Message Digest Strength: Concatenation vs Iteration - security

If I have 3 fields that get exposed "in the clear", and I want to digitally sign these fields to make sure that they're not tampered with using a secure hash function. I have 2 options:
I can concatenate the 3 fields and use a digest to hash the whole thing as a single string, i.e., hash(field1 + field2 + field3 + salt)
I can iteratively hash the individual results, i.e., hash(field1 + hash(field2 + hash(field3 + salt)))
Obviously approach 1 will be faster than approach 2, but will approach 2 be any "stronger" in terms of preventing one from discovering the value of the salt by reverse-engineering the inputs from a wide variety of outputs (I believe so, but is it worth the extra cpu cost)?

First I must issue the standard comment that hashing is not signing. A digital signature is a process which involves keys and verifiers. Here, you just want to hash some data and keep the hash value in a "safe" place, so that you could extend the integrity of the hash value to the hashed data: you make sure that the hash value is not tampered with, and, by recomputing the hash over the data elements, and finding the same hash value, you gain confidence in the idea that the field elements were not tampered with either.
Then I must issue the second standard comment, which is that there is no performance issue until duly measured in realistic conditions. Hashing is fast. With even a not-so-fast hash function, a basic PC will be able to perform millions of hash operations per second.
Now, I see that you want to use a "salt". A salt is a piece of public data, whose purpose is to be distinct for each instance, so as to prevent decryption cost sharing. This makes sense in a setup where there is some encrypted data; as far as I can see from what you describe, there is nothing encrypted in your problem.
... unless you actually mean that you will keep your "salt" secret, and store the hash value along with the data field. In which case we are not talking about hashing anymore. Your "salt" would be more appropriately called a "key", since it is meant to remain confidential. And you do not want a hash but a MAC. Sometimes, MACs are called "signatures". This is not proper, but less improper than calling hashes "signatures". If what you want is a MAC (and your salt is really a key), then you should use neither of your constructions. Building a MAC is not easy: many handmade constructions fail utterly when it comes to security. Fortunately, there is a standard MAC called HMAC. HMAC uses an underlying hash function (use SHA-256) and a key in a smart way which turns them into a MAC. HMAC is supported by many cryptographic libraries.

Use an HMAC (hash-based message authentication code) instead of trying to make up your own. It will be more secure, and almost any platform already has a free implementation that you can use that someone else develops, tests, and maintains.
Who can say whether it "is worth the extra cpu cost"? How often will you be doing this? Will you actually have to buy more CPUs? How much do you pay for electricity? On the other side of the balance, what will it cost you if someone successfully tampers with data "protected" by a home-brewed algorithm?

Related

Why does HashMap need a cryptographically secure hashing function?

