64 bit hash collision probability python. The hash value returned is a 64- bit unsigned integer.

64 bit hash collision probability python. e. This function, at least on the machine I'm developing for (with python 2. I definitely found that out, with only 64 bits of collisions taking over 12 hours to run on my quad-core desktop machine. Normally we see kind of problem being solved by using an approximation 2n/2 2 n / 2 or 2n−−√ 2 n So for a 11-bit hash, the number of messages to hash to have 50% chance of a collision would be Aug 10, 2012 · Finding good hash functions for larger data sets is always challenging. The system could e. This means that to get a collision, on average, you'll need to hash 6 billion files per second for 100 years. It also means we leave all 64 bits of the hash untouched, which feels more correct even if @scottmcm 's back-of-the-envelope calcs show that 32-bits is more than enough to avoid collisions in practice. Understanding these concepts is essential for any aspiring programmer, especially those preparing for technical interviews at major tech companies. hashlib provides cryptographic hash routines, which are far slower than they need to be for non-cryptographic purposes. For example, all objects in the Java programming language can be hashed to 32-bit in-tegers. Jul 9, 2017 · If we take every possible hash (1664 16 64) and rehash it, the amount of possible outcomes for any given rehash is 1 out of 1664 16 64. Mar 13, 2017 · With the announcement that Google has developed a technique to generate SHA-1 collisions, albeit with huge computational loads, I thought it would be topical to show the odds of a SHA-1 collision in the wild using the Birthday Problem. Slightly slower. I've used CRC32 to hash this field, but I'm worrying about duplicates. The concatenation is studied in cryptography, however, you don't consider any of the attack, so just consider the inputs spaces and compare. input given in bits number of possible outputs MD5 SHA-1 32 bit 64 bit 128 bit 256 bit 384 bit 512 bit Number of elements that are hashed You can use also mathematical expressions in your input such as 2^26, (19*7+5)^2, etc. It is a cryptographic hash function that transforms any input data into a fixed-length, 256-bit hash value. Now say that I know that the odds of picking 2 hashes and there being a collision are (For arguments sake) 50000:1. Syntax You have to known how your hash function is used. The same input always generates the same hash value, and a good hash function tends to generate different hash values when given different inputs. Sep 20, 2018 · Created on 2018-09-20 13:27 by jdemeyer, last changed 2022-04-11 14:59 by admin. SpookyHash can produce 64-bit and 128-bit hash values, providing versatility for various use cases, including hash Jul 8, 2015 · I have no idea what the "hashing" function is, but there appears to be collisions. Collisions in Hashing # In computer science, hash functions assign a code called a hash value to each member of a set of individuals. Sep 4, 2015 · Hashing is the fundamental operation of mapping data objects to fixed-size hash values. The hash value is used to create an index for the keys in the hash table. so if your'e generating 1. You will get this graph. I know there are things like SHA-256 and such, but these algorithms are designed to be sec Let be the number of possible values of a hash function, with . [1] The values returned by a hash function are called hash values, hash codes, (hash/message Jan 5, 2012 · Created on 2012-01-03 19:36 by barry, last changed 2022-04-11 14:57 by admin. Jan 10, 2017 · This means that with a 64-bit hash function, there’s about a 40% chance of collisions when hashing 2 32 or about 4 billion items. In random hashing, we pick a hash function at random from somefamily,whereasanadversarymightpickthedatainputs. g. On one hand, the seed helps reduce the probability of collisions. Since it is not, I assume it is the desired final output range. This utilizes the principles of the birthday paradox to greatly increase the probability of a finding a collision, while using significantly less memory than the classic birthday attack, and allowing a larger Absolutely! SipHash for a start. Oct 14, 2022 · The benefits are that bigint is a proper JavaScript primitive, so === will work like normal. A hash function that maps names to integers from 0 to 15. The hash function may return the same hash value for two or more keys. You can be confident that they will not collide. Could somebody show me the probability of collision in this situation? P Feb 25, 2014 · Say I have a hash algorithm, and it's nice and smooth (The odds of any one hash value coming up are the same as any other value). Jul 4, 2024 · There is no way to "map 64-bit variables into a 32-bit representation" while avoiding collisions with good confidence for more than a few thousands 64-bit inputs, unless something is known about the distribution of the 64-bit inputs. When two or more keys have the same hash value, a collision