematical procedure: find a lattice point within a given range. With this reframing, we can use standard integer linear programming tools (LLL basis reduction) to solve it efficiently.
Our lattice is defined by linear combinations of (1, 25214903917, 635791379543541942889), (0, 281474976710656, 0), and (0, 0, 281474976710656). Those are huge and unwieldy numbers! Could we do better? We can! LLL basis reduction can give us three new, smaller, still integer vectors that result in the exact same lattice. A lattice point in the old basis is also a lattice point in the new basis, and vice versa.
This is the weirdest step, so here's a visual (and if this visual is still not enough but you're still curious, go read this explanation (it's the one I used myself to understand this) and/or watch these three videos one two three)
Here's an example from this Wikipedia page. Let's imagine we have our initial vectors v1 and v2, drawn in black in this visual. By adding subtracting any number of v1s and v2s, we create a lattice, which is shown by the blue dots. But, as you can see, the blue dots are pretty densely packed, and v1 and v2 seem like a weird/unintuitive/suboptimal way of describing where the blue dots are. For example, v1 and v2 are very long, and point in nearly the same direction. Lattice reduction on v1 and v2 gives us better basis vectors u1 and u2 (drawn in red). By adding and subtracting any quantity of u1 and u2, we get the exact same set of blue points, or in other words, u1 and u2 generate the exact same lattice as v1 and v2 did. But, these are much better vectors, because they're nearly perpendicular to each other, and they're very short (in this case, as short as can be).
In short, our lattice of (seed, nextSeed(seed), nextSeed(nextSeed(seed))) can be described with those three vectors we came up with, but we can also describe that same lattice in a better and more helpful way with some simpler, shorter, and more perpendicular vectors, and LLL is going to tell us what those vectors are.
Mathematica can do this:
a = 25214903917; b = 11; c = 2^48;
LatticeReduce[{{1, a, a^2}, {0, c, 0}, {0, 0, c}}]
Our new vectors are (1270789291, -2446815537, 2154219555), (-2355713969, 1026597795, 4110294631), and (-3756485696, -2345310016, -2015749696). Note how they're all pretty small now! None are more than ten digits, while our previous basis vectors were bigger. Remember, any combination of these three new vectors will result in a point that also is a combination of our three original vectors. Their lattices are indistinguishable.
Now here's the cool part. We can take our range, the cube that represents our search space, and transform it into a range in this reduced space via a change of basis. If we treat our new basis vectors as the columns of a matrix, then invert that matrix, we have a magic key that transforms points in lattice space, into points in reduced basis space. There are two crucial realizations for why this is helpful: 1. any point with integer coefficients in reduced basis space will become a valid lattice point when converted back into lattice space (since it's a matrix multiplication by the lattice basis vectors, which we can see are integers) 2. the new lattice basis vectors are much smaller and more perpendicular, so the transformed cube (really a polytope now) is very small. If it were larger, we might have to do some complicated iterating through multidimensional space, but in this case, for these specific parameters used in java.util.Random, and given the fact that we get three consecutive samples not just two, this process works so well that we don't even need to transform the entire range of the cube. We can just pick the exact center of our cube (i.e. make a guess of a single point), convert to reduced basis space, and just round to the nearest integer. Recall that we're trying to find any lattice point in our cube, and any point with integer coefficients in reduced basis space represents a valid lattice point. So, if our cube contains any point with integer coefficients we're done, the problem is solved. The lattice basis reduction took the tricky problem of "find a nearby lattice point to this coordinate" and made it as simple as "reexpress the coordinate as a linear combination of the basis vectors, then just round all three coefficients to the nearest integer" (see the "worked example" section later for an example). This can only "go wrong" (produce the wrong answer) if rounding to the nearest integer took us from a point inside the transformed cube to a point outside, but assuming we're operating on good data (aka measurements that truly did come from java.util.Random), there will be an integer point in the transformed cube, so this does work every time (since our transformed cube is tiny). (again, the "worked example" section later on will make this clear and apparent). Anyway this integer point in reduced basis space becomes a valid integer point in lattice space, which solves the problem since we've found a valid lattice point within the cube.
