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What is nowadays (July 2012) the recommended number of bcrypt rounds for hashing a password for an average website (storing only name, emailaddress and home address, but no creditcard or medical information)?

In other words, what is the current capability of the bcrypt password cracking community? Several bcrypt libraries use 12 rounds (2^12 iterations) as the default setting. Is that the recommended workfactor? Would 6 rounds not be strong enough (which happens to be the limit for client-side bcrypt hashing in Javascript, see also Challenging challenge: client-side password hashing and server-side password verification)?

I have read answer which gives an in-depth discussion how to balance the various factors (albeit for PBKDF2-SHA256). However, I am looking for an actual number. A rule of thumb.

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I do 120.000, but it depends on your application. It just depends on your app, and your CPU power you can spend on it. E.g. if you have a 1 user login per second and using 2 cores only, you would not do more than 10.000 I think. Basically you need to check how long it takes with "time" command and see for yourself. Something close to second should be OK. – Andrew Smith Jul 14 '12 at 20:13
@Andrew: The speed of my own system should not be leading for the number of iterations. It is the current speed of the brute-forcers that should dictate how many iterations are considered safe. Hence my question: how many iterations are nowadays considered safe? – Jason Smith Jul 14 '12 at 21:43
@JasonSmith, The speed of your system is relevant, because it determines how many iterations you can reasonably do without bogging down your system. You want as many iterations as possible, because the reality is that no number of iterations is enough to be completely safe: we're just reducing the risk somewhat, not eliminating it. There is no realistic number of rounds that is large enough to be considered safe. If you ask a question here, please be prepared to listen to the answers you get. – D.W. Jul 15 '12 at 22:59
@D.W. wrote "please be prepared to listen to the answers you get", sorry if I gave the impression being pedantic or stubborn. Perhaps as a non-native English speaker my comments conveyed the wrong message. I do appreciate all answers, and try hard to understand the rationale behind them. – Jason Smith Jul 16 '12 at 12:08
@JasonSmith, ok, my fault for misunderstanding, sorry! – D.W. Jul 16 '12 at 17:46

3 Answers 3

up vote 11 down vote accepted

I think the answer to all of your questions is already contained in Thomas Pornin's answer. You linked to it, so you presumably know about it, but I suggest that you read it again.

The basic principles are: don't choose a number of rounds; instead, choose the amount of time password verification will take on your server, then calculate the number of rounds based upon that. You want verification to take as long as you can stand.

For some examples of concrete numbers, see Thomas Pornin's answer. He suggests a reasonable goal would be for password verification/hashing to take 8 milliseconds per password. That still lets your server verify 125 passwords per second, which seems more than enough. Thomas estimates that, if this is your goal, about 20,000 rounds is in the right ballpark.

However, the optimal number of rounds will change with your processor. Ideally, you would benchmark how long it takes on your processor and choose the number accordingly. This doesn't take that long; so for best results, just whip up the script and work out how many rounds are needed to ensure that password hashing takes about 8 milliseconds on your server (or longer, if you can bear it).

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Time doesn't matter, money is why the world spins. – rook Jul 15 '12 at 23:39
P.S. I do not recommend implementing bcrypt in Javascript, as performance will likely be very poor. I assume you are computing bcrypt on the server. (I do not think there is sufficient value to computing bcrypt on the client, so I do not recommend computing bcrypt on the client.) I suggest using a native, optimized implementation of bcrypt; that will run much faster. – D.W. Jul 16 '12 at 17:49
@David天宇Wong, the number of rounds our system can bear is relevant. There is no practical number of rounds that was enough to make it impossible for NSA to crack any passwords (even weak ones). So you can never get 100% security -- it's always a tradeoff between how much harder you are making it for yourself, vs how much harder you are making it for the adversary. But given the realities of how users choose passwords, we can never make it as hard as we would really like for the adversary. This is risk mitigation, not risk elimination. – D.W. Feb 7 at 20:52
@David天宇Wong, a non-trivial number of people choose a weak password (say, 10 bits of entropy). We'd need, say, 2^70 iterations to make that secure against the NSA. If you did 2^70 iterations of bcrypt, no one could use it in practice, because it would be far too slow for the good guys. That's why I say there is no value for the number of iterations that both provides strong security against strong adversaries (like the NSA), and yet is also small enough to be practical for the legitimate users of the system. Anyway, we've gotten a bit far afield from the question that was asked. – D.W. Feb 8 at 1:21
@David天宇Wong, a password with 10 bits of entropy is normal. But if you don't like that, consider a password with 20 bits of entropy. (More than half of all users have a password with fewer than 20 bits of entropy.) Then you'll need 2^60 iterations of bcrypt to provide strong security for those passwords, but that's far too many for the good guys to do. Try working through this on your own. There are lots of resources about what entropy is -- this is not the place to explain/ask about it. Entropy is a fundamental concept that you have to understand, to understand password security. – D.W. Feb 8 at 1:51