I'm reading a Rust book about HashMap hashing functions, and I can't understand these two sentences.
By default, HashMap uses a cryptographically secure hashing function that can provide resistance to Denial of Service (DoS) attacks. This is not the fastest hashing algorithm available, but the trade-off for better security that comes with the drop in performance is worth it.
I know what a cryptographically secure hash function is, but don't I understand the rationale behind it. From my understanding a good hash function for HashMap should only have three properties:
deterministic (the same object has same hash value)
be VERY fast,
has a uniform distribution of bits in hash value (meaning it will reduce collision)
Other properties, in cryptographically secure hash function, are not really relevant 99% (maybe even 99.99%) of the time for hash tables.
So my question is: What does "resistance to DoS attack and better security
" even mean in the context of HashMap?
Let's start backward: how do you DoS a HashMap?
Over the years, there have been multiple attacks on various software stacks based on Hash Flooding. If you know which framework a site is powered by, and therefore which hash function is used, and this hash function is not cryptographically secure then you may be able to pre-compute, offline, a large set of strings hashing to the same number.
Then, you simply inject this set into the site, and for each (simple) request, it does a disproportionately large amount of work as inserting N elements takes O(N2) operations.
Rust was conceived with the benefit of hindsight, and therefore attention was paid to avoiding this attack by default, reasoning that users who really need performance out of HashMap would simply switch the hash function.
Let's say we use HashMap to store some user data in a web-application. Suppose that users can choose (part of) the key in some way – maybe the key is a username or a filename of an uploaded file or anything like that.
If we are not using a cryptographically secure hash function, this means that the attacker could possible craft multiple inputs that all map to the same output. Of course, a hash map has to deal with collisions, because they occur naturally.
But when unnaturally many collisions occur, the hash map implementation might do strange things. For example, looking up some keys could have a runtime of O(n). Or the hash map might think that it has to grow because of all the collisions; but growing won't solve the problem, so the hash map grows until all memory is used. In either case, it's bad. Hash maps just assume that statistically, collisions rarely occur.
Of course, this is not a "stealing user data" attack -- at least not directly. But if one part of a system is weak, this makes it easier for attackers to find other weaknesses.
A cryptographically secure hash function prevents this attack, since the attacker cannot possibly craft multiple keys that map to the same value (at least not without trying out all keys).
is not really relevant 99% (maybe even 99.99%) of the time for hash tables.
Yes, probably. But this is difficult to balance. I guess we all would agree that if 20% of users would have security problems in their application due to an unsecure hash function (while 80% don't care), it's still a good idea to use the "secure by default" approach. What about 5%/95%? What about 1%/99%? Hard to tell where the threshold is, right?
There has been a ton of discussion about this already. Because yes, most people only notice the slowness of the hash map. Maybe the situation I described above is incredibly rare and it isn't worth slowing down all other users' code by default. But this has been decided, the default hash function won't change, and luckily you can choose your own hash function.
If a server application stores user input (such as post data in a web application) in a hash table, a malicious user may try to provide a large number of inputs that all have the same hash value, leading to a large number of hash collisions and thus slowing down operations on the map significantly, to the point that it can be used as a DoS attack (as described in this article for example).
If the hash is cryptographically secure, attackers will have a much harder time trying to find inputs with the same hash value.

Why doesn't having the code to the MD5 function help hackers break it?

I believe I can download the code to PHP or Linux or whatever and look directly at the source code for the MD5 function. Could I not then reverse engineer the encryption?
Here's the code - http://dollar.ecom.cmu.edu/sec/cryptosource.htm
It seems like any encryption method would be useless if "the enemy" has the code it was created with. Am I wrong?
That is actually a good question.
MD5 is a hash function -- it "mixes" input data in such a way that it should be unfeasible to do a number of things, including recovering the input given the output (it is not encryption, there is no key and it is not meant to be inverted -- rather the opposite). A handwaving description is that each input bit is injected several times in a large enough internal state, which is mixed such that any difference quickly propagates to the whole state.
MD5 is public since 1992. There is no secret, and has never been any secret, to the design of MD5.
MD5 is considered cryptographically broken since 2004, year of publication of the first collision (two distinct input messages which yield the same output); it was considered "weak" since 1996 (when some structural properties were found, which were believed to ultimately help in building collisions). However, there are other hash functions, which are as public as MD5 is, and for which no weakness is known yet: the SHA-2 family. Newer hash functions are currently being evaluated as part of the SHA-3 competition.
The really troubling part is that there is no known mathematical proof that a hash function may actually exist. A hash function is a publicly described efficient algorithm, which can be embedded as a logic circuit of a finite, fixed and small size. For the practitioners of computational complexity, it is somewhat surprising that it is possible to exhibit a circuit which cannot be inverted. So right now we only have candidates: functions for which nobody has found weaknesses yet, rather than function for which no weakness exists. On the other hand, the case of MD5 shows that, apparently, getting from known structural weaknesses to actual collisions to attacks takes a substantial amount of time (weaknesses in 1996, collisions in 2004, applied collisions -- to a pair of X.509 certificates -- in 2008), so the current trend is to use algorithm agility: when we use a hash function in a protocol, we also think about how we could transition to another, should the hash function prove to be weak.
It is not an encryption, but a one way hashing mechanism. It digests the string and produces a (hopefully) unique hash.
If it were a reversible encryption, zip and tar.gz formats would be quite verbose. :)
The reason it doesn't help hackers too much (obviously knowing how one is made is beneficial) is that if they find a password to a system that is hashed, e.g. 2fcab58712467eab4004583eb8fb7f89, they need to know the original string used to create it, and also if any salt was used. That is because when you login, for obvious reasons, the password string is hashed with the same method as it is generated and then that resulting hash is compared to what is stored.
Also, many developers are migrating to bcrypt which incorporates a work factor, if the hashing takes 1 second as opposed to .01 second, it greatly slows down generating a rainbow table for you application, and those old PHP sites using md5() only become the low hanging fruit.
Further reading on bcrypt.
One of the criteria of good cryptographic operations is that knowledge of the algorithm should not make it easier to break the encryption. So an encryption should not be reversible without knowledge of the algorithm and the key, and a hash function must not be reversible regardless of knowledge of the algorithm (the term used is "computationally infeasible").
MD5 and other hash function (like SHA-1 SHA-256, etc) perform a one-way operation on data that creates a digest or "fingerprint" that is usually much smaller than than the plaintext. This one way function cannot be reversed to retrieve the plaintext, even when you know exactly what the function does.
Likewise, knowledge of an encryption algorithm doesn't make it any easier (assuming a good algorithm) to recover plaintext from ciphertext. The reverse process is "computationally infeasible" without knowledge of the encryption key used.