Let's say we have a java.util.Random with 123123123123123 as its internal state. If we did nextFloat three times (exactly like in Minecraft), we would get 0.4374212, 0.4570924, and 0.3316006. We're going to forget about 123123123123123 but try to recover it from just those three floats.
The code of nextFloat, for reference:
public float nextFloat() {
this.seed = (this.seed * multiplier + addend) % modulus; // update the seed
int randomInteger = (int) (this.seed >> 24); // take the top 24 bits of the seed
return randomInteger / ((float) (1 << 24)); // divide it by 2^24 to get a number between 0 and 1
}These three floats, 0.4374212, 0.4570924, and 0.3316006, came internally from these 24-bit integers: 7338710, 7668738, and 5563335 (aka the three floats have those numbers as numerator and 2^24 as denominator). This measures the most significant 24 bits of the internal seeds. In other words, we only learn that the first seed value is between 7338710*2^24 and 7338711*2^24, the second seed is between 7668738*2^24 and 7668739*2^24, and the third is between 5563335*2^24 and 5563336*2^24. The first seed was truly 123123123123123, as we picked, and our first measurement already has narrowed it down to between 123123122831360 (aka 7338710*2^24) and 123123139608576 (aka 7338711*2^24).
To simplify things, we can take the center of our range. The center of this cube is at (7338710*2^24 + 2^23, 7668738*2^24 + 2^23, 5563335*2^24 + 2^23) or in other words (123123131219968, 128660082262016, 93337281363968). For sake of mathematical correctness: we should also subtract (0, b, a*b+b) here as mentioned earlier, to make the reduced basis space start at (0, 0, 0), but that doesn't realllly matter and it happens to actually work without it, but let's just do it to be correct:
So we want a lattice point "somewhere near" (123123131219968, 128660082262005, 93059917420870). Even though that first coordinate (what we really want to find) is totally off, the second two coordinates give us enough information that we'll figure out the original first coordinate just fine! The reason is that in 3d space, the points are far apart so even if all three coordinates are off by millions, considering them all put together will let us end up at the correct answer. (48 bits of entropy, 24*3=72 bits of measurement, it ends up being pretty easy and unambiguous, and LLL basis reduction makes that easiness apparent)
Now, let's convert to lattice basis space. Mathematica code: Inverse[Transpose[LatticeReduce[{{1, a, a^2}, {0, c, 0}, {0, 0, c}}]]] . {123123131219968, 128660082262005, 93059917420870}
This gives: (-10000.99799, 7761.998172, -41027.00033). Wow, that's so close to an integer! That's why this works. The critical realization: in this reduced basis space, the real point is incredibly shockingly close to our approximate measurement, even though it was millions away in lattice space.
Let's round to the nearest integer! (-10001, 7762, -41027). This represents a valid point in lattice space, since all three coefficients are now integers. Now, to find that point's real coordinates in lattice space, we take that times our basis vectors (i.e. -10001 times (12707... plus 7762 times (-23557... plus -41027 times (-37564...). We get (123123123123123, 128660088296759, 93059919934059).
