I need to generate string that meets the following requirements:
it should be a unique string;
string length should be 8 characters;
it should contain 2 digits;
all symbols (non-digital characters) should be upper case.
I will store them in a data base after generation (they will be assigned to other entities).
My intention is to do something like this:
Generate 2 random values from 0 to 9—they will be used for digits in the string;
generate 6 random values from 0 to 25 and add them to 64—they will be used as 6 symbols;
concatenate everything into one string;
check if the string already exists in the data base; if not—repeat.
My concern with regard to that algorithm is that it doesn't guarantee a result in finite time (if there are already A LOT of values in the data base).
Question: could you please give advice on how to improve this algorithm to be more deterministic?
Thanks.
it should be unique string;
string length should be 8 characters;
it should contains 2 digits;
all symbols (non-digital characters) - should be upper case.
Assuming:
requirements #2 and #3 are exact (exactly 8 chars, exactly 2 digits) and not a minimum
the "symbols" in requirement #4 are the 26 capital letters A through Z
you would like an evenly-distributed random string
Then your proposed method has two issues. One is that the letters A - Z are ASCII 65 - 90, not 64 - 89. The other is that it doesn't distribute the numbers evenly within the possible string space. That can be remedied by doing the following:
Generate two different integers between 0 and 7, and sort them.
Generate 2 random numbers from 0 to 9.
Generate 6 random letters from A to Z.
Use the two different integers in step #1 as positions, and put the 2 numbers in those positions.
Put the 6 random letters in the remaining positions.
There are 28 possibilities for the two different integers ((8*8 - 8 duplicates) / 2 orderings), 266 possibilities for the letters, and 100 possibilities for the numbers, the total # of valid combinations being Ncomb = 864964172800 = 8.64 x 1011.
edit: If you want to avoid the database for storage, but still guarantee both uniqueness of strings and have them be cryptographically secure, your best bet is a cryptographically random bijection from a counter between 0 and Nmax <= Ncomb to a subset of the space of possible output strings. (Bijection meaning there is a one-to-one correspondence between the output string and the input counter.)
This is possible with Feistel networks, which are commonly used in hash functions and symmetric cryptography (including AES). You'd probably want to choose Nmax = 239 which is the largest power of 2 <= Ncomb, and use a 39-bit Feistel network, using a constant key you keep secret. You then plug in your counter to the Feistel network, and out comes another 39-bit number X, which you then transform into the corresponding string as follows:
Repeat the following step 6 times:
Take X mod 26, generate a capital letter, and set X = X / 26.
Take X mod 100 to generate your two digits, and set X = X / 100.
X will now be between 0 and 17 inclusive (239 / 266 / 100 = 17.796...). Map this number to two unique digit positions (probably easiest using a lookup table, since we're only talking 28 possibilities. If you had more, use Floyd's algorithm for generating a unique permutation, and use the variable-base technique of mod + integer divide instead of generating a random number).
Follow the random approach above, but use the numbers generated by this algorithm instead.
Alternatively, use 40-bit numbers, and if the output of your Feistel network is > Ncomb, then increment the counter and try again. This covers the entire string space at the cost of rejecting invalid numbers and having to re-execute the algorithm. (But you don't need a database to do this.)
But this isn't something to get into unless you know what you're doing.
Are these user passwords? If so, there are a couple of things you need to take into account:
You must avoid 0/O and I/1, which can easily be mistaken for each other.
You must avoid too many consecutive letters, which might spell out a rude word.
As far as 2 is concerned, you can avoid the problem by using LLNLLNLL as your pattern (L = letter, N = number).
If you need 1 million passwords out of a pool of 2.5 billion, you will certainly get clashes in your database, so you have to deal with them gracefully. But a simple retry is enough, if your random number generator is robust.