why should a good hash algorithm not allow attackers to find two messages producing the same hash?

I was reading wikipedia, and it says
Cryptographic hash functions are a third type of cryptographic algorithm.
They take a message of any length as input, and output a short,
fixed length hash which can be used in (for example) a digital signature.
For good hash functions, an attacker cannot find two messages that produce the same hash.
But why? What I understand is that you can put the long Macbeth story into the hash function and get a X long hash out of it. Then you can put in the Beowulf story to get another hash out of it again X long.
So since this function maps loads of things into a shorter length, there is bound to be overlaps, like I might put in the story of the Hobit into the hash function and get the same output as Beowulf, ok, but this is inevitable right (?) since we are producing a shorter length output from our input? And even if the output is found, why is it a problem?
I can imagine if I invert it and get out Hobit instead of Beowulf, that would be bad but why is it useful to the attacker?
Best,
Yes, of course there will be collisions for the reasons you describe.
I suppose the statement should really be something like this: "For good hash functions, an attacker cannot find two messages that produce the same hash, except by brute-force".
As for the why...
Hash algorithms are often used for authentication. By checking the hash of a message you can be (almost) certain that the message itself hasn't been tampered with. This relies on it being infeasible to find two messages that generate the same hash.
If a hash algorithm allows collisions to be found relatively easily then it becomes useless for authentication because an attacker could then (theoretically) tamper with a message and have the tampered message generate the same hash as the original.
Yes, it's inevitable that there will be collisions when mapping a long message onto a shorter hash, as the hash cannot contain all possible values of the message. For the same reason you cannot 'invert' the hash to uniquely produce either Beowulf or The Hobbit - but if you generated every possible text and filtered out the ones that had your particular hash value, you'd find both texts (amongst billions of others).
The article is saying that it should be hard for an attacker to find or construct a second message that has the same hash value as a first. Cryptographic hash functions are often used as proof that a message hasn't been tampered with - if even a single bit of data flips then the hash value should be completely different.
A couple of years back, Dutch researchers demonstrated weaknesses in MD5 by publishing a hash of their "prediction" for the US presidential election. Of course, they had no way of knowing the outcome in advance - but with the computational power of a PS3 they constructed a PDF file for each candidate, each with the same hash value. The implications for MD5 - already on its way down - as a trusted algorithm for digital signatures became even more dire...
Cryptographic hashes are used for authentication. For instance, peer-to-peer protocols rely heavily on them. They use them to make sure that an ill-intentioned peer cannot spoil the download for everyone else by distributing packets that contain garbage. The torrent file that describes a download contains the hashes for each block. With this check in place, the victim peer can find out that he has been handled a corrupted block and download it again from someone else.
The attacker would like to replace Beowulf by Hobbit to increase saxon poetry's visibility, but the cryptographic hash that is used in the protocol won't let him.
If it is easy to find collisions then the attacker could create malicious data, and simply prepend it with dummy data until the collision is found. The hash check would then pass for the malicious data. That is why collisions should only be possible via brute force and be as rare as possible.
Alternatively collisions are also a problem with Certificates.