That first coordinate is our original seed 123123123123123! Success! Given the output of three consecutive nextFloat calls, we successfully recovered what the internal state of java.util.Random must have been. (in the real exploit, at this point we would then step this seed backwards until it matched a mansion seed, revealing what Woodland region a player was just walking around in)
Aside: now, what if we used the original basis vectors of (1, a, a^2), (0, c, 0), and (0, 0, c) instead of the LLL reduced ones? (Code: Inverse[Transpose[{{1, a, a^2}, {0, c, 0}, {0, 0, c}}]] . {123123131219968, 128660082262005, 93059917420870}). We would get coefficients of 123123131219968, -11029534347.32617, -278108648828606394735.834469. Well that's useless. The first component is already an integer, because our first basis vector starts with a 1 and the next two both start with a 0. Rounding to the nearest integer would therefore do nothing to help us find the actual original seed. If we did so, we would get Transpose[{{1, a, a^2}, {0, c, 0}, {0, 0, c}}] . {123123131219968, -11029534347, -278108648828606394736} + {0, b, a*b + b} which is 123123131219968, 220470678913035, 46744522843834. So, these are three valid consecutive seeds (the nextSeed of the first is the second, and nextSeed of the second is the third). So it didn't do anything really useful, it just ignored our second and third measurements entirely and make them match our crappy guess for the first measurement (123123131219968). That's why we need to use the good, short, and most importantly nearly orthogonal basis vectors from LLL. With the better basis vectors, all three component axes (our three measurements) are "treated more equally" so to speak, so it naturally tends towards a solution that balances all three components. This simple way focused on getting something that exactly matches first component while entirely ignoring the second two, but that's no good because each individual component is millions off, but, when considered together, there's one obvious nearby lattice point that the better basis vectors find simply by rounding.
Here's that same approach, but simplified and optimized (no need to read this):
public static long crack(int rngMeasurement1, int rngMeasurement2, int rngMeasurement3) {
long cubeCenterX = ((long)rngMeasurement1 << 24) + 8388608L;
long cubeCenterY = ((long)rngMeasurement2 << 24) + 8388597L;
long cubeCenterZ = ((long)rngMeasurement3 << 24) - 277355554490L;
double basisCoeff0 = 9.555378710501827E-11 * cubeCenterX + -2.5481838861196593E-10 * cubeCenterY + 1.184083942007419E-10 * cubeCenterZ;
double basisCoeff1 = -1.2602185961441137E-10 * cubeCenterX + 6.980727107475104E-11 * cubeCenterY + 1.5362999761237006E-10 * cubeCenterZ;
double basisCoeff2 = -1.5485213111787743E-10 * cubeCenterX + -1.2997958265259513E-10 * cubeCenterY + -5.6285642813236336E-11 * cubeCenterZ;
long seed = Math.round(basisCoeff0) * 1270789291L + Math.round(basisCoeff1) * -2355713969L + Math.round(basisCoeff2) * -3756485696L & 281474976710655L;
long next = seed * 25214903917L + 11L & 281474976710655L;
long nextNext = next * 25214903917L + 11L & 281474976710655L;
return (seed >> 24 ^ rngMeasurement1 | next >> 24 ^ rngMeasurement2 | nextNext >> 24 ^ rngMeasurement3) != 0L ? -1L : seed;
}This has some additional sanity checking at the bottom (to make sure it's a real crack and not garbage-in-garbage-out), and I also changed it slightly for this example (the real version steps the seed back by one LCG step as a final step, just because java.util.Random actually steps the seed before returning the float, rather than after).
crack(7338710, 7668738, 5563335) (those are the three measurements from earlier) will return 123123123123123 as expected.
The idea of that code is:
(cubeCenterX, cubeCenterY, cubeCenterZ)are the x,y,z coordinates of the center of the cube in lattice space. Their offsets are 8388608 (aka 2^23) minus the(0, b, a*b+b)offset mentioned earlier.(basisCoeff0, basisCoeff1, basisCoeff2)are the coefficients of the center of the cube in reduced basis space. Those nine random looking multipliers areInverse[Transpose[LatticeReduce[{{1, a, a^2}, {0, c, 0}, {0, 0, c}}]]](in other words, treating the reduced basis vectors like the columns of a matrix, then doing a change of basis onto them by left multiplying by the inverse of that basis matrix)(roundedCoeff0, roundedCoeff1, roundedCoeff2)are those coefficients rounded to the nearest integer.- The
seedis found by multiplying the first component of the three reduced basis vectors by our reduced basis coordinates. We only care about the first component of course, since that's the seed. (seed, next, nextNext)are the seeds that would produce those three measurements, we computenextandnextNextjust to make sure we're right. We could have gottennextandnextNextby computing the second and third components of the vector in the previous step, but it's faster to just do the LCG step directly.- We return -1 if the computation failed (e.g. garbage data), and the actual seed if it succeeded.