happens. We want distinct objects to be unlikely to hash to the same value. Combine with Other Methods: For applications requiring security, consider using SpookyHash in conjunction with cryptographic hash functions to enhance data integrity without compromising performance. Feb 26, 2014 · With a 64-bit hash code, the chance of collision is one in a million when you hash just six million items, and it goes up pretty quickly from there. Included are the FIPS secure hash algorithms SHA224, SHA256, SHA384, SHA512, (defined in the Dec 27, 2022 · I've read from a couple sources that truncating SHA256 to 128 bits is still more collision resistant compared to MD5. My question is, does taking every other hex nibble instead of truncating the first 32 hex nibbles of the SHA256 hash output affect collision probability in any way? Hash collisions can be unavoidable depending on the number of objects in a set and whether or not the bit string they are mapped to is long enough in length. Assuming each rehash provided a unique hash, with no collisions, doesn't this imply any input larger or smaller than 64 bytes would collide with one of these values? Mar 2, 2017 · Hash tables are one of the most commonly used data structures in computer science, due to their O(1) access time. This is a number low enough that it seems very lik In the world of computer science and programming, hash functions and collision handling play a crucial role in various applications, from data structures to cryptography. That length provides 2128 2 128 collision resistance and 2256 2 256 pre-image and second pre-image resistance for SHA256 and so on. May 4, 2011 · Assuming your hash values are 32-bit, 64-bit or 160-bit, the following table contains a range of small probabilities. Jun 1, 2013 · Use the built-in hash() function. The rough approximation is that the probability of a collision occurring with k keys and n possible hash values with a good hashing algorithm is approximately (k^2)/2n, for k << n. MurmurHash2 [8] yields a 32- or 64-bit value. unsigned long long) any more, because there are so many of them. Suppose you are given 64-bit integers (a long in Java). For example, if you need a collision probability lower than one in a million among one million of files, you will need to have more than 5*10^17 distinct hash values, which means your hashes need to have at least 59 bits. To build a Cryptographic Hashing Cryptographic hash functions were first described in detail by Ralph Merkle in his 1979 PhD thesis. Finding a collision via brute force computing is impractical with current technology. Aug 18, 2023 · In summary, there is an extremely low probability (1 in 2^64) of collision in a 128-bit hash value due to the massive size of the output space. This didn't feel too egregious until I looked at the space of inputs and outputs for SHA-256, which is 2^256 out and an absolutely Jul 4, 2024 · If we only want this hash function to distinguish between all strings consisting of lowercase characters of length smaller than 15, then already the hash wouldn't fit into a 64-bit integer (e. So I'd say any decent 64-bit hash should be sufficient for you. It would only take about 2 16 events in one second (on average) to hit a collision. In short, we are taking a 1 in 100 million event from a 160-bit hash space and turning it into an overwhelmingly likely event if we can reach the required threshold. There are many good ways to achieve this result, but let me add some constraints: The hashing should be strongly universal, also called pairwise independent. The probability of 32-bit hash collision for n n random distinct inputs is about 1 − (1 −2−32)n(n−1)/2 1 (1 2 32) n (n 1) / 2 and that's already >5% for Jun 19, 2024 · A hash function is a mathematical function that takes an input (or ‘message’) and returns a fixed-size string of bytes. Apr 5, 2018 · And if, how could this weaken the collision resistance of their combination? What can be done to avoid this situation, and to achieve the collision resistance of a 64-bit hash (or more) using multiple 32-bit results? Is there a way one can combine two correlated hash outputs to maximize the collision resistance? Collisions are still quite possible even in the same second. Considering how often some programs run, "one in a million" isn't very good odds. We typically assume that given two data objects, the probabil-ity that they have the So: given a good hash function and a set of values, what is the probability of there being a collision? What is the chance you will have a hash collision if you use 32 bit hashes for a thousand items? And how many items could you have if you switched to a 64-bit hash without the risk of collisions going above one-in-a-million? However, given a fixed amount of resources spent trying to find a collision, the probability of finding a collision is (mostly) constant in terms of the input length (if hashing longer strings takes longer, longer strings would actually have a lower chance). Let's make some assumptions about randomness and find