Is it possible to reverse a SHA-1 hash?

Is it possible to reverse a SHA-1?
I'm thinking about using a SHA-1 to create a simple lightweight system to authenticate a small embedded system that communicates over an unencrypted connection.
Let's say that I create a sha1 like this with input from a "secret key" and spice it with a timestamp so that the SHA-1 will change all the time.
sha1("My Secret Key"+"a timestamp")
Then I include this SHA-1 in the communication and the server, which can do the same calculation. And hopefully, nobody would be able to figure out the "secret key".
But is this really true?
If you know that this is how I did it, you would know that I did put a timestamp in there and you would see the SHA-1.
Can you then use those two and figure out the "secret key"?
secret_key = bruteforce_sha1(sha1, timestamp)
Note1:
I guess you could brute force in some way, but how much work would that actually be?
Note2:
I don't plan to encrypt any data, I just would like to know who sent it.
No, you cannot reverse SHA-1, that is exactly why it is called a Secure Hash Algorithm.
What you should definitely be doing though, is include the message that is being transmitted into the hash calculation. Otherwise a man-in-the-middle could intercept the message, and use the signature (which only contains the sender's key and the timestamp) to attach it to a fake message (where it would still be valid).
And you should probably be using SHA-256 for new systems now.
sha("My Secret Key"+"a timestamp" + the whole message to be signed)
You also need to additionally transmit the timestamp in the clear, because otherwise you have no way to verify the digest (other than trying a lot of plausible timestamps).
If a brute force attack is feasible depends on the length of your secret key.
The security of your whole system would rely on this shared secret (because both sender and receiver need to know, but no one else). An attacker would try to go after the key (either but brute-force guessing or by trying to get it from your device) rather than trying to break SHA-1.
SHA-1 is a hash function that was designed to make it impractically difficult to reverse the operation. Such hash functions are often called one-way functions or cryptographic hash functions for this reason.
However, SHA-1's collision resistance was theoretically broken in 2005. This allows finding two different input that has the same hash value faster than the generic birthday attack that has 280 cost with 50% probability. In 2017, the collision attack become practicable as known as shattered.
As of 2015, NIST dropped SHA-1 for signatures. You should consider using something stronger like SHA-256 for new applications.
Jon Callas on SHA-1:
It's time to walk, but not run, to the fire exits. You don't see smoke, but the fire alarms have gone off.
The question is actually how to authenticate over an insecure session.
The standard why to do this is to use a message digest, e.g. HMAC.
You send the message plaintext as well as an accompanying hash of that message where your secret has been mixed in.
So instead of your:
sha1("My Secret Key"+"a timestamp")
You have:
msg,hmac("My Secret Key",sha(msg+msg_sequence_id))
The message sequence id is a simple counter to keep track by both parties to the number of messages they have exchanged in this 'session' - this prevents an attacker from simply replaying previous-seen messages.
This the industry standard and secure way of authenticating messages, whether they are encrypted or not.
(this is why you can't brute the hash:)
A hash is a one-way function, meaning that many inputs all produce the same output.
As you know the secret, and you can make a sensible guess as to the range of the timestamp, then you could iterate over all those timestamps, compute the hash and compare it.
Of course two or more timestamps within the range you examine might 'collide' i.e. although the timestamps are different, they generate the same hash.
So there is, fundamentally, no way to reverse the hash with any certainty.
In mathematical terms, only bijective functions have an inverse function. But hash functions are not injective as there are multiple input values that result in the same output value (collision).
So, no, hash functions can not be reversed. But you can look for such collisions.
Edit
As you want to authenticate the communication between your systems, I would suggest to use HMAC. This construct to calculate message authenticate codes can use different hash functions. You can use SHA-1, SHA-256 or whatever hash function you want.