Yeah so that's how you get the state of java.util.Random from three consecutive calls to nextFloat(). And that ^ optimized Java code can do it in about ten nanoseconds on my laptop.
Here's a fun thought: if cracking the state of Minecraft's RNG is plainly fairly doable in not too many lines of code, as seen above, could it be implemented in-game? Like, within Minecraft itself, using redstone circuits? The answer is yes, go watch this video which is honestly more impressive than anything we've done here. The guys who made that, Matthew Bolan and Earthcomputer and co., were the ones who actually discovered RNG manipulation and lattice methods as applied to Minecraft (years and years before we did anything with it).
private static long WORLD_SEED = -4172144997902289642L; // change this for a server other than 2b2t
public static void receivedPacket(Packet<?> packet) { // call this for incoming packets
if (packet instanceof SPacketSpawnObject) {
SPacketSpawnObject obj = (SPacketSpawnObject) packet;
if (obj.getType() == 2 && obj.getData() == 1 && obj.getSpeedY() == 1600) {
new Thread(() -> crackItemDropCoordinate(obj.getX(), obj.getY(), obj.getZ())).start();
}
}
}
private static void crackItemDropCoordinate(double dropX, double dropY, double dropZ) {
float spawnX = ((float) (dropX - (int) Math.floor(dropX) - 0.25d)) * 2;
float spawnY = ((float) (dropY - (int) Math.floor(dropY) - 0.25d)) * 2;
float spawnZ = ((float) (dropZ - (int) Math.floor(dropZ) - 0.25d)) * 2;
if (spawnX <= 0 || spawnX >= 1 || spawnY <= 0 || spawnY >= 1 || spawnZ <= 0 || spawnZ >= 1) {
System.out.println("Skipping this item because its coordinates are out of bounds. This probably means that the item only coincidentally looked like an item that was dropped from mining a block. Other ways to drop items (e.g. dropping from a player's inventory) can sometimes cause false positives like this.");
return;
}
int measurement1 = (int) (spawnX * (1 << 24));
int measurement2 = (int) (spawnY * (1 << 24));
int measurement3 = (int) (spawnZ * (1 << 24));
long cubeCenterX = ((long) measurement1 << 24) + 8388608L;
long cubeCenterY = ((long) measurement2 << 24) + 8388597L;
long cubeCenterZ = ((long) measurement3 << 24) - 277355554490L;
double basisCoeff0 = 9.555378710501827E-11 * cubeCenterX + -2.5481838861196593E-10 * cubeCenterY + 1.184083942007419E-10 * cubeCenterZ;
double basisCoeff1 = -1.2602185961441137E-10 * cubeCenterX + 6.980727107475104E-11 * cubeCenterY + 1.5362999761237006E-10 * cubeCenterZ;
double basisCoeff2 = -1.5485213111787743E-10 * cubeCenterX + -1.2997958265259513E-10 * cubeCenterY + -5.6285642813236336E-11 * cubeCenterZ;
long seed = Math.round(basisCoeff0) * 1270789291L + Math.round(basisCoeff1) * -2355713969L + Math.round(basisCoeff2) * -3756485696L & 281474976710655L;
long next = seed * 25214903917L + 11L & 281474976710655L;
long nextNext = next * 25214903917L + 11L & 281474976710655L;
if ((seed >> 24 ^ measurement1 | next >> 24 ^ measurement2 | nextNext >> 24 ^ measurement3) != 0L) {
System.out.println("Failed to crack the seed. This probably means that the item only coincidentally looked like an item that was dropped from mining a block. Other ways to drop items (e.g. dropping from a player's inventory) can sometimes cause false positives like this.");
return;
}
long origSeed = seed;
for (int i = 0; i < 5000; i++) {
for (int x = -23440; x <= 23440; x++) {
long z = (((seed ^ 25214903917L) - WORLD_SEED - 10387319 - x * 341873128712L) * 211541297333629L) << 16 >> 16;
if (z >= -23440 && z <= 23440) {
System.out.println("Item drop appeared at " + dropX + " " + dropY + " " + dropZ);
System.out.println("RNG measurements are therefore " + measurement1 + " " + measurement2 + " " + measurement3);
System.out.println("This indicates the java.util.Random internal seed must have been " + origSeed);
System.out.println("Found a woodland match at woodland region " + x + " " + z + " which would have set the seed to " + seed);
System.out.println("Located someone between " + (x * 1280 - 128) + "," + (z * 1280 - 128) + " and " + (x * 1280 + 1151) + "," + (z * 1280 + 1151));