I don't see anything in your requirements that states that the string needs to be random. You could just do something like the following pseudocode:
for letters in ( 'AAAAAA' .. 'ZZZZZZ' ) {
for numbers in ( 00 .. 99 ) {
string = letters + numbers
}
}
This will create unique strings eight characters long, with two digits and six upper-case letters.
If you need randomly-generated strings, then you need to keep some kind of record of which strings have been previously generated, so you're going to have to hit a DB (or keep them all in memory, or write them to a textfile) and check against that list.
I think you're safe well into your tens of thousands of such ID's, and even after that you're most likely alright.
Now if you want some determinism, you can always force a password after a certain number of failures. Say after 50 failures, you select a password at random and increment a part of it by 1 until you get a free one.
I'm willing to bet money though that you'll never see the extra functionality kick in during your life time :)
Do it the other way around: generate one big random number that you will split up to obtain the individual characters:
long bigrandom = ...;
int firstDigit = bigRandom % 10;
int secondDigit = ( bigrandom / 10 ) % 10;
and so on.
Then you only store the random number in your database and not the string. Since there's a one-to-one relationship between the string and the number, this doesn't really make a difference.
However, when you try to insert a new value, and it's already in the databse, you can easily find the smallest unallocated number graeter than the originally generated number, and use that instead of the one you generated.
What you gain from this method is that you're guaranteed to find an available code relatively quickly, even when most codes are already allocated.
For one thing, your list of requirements doesn't state that string has to be necessary random, so you might consider something like database index.
If 'random' is a requirement, you can do a few improvements.
Store string as a number in database. Not sure how much this improves perfromance.
Do not store used strings at all. You can employ 'index' approach above, but convert integer number to a string in a seemingly random fashion (e.g., employing bit shift). Without much research, nobody will notice pattern.
E.g., if we have sequence 1, 2, 3, 4, ... and use cyclic binary shift right by 1 bit, it'll be turned into 4, 1, 5, 2, ... (assuming we have 3 bits only)
It doesn't have to be a shift too, it can be a permutation or any other 'randomization'.
The problem with your approach is clearly that while you have few records, you are very unlikely to get collisions but as your number of records grows the chance will increase until it becomes more likely than not that you'll get a collision. Eventually you will be hitting multiple collisions before you get a 'valid' result. Every time will require a table scan to determine if the code is valid, and the whole thing turns into a mess.
The simplest solution is to precalculate your codes.
Start with the first code 00AAAA, and increment to generate 00AAAB, 00AAAC ... 99ZZZZ. Insert them into a table in random order. When you need a new code, retrieve to top record unused record from the table (then mark it as used). It's not a huge table, as pointed out above - only a few million records.
You don't need to calculate any random numbers and generate strings for each user (already done)
You don't need to check whether anything has already been used, just get the next available
No chance of getting multiple collisions before finding something usable.
If you ever need more 'codes', just generate some more 'random' strings and append them to the table.
Related
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: dedicated hardware, 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. :)
Your analysis is correct: seeding a pseudo-random number generator with any specific seed must yield the same sequence after a shuffle, limiting the number of permutations that you could obtain to 264. This assertion is easy to verify experimentally by calling Collection.shuffle twice, passing a Random object initialized with the same seed, and observing that the two random shuffles are identical.
A solution to this, then, is to use a random number generator that allows for a larger seed. Java provides SecureRandom class that could be initialized with byte[] array of virtually unlimited size. You could then pass an instance of SecureRandom to Collections.shuffle to complete the task:
byte seed[] = new byte[...];
Random rnd = new SecureRandom(seed);
Collections.shuffle(deck, rnd);
In general, a pseudorandom number generator (PRNG) can't choose from among all permutations of a 52-item list if its maximum cycle length is less than 226 bits.
java.util.Random implements an algorithm with a modulus of 248 and a maximum cycle length of not more than that, so much less than 2226 (corresponding to the 226 bits I referred to). You will need to use another PRNG with a bigger cycle length, specifically one with a maximum cycle length of 52 factorial or greater.