And to authenticate the response to a specific request, I would send a nonce along with the request that needs to be used as salt to authenticate the response.
It is not entirely true that you cannot reverse SHA-1 encrypted string.
You cannot directly reverse one, but it can be done with rainbow tables.
Wikipedia:
A rainbow table is a precomputed table for reversing cryptographic hash functions, usually for cracking password hashes. Tables are usually used in recovering a plaintext password up to a certain length consisting of a limited set of characters.
Essentially, SHA-1 is only as safe as the strength of the password used. If users have long passwords with obscure combinations of characters, it is very unlikely that existing rainbow tables will have a key for the encrypted string.
You can test your encrypted SHA-1 strings here:
http://sha1.gromweb.com/
There are other rainbow tables on the internet that you can use so Google reverse SHA1.
Note that the best attacks against MD5 and SHA-1 have been about finding any two arbitrary messages m1 and m2 where h(m1) = h(m2) or finding m2 such that h(m1) = h(m2) and m1 != m2. Finding m1, given h(m1) is still computationally infeasible.
Also, you are using a MAC (message authentication code), so an attacker can't forget a message without knowing secret with one caveat - the general MAC construction that you used is susceptible to length extension attack - an attacker can in some circumstances forge a message m2|m3, h(secret, m2|m3) given m2, h(secret, m2). This is not an issue with just timestamp but it is an issue when you compute MAC over messages of arbitrary length. You could append the secret to timestamp instead of pre-pending but in general you are better off using HMAC with SHA1 digest (HMAC is just construction and can use MD5 or SHA as digest algorithms).
Finally, you are signing just the timestamp and the not the full request. An active attacker can easily attack the system especially if you have no replay protection (although even with replay protection, this flaw exists). For example, I can capture timestamp, HMAC(timestamp with secret) from one message and then use it in my own message and the server will accept it.
Best to send message, HMAC(message) with sufficiently long secret. The server can be assured of the integrity of the message and authenticity of the client.
You can depending on your threat scenario either add replay protection or note that it is not necessary since a message when replayed in entirety does not cause any problems.
Hashes are dependent on the input, and for the same input will give the same output.
So, in addition to the other answers, please keep the following in mind:
If you start the hash with the password, it is possible to pre-compute rainbow tables, and quickly add plausible timestamp values, which is much harder if you start with the timestamp.
So, rather than use
sha1("My Secret Key"+"a timestamp")
go for
sha1("a timestamp"+"My Secret Key")
I believe the accepted answer is technically right but wrong as it applies to the use case: to create & transmit tamper evident data over public/non-trusted mediums.
Because although it is technically highly-difficult to brute-force or reverse a SHA hash, when you are sending plain text "data & a hash of the data + secret" over the internet, as noted above, it is possible to intelligently get the secret after capturing enough samples of your data. Think about it - your data may be changing, but the secret key remains the same. So every time you send a new data blob out, it's a new sample to run basic cracking algorithms on. With 2 or more samples that contain different data & a hash of the data+secret, you can verify that the secret you determine is correct and not a false positive.
This scenario is similar to how Wifi crackers can crack wifi passwords after they capture enough data packets. After you gather enough data it's trivial to generate the secret key, even though you aren't technically reversing SHA1 or even SHA256. The ONLY way to ensure that your data has not been tampered with, or to verify who you are talking to on the other end, is to encrypt the entire data blob using GPG or the like (public & private keys). Hashing is, by nature, ALWAYS insecure when the data you are hashing is visible.