return;
}
}
seed = (seed * 246154705703781L + 107048004364969L) & 281474976710655L;
}
System.out.println("Failed to crack. This probably means that your world seed is incorrect, or there were no chunk loads recently.");
}For example, I pasted this into jshell, then I ran an actual coordinate that we measured on 2b2t. (although, I've replaced the actual block part of the coordinate with zero to not reveal where our bot was):
jshell> crackItemDropCoordinate(0.41882818937301636, 0.6833633482456207, 0.46088552474975586)
Item drop appeared at 0.41882818937301636 0.6833633482456207 0.46088552474975586
RNG measurements are therefore 5664934 14541261 7076144
This indicates the java.util.Random internal seed must have been 95041827771683
Found a woodland match at woodland region -12008 0 which would have set the seed to 275473502409504
Located someone between -15370368,-128 and -15369089,1151
jshell>
And would you look at that, hidden deep within the digits of the coordinates of that item drop, the server was secretly revealing to us that there's someone on the -x highway at 15.4 million out. This secret information has been present in every item drop, on every server, on every version of the game until 1.13. For earlier than 1.11, you'll need other code because the exploitable structure is something else (not Woodland Mansion), starting when the Village was added as the first structure in Beta 1.8. Another thing to note is that before 1.9, item positions were sent to the client as fixed-point numbers (with only 5 bits dedicated to the fractional part), rather than doubles. This means that it is impractical to crack the RNG state with only one item position, and you'll likely need a different strategy to measure the state of World.rand.
And on the coordinates used as a worked example in this diagram, this is what the above code outputs:
jshell> crackItemDropCoordinate(0.730696, 0.294929355, 0.634865435)
Item drop appeared at 0.730696 0.294929355 0.634865435
RNG measurements are therefore 16129481 1507579 12913941
This indicates the java.util.Random internal seed must have been 270607788940196
Found a woodland match at woodland region 123 456 which would have set the seed to 261215197308064
Located someone between 157312,583552 and 158591,584831
jshell>
Note how it locates Woodland Region 123,456, and note how the final "located someone between" does include the real coordinate that we had originally inputted, which was x=157440 z=583680. Additionally, the RNG measurements match the hexadecimal in red: 0xf61dc9 equals 16129481, 0x1700fb equals 1507579, and 0xc50d15 equals 12913941. And for the seeds, 0xed92e70ba4a0 equals 261215197308064 and 0xf61dc9221ba4 equals 270607788940196.
You can probably find patches or config options for disabling RNG manipulation, something like that will work for patching Randar and it's probably the easiest way. If you can't find an easy way to disable RNG manipulation, here is the code that needs to be tweaked in the World class:
Vulnerable version:
public Random setRandomSeed(int seedX, int seedY, int seedZ) {
this.rand.setSeed(seedX * 341873128712L + seedY * 132897987541L + seedZ + this.getWorldInfo().getSeed());
return this.rand;
}Simply change this function to instead return a different Random each time, if you want perfect protection:
Patched version:
public Random setRandomSeed(int seedX, int seedY, int seedZ) {
return new Random(seedX * 341873128712L + seedY * 132897987541L + seedZ + this.getWorldInfo().getSeed());
}That might not have great performance, so if you like you can introduce a new field, separateRandOnlyForWorldGen, which isn't shared with anything else, e.g.:
private final Random separateRandOnlyForWorldGen = new Random(); // new field on the World class
public Random setRandomSeed(int seedX, int seedY, int seedZ) {
this.separateRandOnlyForWorldGen.setSeed(seedX * 341873128712L + seedY * 132897987541L + seedZ + this.getWorldInfo().getSeed());
return this.separateRandOnlyForWorldGen;
}If you use PaperMC for 1.12.2, here is a patch you can apply. Alternate link.