the probability that there is no collision. Additional tests, which evaluate more thoroughly speed and collision properties of 64-bit hashes, are also provided. Due to the pigeonhole principle (where we're mapping an infinite input space to a finite output space), collisions are mathematically inevitable - the question is not if they exist, but how hard they are Oct 5, 2020 · I'm looking for the best 64-bit (or at least 32-bit) hash function for NumPy that has next properties: It is vectorized for numpy, meaning that it should have functions for hashing all elements of 1 Introduction Hashing is the fundamental operation of mapping data ob-jects to fixed-size hash values. We would like to show you a description here but the site won’t allow us. A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. Aug 21, 2017 · If you we use less than, for instance 1 billion of hashes, the probability of collision is negligible. Jan 28, 2025 · 2^32 and especially 2^64 are big. If two individuals are assigned the same value, there is a collision, and this causes trouble in identification. 123 Jul 5, 2024 · Universally Unique Identifiers (UUIDs), also known as Globally Unique Identifiers (GUIDs), are 128-bit identifiers designed to provide a standardized way of generating unique values across distributed systems. Many algorithms and data structures rely on hashing: e. What is the probability that all N keys were inserted and no collision has occurred? The 128-bit variant is called XXH128. , as long as ε 2 <2 70 ε <2 35. [9] MurmurHash2A (32-bit, x86)—A fixed variant using Merkle–Damgård construction. It successfully completes the SMHasher test suite which evaluates collision, dispersion and randomness qualities of hash functions. Code is highly portable, and hashes are identical on all platforms (little / big endian). It is a 64-bit hash function with a 4x 64-bit (256-bit) internal state. That is, we want a low collision probability. For example, all objects in the Java programming language can be hashed to 32-bit integers. Comparatively, 128-bit hashes provide good collision resistance for most applications while optimizing performance. Given that the offset basis and FNV Prime are constants within the module, and are equal to the parameters for a 64-bit hash, the value of mod should also be fixed at 2 64. I managed to get 64 bits of collisions and I’d love to share the method I did so. Effectively combining multiple uncorrelated 32-bit states. If you are using hundred millions of hashed keys, the probability of collision is 0% using md5. However, this assumes a perfect hash function — the complexity can increase to O(n) when there are a lot of hash collisions. Dec 20, 2016 · This technique allows us to find hash collisions easily in SHA-3. Oct 10, 2023 · xxhash64 function Applies to: Databricks SQL Databricks Runtime Returns a 64-bit hash value of the arguments. Jun 2, 2016 · The algorithm calls for the calculations to be done modulo 2 n where n is the number of bits in the desired hash. Cryptographic hash functions take an digital input of any finite size and produce a fixed size output. The input items can be anything: strings, compiled shader programs, files, even directories. Abstract—In this paper, we realized a memory efficient general parallel Pollard’s rho method for collision search on hash functions introduced by Van Oorschot and Wiener in 1996. Therefore, 64-bit should be considered now an insecur Feb 15, 2016 · then, to truncate the output of the chosen hash function to 96 bits (12 bytes) - that is, keep the first 12 bytes of the hash function output and discard the remaining bytes then, to base-64-encode the truncated output to 16 ASCII characters (128 bits) yielding effectively a 96-bit-strong cryptographic hash. if used in hash table with linear collision and the size is not by primed but modulo 2 (and you know the random seed), then you only need a few bits of the resulting hash, and this can easily brute forced. generate new datum G or I and recalculate hash, if conflict happens. Having more intenal state than the output is a good idea for a few reasons, but mostly it improves distribution of the output, reduces spectral artifacts, and 1 day ago · Source code: Lib/hashlib. 00000001% collision probability requires 1. 3. CMurmurHash2A (32-bit, x86 Which hashing algorithm is best for uniqueness and speed? Example (good) uses include hash dictionaries. This issue is now closed. The hash value returned is a 64- bit unsigned integer. n=64 in the PrColl equation from above, and the number of inputs is k in the PrColl equation. How many minimum messages do we have to hash to have a 50% probability of getting a collision. 