Practically speaking it really depends on the application and purpose of why you are hashing in the first place. If the level of security required is trivial or say you are inside of a 100% completely trusted network, then perhaps hashing would be a viable option. Hope no one on the network, or any intruder, is interested in your data. Otherwise, as far as I can determine at this time, the only other reliably viable option is key-based encryption. You can either encrypt the entire data blob or just sign it.
Note: This was one of the ways the British were able to crack the Enigma code during WW2, leading to favor the Allies.
Any thoughts on this?
SHA1 was designed to prevent recovery of the original text from the hash. However, SHA1 databases exists, that allow to lookup the common passwords by their SHA hash.
Is it possible to reverse a SHA-1?
SHA-1 was meant to be a collision-resistant hash, whose purpose is to make it hard to find distinct messages that have the same hash. It is also designed to have preimage-resistant, that is it should be hard to find a message having a prescribed hash, and second-preimage-resistant, so that it is hard to find a second message having the same hash as a prescribed message.
SHA-1's collision resistance is broken practically in 2017 by Google's team and NIST already removed the SHA-1 for signature purposes in 2015.
SHA-1 pre-image resistance, on the other hand, still exists. One should be careful about the pre-image resistance, if the input space is short, then finding the pre-image is easy. So, your secret should be at least 128-bit.
SHA-1("My Secret Key"+"a timestamp")
This is the pre-fix secret construction has an attack case known as the length extension attack on the Merkle-Damgard based hash function like SHA-1. Applied to the Flicker. One should not use this with SHA-1 or SHA-2. One can use
HMAC-SHA-256 (HMAC doesn't require the collision resistance of the hash function therefore SHA-1 and MD5 are still fine for HMAC, however, forgot about them) to achieve a better security system. HMAC has a cost of double call of the hash function. That is a weakness for time demanded systems. A note; HMAC is a beast in cryptography.
KMAC is the pre-fix secret construction from SHA-3, since SHA-3 has resistance to length extension attack, this is secure.
Use BLAKE2 with pre-fix construction and this is also secure since it has also resistance to length extension attacks. BLAKE is a really fast hash function, and now it has a parallel version BLAKE3, too (need some time for security analysis). Wireguard uses BLAKE2 as MAC.
Then I include this SHA-1 in the communication and the server, which can do the same calculation. And hopefully, nobody would be able to figure out the "secret key".
But is this really true?
If you know that this is how I did it, you would know that I did put a timestamp in there and you would see the SHA-1. Can you then use those two and figure out the "secret key"?
secret_key = bruteforce_sha1(sha1, timestamp)
You did not define the size of your secret. If your attacker knows the timestamp, then they try to look for it by searching. If we consider the collective power of the Bitcoin miners, as of 2022, they reach around ~293 double SHA-256 in a year. Therefore, you must adjust your security according to your risk. As of 2022, NIST's minimum security is 112-bit. One should consider the above 128-bit for the secret size.
Note1: I guess you could brute force in some way, but how much work would that actually be?
Given the answer above. As a special case, against the possible implementation of Grover's algorithm ( a Quantum algorithm for finding pre-images), one should use hash functions larger than 256 output size.
Note2: I don't plan to encrypt any data, I just would like to know who sent it.
This is not the way. Your construction can only work if the secret is mutually shared like a DHKE. That is the secret only known to party the sender and you. Instead of managing this, a better way is to use digital signatures to solve this issue. Besides, one will get non-repudiation, too.
Any hashing algorithm is reversible, if applied to strings of max length L. The only matter is the value of L. To assess it exactly, you could run the state of art dehashing utility, hashcat. It is optimized to get best performance of your hardware.
That's why you need long passwords, like 12 characters. Here they say for length 8 the password is dehashed (using brute force) in 24 hours (1 GPU involved). For each extra character multiply it by alphabet length (say 50). So for 9 characters you have 50 days, for 10 you have 6 years, and so on. It's definitely inaccurate, but can give us an idea, what the numbers could be.