This will be an additional section where I go over some extra stuff that would make more sense to explain from my point-of-view, as other than the basic ideas, we mostly independently developed things.
First thing I would like to mention, is the system for locating the coordinates from a seed. The Mason's used a large lookup table and GPU processing, I instead relied on a cache for speed. Whenever a hit occurs, its coordinates, and all the coordinates within a radius are put into a HashMap. Seeds are processed in two passes. The first pass steps the RNG back, and checks if the seed is either present in the cache, or it was the same seed processed last time, which is considered differently. The second pass only happens if the first pass fails, is much slower, and uses the relatively expensive algorithm described previously. A pleasant side effect of this system, is that the first pass has the potential to "skip over" an otherwise "valid", but less likely to be correct location, which helps with false positives.
Here is that code:
public class RandarCoordFinder
{
public static final long X_MULT = 341873128712L;
public static final long Z_MULT = 132897987541L;
public static final long Z_MULT_INV = 211541297333629L;
public static final int MANSION_SALT = 10387319;
public static final int MANSION_SPACING = 80;
public static final int CITY_SALT = 10387313;
public static final int CITY_SPACING = 20;
// the last seed we processed
public long lastSeed = -1;
// a mapping of seed -> x,z that is updated everytime we get a hit
public final HashMap<Long, Long> hitCache = new HashMap<>();
// set this according to the server's seed
public long worldSeed;
// change these if you need to use different structures
public int salt = MANSION_SALT;
public int spacing = MANSION_SPACING;
public RandarCoordFinder(long worldSeed)
{
this.worldSeed = worldSeed;
}
// a simple class that extends java.util.Random and provides some extra methods and constants we need
public static class RandarRandom extends Random
{
public static final long MULT = 0x5DEECE66DL;
public static final long ADDEND = 0xBL;
public static final long MASK = (1L << 48) - 1;
public static final long MULT_INV = 0xDFE05BCB1365L;
public long seed;
public RandarRandom(long seed)
{
this.seed = seed;
}
@Override
public void setSeed(long seed)
{
this.seed = seed;
}
@Override
public int next(int bits)
{
seed = (seed * MULT + ADDEND) & MASK;
return (int)(seed >> 48 - bits);
}
public int prevInt()
{
seed = ((seed - ADDEND) * MULT_INV) & MASK;
return (int)(seed >> 16);
}
}
public enum FindType
{
HIT,
SKIP,
FAIL;
}
public record FindResult(FindType type, int xCoord, int zCoord, int steps)
{
}
public FindResult findCoordsSeed(long seed, int maxSteps)
{
seed &= RandarRandom.MASK;
// remember and update lastSeed
long last = lastSeed;
lastSeed = seed;
RandarRandom random = new RandarRandom(seed);
// first pass - this is meant to be quick
for (int i = 0; i < maxSteps + 100000; i++)
{
if (random.seed == last && i > 0)
{
// we encountered the last processed seed while stepping back, skip
return new FindResult(FindType.SKIP, 0, 0, i);
}
else
{
Long hashValue = hitCache.get(random.seed);
if (hashValue != null)
{
// we found a hit in our cache
int xCoord = (int)((hashValue >> 32) & 0xFFFFFFFF);
int zCoord = (int)(hashValue & 0xFFFFFFFF);
cacheNearby(xCoord, zCoord, 8);
return new FindResult(FindType.HIT, xCoord, zCoord, i);
}
}
random.prevInt();
}
random.seed = seed;
// second pass - this is slow and should only happen if the first pass fails
for (int i = 0; i < maxSteps; i++)
{
// undo worldSeed and salt
long seedValue = (random.seed ^ RandarRandom.MULT) - worldSeed -
(long)salt;
Coords coords = findCoords(seedValue, 1875000 / spacing + 8);
if (coords != null)
{
// we found a hit
cacheNearby(coords.x, coords.z, 8);
return new FindResult(FindType.HIT, coords.x, coords.z, i);
}
random.prevInt();
}
// we could not find anything
return new FindResult(FindType.FAIL, 0, 0, -1);
}
public static long getRandomSeed(int x, int z, int salt, long seed)