48 bytes/384 bits or 64 bytes/512 bits provides greater security and would be more sensible to use under certain circumstances but unnecessary in others. Hackers can not get password from storage. The XOR is an 8- bit operation that modifies only the lower 8- bits of the hash value. Apr 4, 2018 · The difference between MurmurHash2_x86_64 and MurmurHash3_x86_128 is that the former only does one [32-bit 32-bit] -> 64-bit mix, while the latter does a 128-bit mix in each 16 bytes (though not a full-fledged mix, but it is enough for this purpose). This means that if Nov 11, 2022 · I have a 10-character string key field in a database. It needs around 4 min to create usable DoS collisions even for hash tables using SHA256 then. If you use xxhash64, Assuming that xxhash64 produce a 64-bit hash. If x is the input, and x’ represents any single flipped bit of x, then cryptographic hashes have the property that each output bit has equal and independent probability Jun 22, 2025 · A more naive but less complex way to avoid overflows would be to use the original factorial expression but work with logs - in a rough experiment with python for k=10^8 and N=10^17 (numbers plucked out of thin air), the calculation takes ~20s on an M1 MacBook Pro. For example, many people like to use 64-bit integers. Oct 28, 2018 · In Feb 2017, CWI and Google announced SHAttered hash collision attack on SHA1, which took $2^{63. SHA-256 is widely used for ensuring data integrity, authenticating digital signatures, and securing blockchain transactions. It was created by Glenn Fowler, Landon Curt Noll, and Kiem-Phong Vo. 1. Python hash function converts maps data to 64 bits (range of int). SHA-224 and SHA-384) and all variants of SHA-3. 71e+19. Part of the assignment was to demonstrate to us how difficult it is to find collisions in this best hash function. Jan 12, 2021 · 64-bit already small, since 232 2 32 which is around 4 billion hashing, there should be a collision in the database. In both cases, we present very efficient hash function if the keys are 32- or 64-bit integers and the hash values are bit strings. These worked well for random strings, but the simplicity of the hash Is there a way to find a collision for a given hash function without brute forcing? The particular hash function I'm talking about is the one used by Python (simplified version given below). Aug 24, 2020 · The hash function can heavily favour computational efficiency and let each 64-bit half collide with probability ε significantly worse than 2 64, as long as the collision probability for the concatenated fingerprint, ε 2, is small enough, i. With a 64 bit hash, the probability of collision is 1 in 2^32 (due to the birthday bound) -- 1 in roughly 4 billion. Aug 26, 2013 · 64 bit runs to about 18,446,744,073,709,551,616 combinations which is around 18 and a half quintillion. Comprehensive guide to cryptography covering basic concepts, advanced topics, CTF challenges, and practical implementations. The Hash collision When two strings map to the same table index, we say that they collide. The FNV_prime is the 64- bit value 1099511628211 (in hex, 0x100000001b3). SHA-256 (Secure Hash Algorithm 256-bit) is a member of the SHA-2 family, designed by the National Institute of Standards and Technology (NIST). Additionally, some variants of SHA-2 (those with non-power-of-two output sizes, e. Dec 2, 2017 · A cryptographic hash function has provable security against collision attacks if finding collisions is provably polynomial-time reducible from problem P which is supposed to be unsolvable in polynomial time. [2] Aug 15, 2018 · In software, hashing is the process of taking a value and mapping it to a random-looking value. If the output of the hash function is discernibly different from random, the probability of collisions may be higher. [4] Another reason hash For example, if there are 1,000 available hash values and only 5 individuals, it doesn't seem likely that you'll get a collision if you just pick a random sequence of 5 values for the 5 individuals. It’s important that each individual be assigned a unique value. Website The 128-bit variant is called XXH128. py This module implements a common interface to many different hash algorithms. MurmurHash2 (32-bit, x86)—The original version; contains a flaw that weakens collision in some cases. Matt I'll provide a rough approximation to the exact formulas provided in the other answers; the approximation may be able to help you answer #3. Mar 30, 2025 · FNV-1a: hash= offset_basisfor each octet_of_datato be hashed hash= hashxor octet_of_datahash= hash* FNV_primereturn hash The only difference between the FNV-1ahash and the FNV-1hash is the order of the xor and multiply. The FNV-1ahash uses the same FNV_primeand offset_basisas the FNV-1hash of the same n-bit size. For any two inputs of s bytes or fewer, the probability that a randomly parameterised UMASH assigns them the same 64 bit hash value is less than ceil(s / 4096) 2**-55. 