See also "Shuffling" in my article on random number generators.
This consideration is independent of the nature of the PRNG; it applies equally to cryptographic and noncryptographic PRNGs (of course, noncryptographic PRNGs are inappropriate whenever information security is involved).
Although java.security.SecureRandom allows seeds of unlimited length to be passed in, the SecureRandom implementation could use an underlying PRNG (e.g., "SHA1PRNG" or "DRBG"). And it depends on that PRNG's maximum cycle length whether it's capable of choosing from among 52 factorial permutations.
Let me apologize in advance, because this is a little tough to understand...
First of all, you already know that java.util.Random is not completely random at all. It generates sequences in a perfectly predictable way from the seed. You are completely correct that, since the seed is only 64 bits long, it can only generate 2^64 different sequences. If you were to somehow generate 64 real random bits and use them to select a seed, you could not use that seed to randomly choose between all of the 52! possible sequences with equal probability.
However, this fact is of no consequence as long as you're not actually going to generate more than 2^64 sequences, as long as there is nothing 'special' or 'noticeably special' about the 2^64 sequences that it can generate.
Lets say you had a much better PRNG that used 1000-bit seeds. Imagine you had two ways to initialize it -- one way would initialize it using the whole seed, and one way would hash the seed down to 64 bits before initializing it.
If you didn't know which initializer was which, could you write any kind of test to distinguish them? Unless you were (un)lucky enough to end up initializing the bad one with the same 64 bits twice, then the answer is no. You could not distinguish between the two initializers without some detailed knowledge of some weakness in the specific PRNG implementation.
Alternatively, imagine that the Random class had an array of 2^64 sequences that were selected completely and random at some time in the distant past, and that the seed was just an index into this array.
So the fact that Random uses only 64 bits for its seed is actually not necessarily a problem statistically, as long as there is no significant chance that you will use the same seed twice.
Of course, for cryptographic purposes, a 64 bit seed is just not enough, because getting a system to use the same seed twice is computationally feasible.
EDIT:
I should add that, even though all of the above is correct, that the actual implementation of java.util.Random is not awesome. If you are writing a card game, maybe use the MessageDigest API to generate the SHA-256 hash of "MyGameName"+System.currentTimeMillis(), and use those bits to shuffle the deck. By the above argument, as long as your users are not really gambling, you don't have to worry that currentTimeMillis returns a long. If your users are really gambling, then use SecureRandom with no seed.
I'm going to take a bit of a different tack on this. You're right on your assumptions - your PRNG isn't going to be able to hit all 52! possibilities.
The question is: what's the scale of your card game?
If you're making a simple klondike-style game? Then you definitely don't need all 52! possibilities. Instead, look at it like this: a player will have 18 quintillion distinct games. Even accounting for the 'Birthday Problem', they'd have to play billions of hands before they'd run into the first duplicate game.
If you're making a monte-carlo simulation? Then you're probably okay. You might have to deal with artifacts due to the 'P' in PRNG, but you're probably not going to run into problems simply due to a low seed space (again, you're looking at quintillions of unique possibilities.) On the flip side, if you're working with large iteration count, then, yeah, your low seed space might be a deal-breaker.
If you're making a multiplayer card game, particularly if there's money on the line? Then you're going to need to do some googling on how the online poker sites handled the same problem you're asking about. Because while the low seed space issue isn't noticeable to the average player, it is exploitable if it's worth the time investment. (The poker sites all went through a phase where their PRNGs were 'hacked', letting someone see the hole cards of all the other players, simply by deducing the seed from exposed cards.) If this is the situation you're in, don't simply find a better PRNG - you'll need to treat it as seriously as a Crypto problem.
Short solution which is essentially the same of dasblinkenlight:
// Java 7
SecureRandom random = new SecureRandom();
// Java 8
SecureRandom random = SecureRandom.getInstanceStrong();
Collections.shuffle(deck, random);
You don't need to worry about the internal state. Long explanation why:
When you create a SecureRandom instance this way, it accesses an OS specific
true random number generator. This is either an entropy pool where values are
accessed which contain random bits (e.g. for a nanosecond timer the nanosecond
precision is essentially random) or an internal hardware number generator.