When BCrypt was first published, in 1999, they listed their implementation's default cost factors:

  • normal user: 6
  • super user: 8

They also note:

Of course, whatever cost people choose should be reevaluated from time to time

A bcrypt cost of 6 means 64 rounds (26 = 64).

If we use that initial "normal user" value, we want to try adjusting for computing power inflation (assuming on average it doubles every 18 months).

R = R0 × 2(months/18)
R = 64 × 2(months/18)

Today (March 9, 2015) is 171 months since 12/31/1999 (or use 1/1/2000 for simplicity), the number of rounds should have doubled a little over 9 times:

R = 64 × 2(171/18)
R = 64 × 29.5
R = 64 × 724.1
R = 46,341.0

In the end, we want to convert that back to a cost factor

cost = ln(R) / ln(2)
cost = ln(46,341.0) / ln(2)
cost = 15.5

The practicality of a cost factor or 15 depends on the computing power of your server. For example, my desktop PC is an Intel Core i7-2700K CPU @ 3.50 GHz. I originally benchmarked a BCrypt implementation on 1/23/2014:

1/23/2014  Intel Core i7-2700K CPU @ 3.50 GHz

| Cost | Iterations        |    Duration |
|  8   |    256 iterations |     38.2 ms | <-- minimum allowed by BCrypt
|  9   |    512 iterations |     74.8 ms |
| 10   |  1,024 iterations |    152.4 ms | <-- current default (BCRYPT_COST=10)
| 11   |  2,048 iterations |    296.6 ms |
| 12   |  4,096 iterations |    594.3 ms |
| 13   |  8,192 iterations |  1,169.5 ms |
| 14   | 16,384 iterations |  2,338.8 ms |
| 15   | 32,768 iterations |  4,656.0 ms |
| 16   | 65,536 iterations |  9,302.2 ms |

But that was 2014

Those timings were originally calculated at the start of 2014. Only 156 months (rather than 171) months should have been used in my calculation:

R = 64 × 2(156/18)
R = 64 × 28.66
R = 64 × 406.8
R = 26,035.2

cost = ln(R) / ln(2)
cost = ln(26,035.2) / ln(2)
cost = 14.7

But the i7-2700K was already discontinued

The i7-2700K was already discontinued (Q1 2013) by the time i ran my benchmarks. It was released, and was state of the art, in Q4 2011. If i run the numbers for Q4 2011:

R = 64 × 2(129/18)
R = 64 × 27.16
R = 64 × 143.7
R = 9,196.8

cost = ln(R) / ln(2)
cost = ln(9,196.8) / ln(2)
cost = 13.2

A cost of 13 is, on my desktop, nearly 2 seconds over a second.

How long can you stand it?

That gives you a flavor of the kind of delays that the original implementers were considering when they wrote it: ~0.5-1 second.

But, of course, the longer you can stand, the better. Every BCrypt implementation i've seen used 10 as the default cost. And my implementation used that. I believe it is time for me to to increase the default cost to 12.