{
return ((long)x * X_MULT + (long)z * Z_MULT) + seed + (long)salt;
}
private void cacheNearby(int x, int z, int radius)
{
for (int xOff = -radius; xOff <= radius; xOff++)
{
for (int zOff = -radius; zOff <= radius; zOff++)
{
int cacheX = x + xOff;
int cacheZ = z + zOff;
long cacheSeed = (getRandomSeed(cacheX, cacheZ, salt,
worldSeed) ^ RandarRandom.MULT) & RandarRandom.MASK;
hitCache.put(cacheSeed, (long)cacheX << 32 | cacheZ &
0xFFFFFFFFL);
}
}
}
public record Coords(int x, int z)
{
}
public static Coords findCoords(long value, int distance)
{
value &= RandarRandom.MASK;
for (int x = -distance; x <= distance; x++)
{
long testValue = (value - X_MULT * x) & RandarRandom.MASK;
long z = (testValue * Z_MULT_INV) << 16 >> 16;
if (Math.abs(z) <= distance)
{
return new Coords(x, (int)z);
}
}
return null;
}
}Another thing I would like to mention, is how I used this in The End. As mentioned previously, chunks in The End only affect the RNG once ever when they are first generated. This makes things much trickier, as unlike in the Overworld, a player cannot be found by simply loading a chunk at their base.
Instead, there are two other main scenarios which we must rely on:
- Someone who is already at their base, wanders around, encounters ungenerated chunks, and causes them to generate.
- Someone travels to their base, whom will likely encounter and generate a "trail" of new chunks along the way.
The first scenario essentially means that we can still use the naive method of simply counting how many distinct times a region was hit, however we will be heavily limited since hits may be very infrequent, and can be confused by someone simply flying by an area in a few distinct enough times. The second scenario requires us to identify and follow these trails.
So how exactly do we follow trails? In theory you could create a system to automatically identify and follow trails, however I never implemented this and just manually followed trails visually. When following trails, there are a few ideas that can help. For example, multiple trails leading to the same place likely means there is a base. Knowing that a certain hit or trail was caused by a specific player can also help, more on that later.
So how can we tell which player caused a certain hit? In the Overworld, we can simply look for "distinct" hits that happen right after a player joins. However, that is unlikely to work here, so we must do something else. There's actually a neat system for this. It's based on the assumption that not too many players are actually online in The End at once, and the idea that we can tell who these players are. The idea is that the number of RNG calls per tick is, in part, correlated to the number of currently loaded chunks, thus the number of players in that dimension. By watching for a sudden increase or decrease in the number of these calls right after a player joins or leaves respectively, we can identify players that are in The End. We will call this system the "End Occupancy Tracker" (EOT).
The EOT maintains two sets. The first keeps track of who we think is in The End "right now". This can miss players, so it is considered to be more prone to false negatives. The second keeps track of who we think was in The End "overall", backwards and forwards a certain amount of time. This gets combined with the players that are currently online, and is considered to be more prone to false positives. By looking at these sets when a hit occurs, and doing some manual inference, we can get a rough idea of who may have caused a certain hit.
It should be noted that the EOT was only ever tested on 9b9t and currently may rely on conditions that may not be true on other servers such as 2b2t. It assumes that the RNG can be sampled every tick without much fluctuation, which may be trickier for 2b2t because of the block place speed limit. Things might also be made trickier if there is significantly more player activity in The End on the server, which could likely be true for 2b2t as it is a much larger server.