This input (!) which may still contain spurious traces are fed into a
cryptographically strong hash which removes those traces. That is the reason those CSPRNGs are used, not for creating those numbers themselves! The SecureRandom has a counter which traces how many bits were used (getBytes(), getLong() etc.) and refills the SecureRandom with entropy bits when necessary.
In short: Simply forget objections and use SecureRandom as true random number generator.
If you consider the number as just an array of bits (or bytes) then maybe you could use the (Secure)Random.nextBytes solutions suggested in this Stack Overflow question, and then map the array into a new BigInteger(byte[]).
A very simple algorithm is to apply SHA-256 to a sequence of integers incrementing from 0 upwards. (A salt can be appended if desired to "get a different sequence".) If we assume that the output of SHA-256 is "as good as" uniformly distributed integers between 0 and 2256 - 1 then we have enough entropy for the task.
To get a permutation from the output of SHA256 (when expressed as an integer) one simply needs to reduce it modulo 52, 51, 50... as in this pseudocode:
deck = [0..52]
shuffled = []
r = SHA256(i)
while deck.size > 0:
pick = r % deck.size
r = floor(r / deck.size)
shuffled.append(deck[pick])
delete deck[pick]
My Empirical research results are Java.Random is not totally truly random. If you try yourself by using Random class "nextGaussian()"-method and generate enough big sample population for numbers between -1 and 1, the graph is normal distbruted field know as Gaussian Model.
Finnish goverment owned gambling-bookmarker have a once per day whole year around every day drawn lottery-game where winning table shows that the Bookmarker gives winnings in normal distrbuted way. My Java Simulation with 5 million draws shows me that with nextInt() -methdod used number draw, winnings are normally distributed same kind of like the my Bookmarker deals the winnings in each draw.
My best picks are avoiding numbers 3 and 7 in each of ending ones and that's true that they are rarely in winning results. Couple of times won five out of five picks by avoiding 3 and 7 numbers in ones column in Integer between 1-70 (Keno).
Finnish Lottery drawn once per week Saturday evenings If you play System with 12 numbers out of 39, perhaps you get 5 or 6 right picks in your coupon by avoiding 3 and 7 values.
Finnish Lottery have numbers 1-40 to choose and it takes 4 coupon to cover all the nnumbers with 12 number system. The total cost is 240 euros and in long term it's too expensive for the regural gambler to play without going broke. Even if you share coupons to other customers available to buy still you have to be quite a lucky if you want to make profit.
I have read and watched many youtube videos & links which all provide same solution which is:
Use a distributed counter like zookeeper
Counter max limit can be 3.5 trillion
Convert the Counter value to Base62
which is all fine when the counter value is small.
e.g.
generated counter value: 120001 => base62 value FMJQmhBR
but when the counter provides large counter value like below the base62 value length also increases.
generated counter value: 120003658=> base62 value HRGZF8RiHC6y
So how can this be a solution for exact tiny url with exact 8 length.
https://www.linqz.io/2018/10/how-to-build-a-tiny-url-service-that-scales-to-billions.html
https://www.youtube.com/watch?v=eCLqmPBIEYs
https://www.youtube.com/watch?v=JQDHz72OA3c&t=1862s
First: there absolutely is a compression limit. If your chosen representation has a maximum length, that imposes a hard limit on your key space.
Let's unpack that a little. Let's say you've got 80 guests at a party, and you want to give each guest a unique label (for their drink cup or something). If you've decided that each label will be a single letter from the English alphabet, then you only have enough unique labels for 26 guests.