Future Proofing

I might also change the hash function:

hash = HashPassword("correct battery horse stapler");

i.e. the one where you rely on the default cost, to instead use an automatically sliding cost. This way the cost is self-increasing with time. Changing:

String HashPassword(String password)
   return BCrypt.HashPassword(password, BCRYPT_DEFAULT_COST);

to something like:

String HashPassword(String password)
     Rather than using a fixed default cost, run a micro-benchmark
     to figure out how fast the CPU is.
     Use that to make sure that it takes **at least** 250ms to calculate
     the hash
   Int32 costFactor = this.CalculateIdealCost();
   //Never use a cost lower than the default hard-coded cost
   if (costFactor < BCRYPT_DEFAULT_COST) 
      costFactor = BCRYPT_DEFAULT_COST;

   return BCrypt.HashPassword(password, costFactor);

Int32 CalculateIdealCost()
    //Benchmark using a cost of 5 (the second-lowest allowed)
    Int32 cost = 5;

    var sw = new Stopwatch();
    this.HashPassword("microbenchmark", cost);

    Double durationMS = sw.Elapsed.TotalMilliseconds;

    //Increasing cost by 1 would double the run time.
    //Keep increasing cost until the estimated duration is over 250 ms
    while (durationMS < 250)
       cost += 1;
       durationMS *= 2;

    return cost;

Edit 3/12/2015: Updated speed numbers. The Delphi XE6 32-bit compiler (c.2013) generates code an order of magnitude faster than Delphi 5 (c.1999) did for the same processor. The Delphi XE6 64-bit compiler generates code 20% slower than the 32-bit compiler.

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Great post, though I'd recommend against the automatic cost increase over time. Moore's law is more so about transistor density rather than CPU performance, the latter which has shown rather lacklustre growth the past few years. Also Moore's law is close to hitting a wall, where we'll need to change the foundational technology for processors to proceed growing. Nifty nonetheless! – andrewb Oct 20 at 22:52
@andrewb You're absolutely right about using Moore's law. I've since changed it to do a microbenchmark (e.g. BCrypt.HashPassword("benchmark", 5);) – Ian Boyd Oct 21 at 16:54
Uhm. Wouldn't that also reduce the cost if the server is under load when the microbenchmark runs? – John Morahan Oct 21 at 20:28
@JohnMorahan No; it only increases the cost. See comment //Never use a cost lower than the default hard-coded cost – Ian Boyd Oct 22 at 19:12
Yes, but if it's already been automatically increased from that, then returning to the hard-coded lower bound is still a decrease. – John Morahan Oct 22 at 22:45

Stronger Key Derivation via Sequential Memory-Hard Functions is a very good paper on the topic of key stretching. On page 14 it compares various hashing algorithms with how much money it will cost to break the hash, which is a useful way of thinking about these things. (On a side note ChromeOS uses Scrypt if TPM isn't available.)

The idea is that you want these password hashes to be unbroken for as long as possible. With Moore's law this is a exponentially fast moving target. Scrypt uses variable amount of memory and cpu, this variable could become heavier as a function of time. In that each time the client logs in you can update the password hash to be more secure. In the case of PBKDF2 this could look like rounds=2^(current_year-2000) or something like that.

Its important to note that you can't just offload this processing onto the client and expect your protocol to be secure. All client-side hashing authentication protocols I know of require the server to make an identical calculation in order to verify the authentication credentials (NTLM, NTLMv2, SRP, WPA-PSK...).

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I am aware I should match Moore's law. But that is exactly my question: how many iterations are nowadays considered safe given the current speed of the brute-forcers? – Jason Smith Jul 14 '12 at 21:47
@Jason Smith I don't think anyone can give you a real number because it is circumstantial. My answer was 2^12, which is 4096 and my rationale is because its 2012. – rook Jul 14 '12 at 22:02
Ah, I thought 2^(current_year-2000) was just an arbitrary example. Ok, so 12 rounds in 2012. – Jason Smith Jul 15 '12 at 10:44
No, 12 rounds is almost certainly not enough. – D.W. Jul 15 '12 at 22:59
@D.W. 4096 iterations is larger than most implementations i have seen, keep in mind next year it will be 8192... – rook Jul 15 '12 at 23:42

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