Is It Possible To Reconstruct a Cryptographic Hash's Key

We would like to cryptographically (SHA-256) hash a secret value in our database. Since we want to use this as a way to lookup individual records in our database, we cannot use a different random salt for each encrypted value.
My question is: given unlimited access to our database, and given that the attacker knows at least one secret value and hashed value pair, is it possible for the attacker to reverse engineer the cryptographic key? IE, would the attacker then be able to reverse all hashes and determine all secret values?
It seems like this defeats the entire purpose of a cryptographic hash if it is the case, so perhaps I'm missing something.
There are no published "first pre-image" attacks against SHA-256. Without such an attack to open a shortcut, it is impossible for an attacker to the recover a secret value from its SHA-256 hash.
However, the mention of a "secret key" might indicate some confusion about hashes. Hash algorithms don't use a key. So, if an attacker were able to attack one "secret-value–hash-value" pair, he wouldn't learn a "key" that would enable him to easily invert the rest of the hash values.
When a hash is attacked successfully, it is usually because the original message was from a small space. For example, most passwords are chosen from a relatively short list of real words, perhaps with some simple permutations. So, rather than systematically testing every possible password, the attacker starts with an ordered list of the few billion most common passwords. To avoid this, it's important to choose the "secret value" randomly from a large space.
There are message authentication algorithms that hash a secret key together with some data. These algorithms are used to protect the integrity of the message against tampering. But they don't help thwart pre-image attacks.
In short, yes.
No, a SHA hash is not reversible (at least not easily). When you Hash something if you need to reverse it you need to reconstruct the hash. This is usually done with a private (salt) and public key.
For example, if I'm trying to prevent access based off my user id. I would hash my user id and the salt. Let say MD5 for example. My user id is "12345" and the salt is "abcde"
So I will hash the string "12345_abcde", which return a hash of "7b322f78afeeb81ad92873b776558368"
Now I will pass to the validating application the hash and the public key, "12345" which is the public key and the has.
The validating application, knows the salt, so it hashes the same values. "12345_abcde", which in turn would generate the exact same hash. I then compare the hash i validated with the one passed off and they match. If I had somehow modified the public key without modifying the hash, a different has would have been generated resulting in a mismatch.
Yes it's possible, but not in this lifetime.
Modern brute-force attacks using multiple GPUs could crack this in short order. I recommend you follow the guidelines for password storage for this application. Here are the current password storage guidelines from OWASP. Currently, they recommend a long salt value, and PBKDF2 with 64,000 iterations, which iteratively stretches the key and makes it computationally complex to brute force the input values. Note that this will also make it computationally complex for you to generate your key values, but the idea is that you will be generating keys far less frequently than an attacker would have to. That said, your design requires many more key derivations than a typical password storage/challenge application, so your design may be fatally flawed. Also keep in mind that the iteration count should doubled every 18 months to make the computational complexity follow Moore's Law. This means that your system would need some way of allowing you to rehash these values (possibly by combining hash techniques). Over time, you will find that old HMAC functions are broken by cryptanalysts, and you need to be ready to update your algorithms. For example, a single iteration of MD5 or SHA-1 used to be sufficient, but it is not anymore. There are other HMAC functions that could also suit your needs that wouldn't require PBKDF2 (such as bcrypt or scrypt), but PBKDF2 is currently the industry standard that has received the most scrutiny. One could argue that bcrypt or scrypt would also be suitable, but this is yet another reason why a pluggable scheme should be used to allow you to upgrade HMAC functions over time.

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