Second: FMJQmhBR is not the most efficient way to represent the number 120001. It takes 17 bits in binary: 11101010011000001 (not sure which endianness that is). 16 bits is just two ASCII characters, and three ASCII characters can accommodate nearly 17 million unique values. And that's without any kind of special, ZIP-like compression.
--
I think most URL shorteners work essentially by assigning a counting number to each URL that someone shortens. So, the very first URL that gets submitted will be given ID=1: they save the whole URL in the database and associate it with that number. The second URL gets ID=2, etc.
That's pretty crude, though. For a variety of reasons, they don't want to hand those IDs out in order. But if they know how long they want the identifiers to be, it's not hard hand those IDs out in random order:
When someone submits a URL, the system picks a random number between 0 and the highest-possible ID. If the URL identifiers are all supposed to be 8 ASCII characters, that means they pick a random number between 0 and 2^(8*8) = 1.844674407e19.
Then they check their DB to see if they've handed out that ID. If they have, they pick a different random number. They repeat this until they pick an ID that hasn't been handed out. (I think there are more efficient algorithms for this, but the effect is the same and this is easiest to understand.)
Given that you are not hashing every url, but a vaguely-predictable number, you could hash the result and take the first N bits
However, there are many solutions for what to do for collisions
ignore them - they will be rare (ideally)
choose the next value
hash the result again (with your input)
increment the size of the returned string
...
Here's a great video on cuckoo hashing (which is a structure of hashes relevant here):
https://www.youtube.com/watch?v=HRzg0SzFLQQ
Here's an example in Python which finds an 8-character string from the hash which should be fairly unique (this could then be collected into a sorted data structure mapping it into a URL)
This works by first hashing the value with an avalanching hash (SHA-265) and then loops to find the minimum amount of it (slice from the front of the hex string) to form an 8-char base62 string
This could be made much more efficient (even, for example by bisecting), but may be clearer as-is and depends hugely on unspecified algorithm requirements
import hashlib
BASE62 = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
m = hashlib.sha256()
m.update("https://stackoverflow.com/questions/65714033/tiny-url-system-design".encode())
digest = m.digest() # hash as bytes b',\xdb3\x8c\x98g\xd6\x8b\x99\xb6\x98#.\\\xd1\x07\xa0\x8f\x1e\xb4\xab\x1eg\xdd\xda\xd6\xa3\x1d\xb0\xb2`9'
hex_str = digest.hex() # string of hex chars 2cdb338c9867d68b99b698232e5cd107a08f1eb4ab1e67dddad6a31db0b26039
for hashlen in range(100, 1, -1):
number = int(hex_str[:hashlen], 16) # first_n_chars(str(hex)) -> decimal
val = ""
while number != 0:
val = "{}{}".format(BASE62[number % 62], val) # append new chars to front
number = number // 62 # integer division
if len(val) <= 8:
break
print(val) # E0IxW0zn
base62 logic from How to fix the code for base62 encoding with Python3?
I'm looking for a way to implement a hashing mechanism to hash an input (0 to 2^32 - 1) to a fixed possibly 12 character hash.
Background:
I have a transaction table, where the primary key is auto increment (max size is 2^32) and I have to show an invoice no to the client which has to be of decent characters length (I'm thinking 12) and so since the client shouldn't get id as 0000-0000-0001, I was thinking hashing is the best way to go.
The main requirement (that I can think of) is that many to one mapping should never take place, and should not be slow.
Would it be okay if I use a common hashing mechanism and then drop the extra characters. (md5 for example in php generates 32 character string)?
The way I understand, there is no need to be secure cryptographically, and so I can generate a custom hash if possible.
Similar links:
1) Symmetric Bijective Algorithm for Integers
2) Pseudo-random-looking one-to-one int32->int32 function
Using md5 and chopping off most of it is not a good idea, because there is no guarantee that you would get a unique cache. Besides, you have much easier alternatives available to you, because you have a lot more bits than you need.
