Is javautilRandom really that random How can I generate 52 factorial possible sequences

The quest for true randomness in computing is a fascinating and often misunderstood topic. Many developers, when needing a random number, instinctively reach for java.util.Random. While convenient, this class is a pseudorandom number generator (PRNG), meaning its sequences are deterministic and predictable given the initial seed. This raises a critical question: Is java.util.Random really that random? How can I generate 52! (factorial) possible sequences? The answer depends entirely on your use case. For simple games or non-security-sensitive simulations, java.util.Random might suffice. However, when dealing with cryptographic operations, unique identifiers, or the immense number of permutations represented by 52! (the number of ways to shuffle a deck of 52 cards), its limitations become starkly apparent, necessitating a deeper understanding of true entropy and robust algorithms.

Understanding Pseudorandomness: The Nature of java.util.Random

At its core, java.util.Random is not truly random but rather a pseudorandom number generator (PRNG). This means it produces a sequence of numbers that appear random but are, in fact, entirely determined by an initial value known as a “seed.” If you start with the same seed, java.util.Random will produce the exact same sequence of numbers every single time. This predictability is a fundamental characteristic of PRNGs, making them unsuitable for scenarios where unpredictability is paramount.

The algorithm most commonly used by java.util.Random is a variation of the Linear Congruential Generator (LCG). While efficient, LCGs have a relatively short period (the number of values before the sequence repeats) and can exhibit statistical biases, especially when used for complex simulations or security-sensitive tasks. For instance, if you’re trying to simulate a truly random event many times, an LCG might eventually show patterns that skew your results. Better PRNGs, like the Mersenne Twister, exist and offer much longer periods and better statistical properties, but even they are still deterministic.

For most everyday programming tasks, like generating a random index for an array or shuffling a small list for a non-critical application, java.util.Random is perfectly adequate. Its performance is excellent, and the “randomness” it provides is sufficient for such applications. However, it’s crucial to understand its deterministic nature to avoid misusing it in contexts where genuine unpredictability is a non-negotiable requirement.

The Quest for True Randomness: When java.util.Random Falls Short

While java.util.Random excels at quickly generating numbers for non-critical tasks, its deterministic nature makes it fundamentally unsuitable for applications requiring high-quality, unpredictable random numbers. This is where the concept of cryptographic randomness comes into play. Cryptographically Secure Pseudorandom Number Generators (CSPRNGs) are designed to produce sequences that are computationally infeasible to predict, even if you know previous outputs. This is vital for security-related functions like generating encryption keys, session tokens, or secure passwords.

In Java, the go-to class for cryptographic randomness is java.security.SecureRandom. Unlike java.util.Random, SecureRandom leverages sources of “entropy” from the operating system or hardware. Entropy refers to true unpredictable physical phenomena, such as mouse movements, keyboard timings, disk I/O, or specific hardware noise, which are then used to seed and continuously re-seed its internal state. This ensures that the generated numbers are not reproducible and are resistant to cryptographic attacks.

For applications demanding genuine unpredictability, such as generating unique identifiers or cryptographic keys, java.security.SecureRandom is the essential choice because it harvests true entropy from the system’s environment to create a sequence that is computationally impossible to guess or reproduce. This makes it suitable for scenarios where a compromise of the random number generator could lead to severe security vulnerabilities, unlike java.util.Random which is predictable if its seed is known.

Relying on java.util.Random for security-critical operations is a common mistake that can lead to significant vulnerabilities. For instance, if a system uses a predictable random number generator to create session IDs, an attacker could potentially guess valid IDs and hijack user sessions. The difference in security guarantees between a simple PRNG and a CSPRNG is profound and must be carefully considered based on the application’s risk profile. [dedicated hardware](<https://docs. Question & Answer :

I’ve been using Random (java.util.Random) to shuffle a deck of 52 cards. There are 52! (8.0658175e+67) possibilities. Yet, I’ve found out that the seed for java.util.Random is a long, which is much smaller at 2^64 (1.8446744e+19).

From here, I’m suspicious whether java.util.Random is really that random; is it actually capable of generating all 52! possibilities?

If not, how can I reliably generate a better random sequence that can produce all 52! possibilities?

Selecting a random permutation requires simultaneously more and less randomness than what your question implies. Let me explain.

The bad news: need more randomness.

The fundamental flaw in your approach is that it’s trying to choose between ~2²²⁶ possibilities using 64 bits of entropy (the random seed). To fairly choose between ~2²²⁶ possibilities you’re going to have to find a way to generate 226 bits of entropy instead of 64.

There are several ways to generate random bits: <a href=>), CPU instructions, OS interfaces, online services. There is already an implicit assumption in your question that you can somehow generate 64 bits, so just do whatever you were going to do, only four times, and donate the excess bits to charity. :)

The good news: need less randomness.

Once you have those 226 random bits, the rest can be done deterministically and so the properties of java.util.Random can be made irrelevant. Here is how.

Let’s say we generate all 52! permutations (bear with me) and sort them lexicographically.

To choose one of the permutations all we need is a single random integer between 0 and 52!-1. That integer is our 226 bits of entropy. We’ll use it as an index into our sorted list of permutations. If the random index is uniformly distributed, not only are you guaranteed that all permutations can be chosen, they will be chosen equiprobably (which is a stronger guarantee than what the question is asking).

Now, you don’t actually need to generate all those permutations. You can produce one directly, given its randomly chosen position in our hypothetical sorted list. This can be done in O(n²) time using the Lehmer^[1] code (also see numbering permutations and factoriadic number system). The n here is the size of your deck, i.e. 52.

There is a C implementation in this StackOverflow answer. There are several integer variables there that would overflow for n=52, but luckily in Java you can use java.math.BigInteger. The rest of the computations can be transcribed almost as-is:

public static int[] shuffle(int n, BigInteger random_index) { int[] perm = new int[n]; BigInteger[] fact = new BigInteger[n]; fact[0] = BigInteger.ONE; for (int k = 1; k < n; ++k) { fact[k] = fact[k - 1].multiply(BigInteger.valueOf(k)); } // compute factorial code for (int k = 0; k < n; ++k) { BigInteger[] divmod = random_index.divideAndRemainder(fact[n - 1 - k]); perm[k] = divmod[0].intValue(); random_index = divmod[1]; } // readjust values to obtain the permutation // start from the end and check if preceding values are lower for (int k = n - 1; k > 0; --k) { for (int j = k - 1; j >= 0; --j) { if (perm[j] <= perm[k]) { perm[k]++; } } } return perm; } public static void main (String[] args) { System.out.printf("%s\n", Arrays.toString( shuffle(52, new BigInteger( "7890123456789012345678901234567890123456789012345678901234567890")))); } 

^[1] Not to be confused with Lehrer. :)