2 Likes zicklag October 15, 2022, 2:48am 8 Jul 5, 2022 · Yes, 32 bytes/256 bits is considered enough (seriously read this blog post). For hash function h (x) and table size s, if h (x) s = h (y) s, then x and y will collide. UUIDs were originally defined by the Open xxHash - Extremely fast hash algorithm xxHash is an Extremely fast Hash algorithm, running at RAM speed limits. Use hashlib. E. There is a collision between keys "John Smith" and "Sandra Dee". The well know hashes, such as MD5, SHA1, SHA256 are fairly slow with large data processing and their added extra functions (such as being cryptographic hashes) isn’t always required either. So, all possible rehashes is equal to all possible unique hashes. It turned out to be a lot harder than I expected, but I eventually Jul 23, 2019 · This is the method used by Alexander Klink and Julian in their CCC presentation, as well as the technique explored more deeply for 64-bit Python by Robert Grosse. Getting the random seed is usually Jul 23, 2025 · In Hashing, hash functions were used to generate hash values. UMASH also offers a fingerprinting function that computes a second 64-bit hash concurrently with the regular UMASH value. For 100,000 keys with a 64 bit hash, that's 10^10 / 32x10^18 or about Hash Collision Probabilities A hash function takes an item of a given type and generates an integer hash value within a given range. Performance and low collision rate on the other hand is very important, so many new hash functions were inverted in the past few It is essential to follow best practices when using the hash () function to avoid encountering hash collisions, such as using high-quality hash functions and immutable objects. Jan 15, 2023 · I'm working on a problem where I need to track some state that's 64-bit integers. We typically assume that given two data objects, the probability that they have the same hash value Mar 10, 2025 · This graphs the probability of a hash collision for a 64-bit hash for various numbers of input values. Sep 26, 2020 · I want the same collision resistance as the original SHA-256 with variable length input or a stronger collision resistance. Dec 17, 2015 · You shouldn't rely on hash if your program cannot handle the collisions or you want to save hash values or use multiprocessing. 7, and a 64-bit cpu) produces an integer that fits within 32 bits - not large enough for my purposes. Can i take a SHA-256 hash and split it evenly into 4 and XOR it to make it a 64 bit hash? What is the likelihood of it having a collision? SpookyHash is a high-performance non-cryptographic hash function designed by Bob Jenkins. To have a 50% chance of any hash colliding with any other hash you need 264 hashes. To handle this collision, we use Collision Resolution Techniques. Mar 2, 2017 · I couldn’t find any public information about how to generate 64 bit FNV collisions, so I had to figure it out myself. I am interested in knowing what the expected number of collisions is with a general purpose 36 bit hashing function and 80,000 entries. Jan 5, 2019 · This means that with a 64-bit hash function, there’s about a 40% chance of collisions when hashing 232 or about 4 billion items. Use a secret value before hashing so that no one else can modify M and hash Can encrypt Message, hash, or both for confidentiality Digital Signatures: Encrypt hash with private key Password storage: Hash of the user’s password is compared with that in the storage. The FNV (Fowler-Noll-Vo) hash algorithm is a non-cryptographic hash function designed for fast hashing of small to medium-sized data. Say you want a unique ID in 64 bits, with a 32 bit field for time and a 32 bit field for a per-second random value. The multiply returns the lower 64 bits of the product. The offset_basisand Nov 20, 2024 · Various aspects and real-life analogies of the odds of having a hash collision when computing Surrogate Keys using MD5, SHA-1, and SHA-256. The most basic analysis of hashing is limited to viewing it as birthday problem. While 64-bit is faster, 128-bit may provide better collision resistance. A 160-bit hash with 0. (Sorting the outputs and scanning for collisions requires an additional O(` · 2`/2) time). hash collisions are not likely if the hash functions used are good enough (and those that python uses are). You might want to “hash” these integers to other 64-bit values. With a birthday attack, it is possible to find a collision of a hash function with chance in where is the bit length of the hash output, [1][2] and with being the classical preimage resistance security with the same probability. Apr 4, 2023 · Proposal Increase the size of TypeId's hash from 64 bits to 128 bits. Using a 45-bit prime and a 17-bit base sounds like a cute trick, but using p = 261 − 1 p = 2 61 1 is both 10% faster 96073867 and it gives you better provable bounds on the collision probability. If you assign two 64-bit integers at random to distinct objects, the probability of a collision is very, very small. All variants successfully complete the SMHasher test suite which evaluates the quality of hash functions (collision, dispersion and randomness). The Python hash () function has various use cases, including indexing, data retrieval, and database implementation. Apr 6, 2018 · Produces an n-bit hash digest, greater or equal to 64-bit, with the expected collision probability of a hash of that size. Nov 29, 2021 · For 64-bit hashes and 40 million unique