Values in the range [0..232] need 32 bit (duh!). You have 12 printable characters, which give you 72 bits if you stay within Base-64 encoding range of characters. You don't even need that many characters - you can use three bits per character for the initial eight characters, and two bits per character for the last four digits. This way your 12 characters would stay in the range ['0'..'7'], and the last four would be in the range ['0'..'3']. Of course you are not bound to numeric digits - you could use letters for some groups of digits, to give it a more "randomized" appearance.
the id is auto increment, and I don't think that I should give invoice numbers as 000...001 and so on.
Start with least significant bits when you generate these representations, then proceed to least significant, or make an arbitrary (but fixed) map of which bits go to what digit in the 12-character representation. This way the IDs would not look sequential, but would remain fully reversible.
I am developing a application where user is only authenticated if he enters a serial key correctly. This serial key is matched with the serial key already present in database. This serial key should consists of 6 digit and 3 alphabets. Users get these key in written form from me.
How do I generate a large number (100,000,000 approx) of serial keys?
Simplest way in my opinion is:
find a desired number in range [1,10000000), let it be x and it
will represent your 6 digits.
Find 3 characters (let's assume in range a-z). Let them be a,b,c.
Your number is (a-'a' + b-'a'*26 + c-'a'*26*26)*10000000 + x
(Where 'a' is the ascii representation of the character 'a', and a-'a' means the numeric ascii subtraction)
Note that the generated number can even fit in a long - assuming it is 64 bits.
Generation of several numbers can be simply done with iteration, start with a=b=c='a', and x=0, and start advancing (increase by 1). Once you reached x=10000000, increase a, if a passed z - increase b, .... (similar to what you would do in normal integer addition arithmetic).
You can use a secure random number generator like SecureRandom to generate the keys.
But as already mentioned in a comment, if you generate that many keys, the space of all possible keys is not much larger. So it will be easy for an attacker to try out keys until one is found that works.
I want to convert a number value of 100 digits into lessthan 10 digits and vice versa.
So I pass that encoded number to mobile user and on getting back can make 100 digits number again.
I want to use it in PHP, .NET or JS.
But before that I need an algorithm for that.
I have some idea to use simple divide-subtract and add-multiply options in my mind to implement. But need some more secure than that.
What you're asking for is impossible. You are trying to pigeonhole 10^100 items into 10^10 boxes. Some box will get more than one item and so it's impossible to invert back to "the" original item.
You could encode the 100-digit base-10 numbers as a 56-digit base-62 number (use uppercase and lowercase Roman alphabet and digits 0-9). The math here is 100 * log(10) / log(62).
To encode using less than ten characters from some alphabet, you need an alphabet with ~2^34 symbols. The math here is 100 * log(10) / log(number of symbols). Good luck with that.
If you have more than 10 000 000 000 different possible values in the 100 digit number you can not possibly map that to a 10 digit number and reliably map back to the original number.
A 100 digit number, I assume this is a base ten number, When talking about numbers on computers talk of 'digits' is almost meaningless.
If you actually mean a 100bit integer, then this wont easily fit into a single 64bit integer ( range +/- 9,223,372,036,854,775,808 ) then you have not phrased your question all that well. And no amount of compression or encoding will let you represent 100bits using no more than 10bits.
If you mean 100 figures in base ten, then you are dealing with bignums so should probably just treat them as bytes and use a bignum library.
100 base ten figures is still less than 512 bits.
Assuming that the 100-digit number is base 10, then if my math is not wrong you'll need 10 base 100 digits to represent the same number. So instead of using just characters from 0-9, you'll need to expand the characters to include other glyphs, including upper-case and lower-case letters, etc., to complete a 100 character alphabet. OK, my math is wrong, so disregard this, but consider the next paragraph.
Another thought is to use a hashing algorithm to derive a 10-byte hash from your 100-digit number and use that as key in a server-side database (hash-table). No encoding/decoding, just send the key to the mobile client, the mobile client uses the key to fetch the 100-digit number from the server.