tiles, the probability of a collision is ~1 in 23,000 For 64-bit hashes and 200 million unique tiles, the probability is ~1 in 922 These lemmas imply that the birthday attack finds a collision with high probability using q = ⇥(2`/2) hash-function evaluations. Mar 10, 2021 · You have a hash which gives a 11-bit output. input given in bits number of hash 2 16 2 32 2 64 2 128 2 256 Compute Collision probability Approximated Dec 12, 2019 · Often, these identifiers are integers. Even with an excellent hashing algorithm, there’s still a chance of generating the same hash value for different data. That helps a bit, but I am still confused, so let me get to the point: Will all 2^128-1 unique (nonzero) initial states of xoshiro128 return a 100% unique sequence (full period)? That is, unless the seed collides, the PRNG output cannot collide? I suppose what I am truly asking is: "How many total unique sequences can a PNRG produce given a seed", rather than a probability of collision. It turns out this state can tracked by simply accumulating a sum of differences, which in my case turns out to nat Dec 20, 2016 · One of the most interesting assignments that we got to do for the class was to see how many bits of hash collisions on the SHA-3 hash algorithm that we could generate given a starting string. However, note that e. So, logically, MurmurHash2_x86_64 splits the input into 2 totally separated streams, calculates a 32-bit hash for each of them, then mix the two . compiler can use a numerical computation, called a hash, to produce an integer from a string. 92 million hashes, the odds of a collision will be 1 in 10 million First we introduce universal hashing in Section 2, then we introduce strongly universal hashing in Section 3. dict ’s implementation only uses some of those bits for reasons of practicality, and will therefore have hash collisions all the time. However, what about the case where you have 300 million objects? Or maybe 7 billion With expectation that billions of pairs need to be supported, 64 bit hash appears risky (it is completely possible that collision predicted by birthday paradox happens), thus I would recommend that no matter what hash is used, the system is prepared for hash conflicts. In Section 4 we show how we can efficiently produce hash values in arbitrary integer ranges. When there is a set of n objects, if n is greater than | R |, which in this case R is the range of the hash value, the probability that there will be a hash collision is 1, meaning it is guaranteed to occur. A well-designed hash function, h, distributes those integers so that few strings produce the same hash value. Nov 30, 2024 · Released on 2024-11-16 Original implementation 42 cycles/hash for short strings Basic seed mixing (affects only 64 bits of initial state) Passes most smhasher tests When Not to Use Cryptographic purposes Protection against collision attacks (Use SipHash instead) When extremely low collision probability is required (Consider xxhash64) Original ChibiHash implementation by N-R-K. For Python developers working with databases like PostgreSQL, understanding UUIDs is crucial for effective data management and system design. Hash Collisions: Understanding the Fundamentals What is a Hash Collision? A hash collision occurs when two different inputs produce the same hash output when processed through a hash function. For example, if you were to However if you keep all the hashes then the probability is a bit higher thanks to birthday paradox. 1}$ work estimated 6500 CPU years, to achieve. Historically, most libraries used weak, non cryptographic hashes for efficiency. In this comprehensive guide, we’ll dive deep into the world of hash We present the Mathematical Analysis of the Probability of Collision in a Hash Function. , authentication codes, Bloom filters and hash tables. There is a nice SO answer and a detailed wiki page about that. It comes in multiple variants, including some that allow incremental hashing and aligned or neutral versions. If you know the number of hash values, simply find the nearest matching row. You will learn to calculate the expected number of collisions along with the values till which no collision will be expected and much more. 1Thelow-powerAMDJaguarmicroarchitecturedoesevenbetterwith a throughput of one cycle and a latency of three cycles. It is known for its speed and quality, making it an excellent choice for applications that require efficient hashing of data without the overhead associated with cryptographic security. Aug 6, 2019 · In the 32-bit version’s method call, you need to provide a seed. To prove this, we will use a hash function with a very small hash value (3 bytes) and a dictionary with words of 3 letter length combinations, so the probability of getting a collision is increased. Let's round to 64 to account for possibly bad uniformity. With a bounded input this would basically mean no collisions at all with the 2^64 inputs, like with the 8 bit input example. bnlyx wheem lcolkm ufrwb dgs uraxwta mapoep rtwcji hpj hdl