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Date: Wed, 03 Sep 2014 14:11:07 -0400
From: Bill Cox <>
Subject: A review per day - OmegaCrypt

Hash: SHA1

It's OmegaCypt's turn, assuming people don't mind me doing 2 per day :-)

OmegaCrypt uses CubeHash for it's cryptographic strength security, and
ChaCha for filling memory initially, and for generating pseudo-random
numbers.  I will not attempt to analyze these choices, or check their
implementation, since we could substitute CubeHash with Blake2b or
whatever if we wanted.  I think that the OmegaCrypt architecture can
easily be seen to produce secure hashes, as can easily be seen from
various choices, including the decision to only use the output from
respected cryptographic hash primitives for filling memory and for
producing pseudo-random data and addresses.  I have no security
concerns about OmegaCrypt, other than the concerns I have about all
the Catena-like algoritms.

OmegaCrypt does small unpredictable reads, based on the password, like
bcrypt.  However, in OmegaCrypt's case, I believe it should not.  What
"Practical" algorithns like bcrypt and Scrypt do rapid small
unpredictable addressing to foil both GPU and ASIC attacks.
OmegaCrypt dribbles them out so slowly as to not provide enough
defense to be worthwhile.  I recommend that his ChaCha state be
initialized with a constant, rather than the input data.  I also
recommend that case 2 and 3 be modified to not do memory dependent
addressing.  With both of these changes, OmegaCrypt would become a
competitor in the Catena-like category of entries concerned more about
what I call "mathematical" defense rather than "practical" defense.
In terms of competing against more practical algorithms like
PufferFish, OmegaCrypt gets crushed in speed.  It fairs better against
Catena and Gambit.

Like the other bcrypt-like and Catena-like entries, OmegaCrypt is
essentially a cache-bound algorithm, suffering from excessive delay
when accessing external DRAM.  However, because of it's calls to
ChaCha for the pseudo-random addresses and data, it runs closer to the
speed of the Catena-like algorithms, though easily 10X slower than the
bcrypt-like algorithms.  The choice to use only output from strong
cryptographic hashes is shared among the Catena-like entries, which is
why they run so slowly.  I think this is the group of people who feel
that mathematical security is paramount, rather than what I consider
to be "practical" security.  This is also why they all decided to
focus on purely cache-timing resistant algorithms, except for OmegaCrypt.

Because of OmegaCrypt's choice to focus on mathematical security at
the expense of bcrypt-like speed, while not being cache-timing
resistant, I feel it does not have an area where it is competitive. I
believe the choice of unpredictable reads is reasonable for practical
security, since this is what frustrates GPU and ASIC attacks, leaving
all of the cache-timing resistant algorithms subject to the full power
of ASIC acceleration of their ASIC-friendly hashes.

Here's just some quick observations when reading the code:

- - Input parameters are carefully checked.  I appreciate it.
- - Solid comments - again, I appreciate it.
- - Nice error codes and more. I like the author's coding ability and style.
- - All inputs are properly hashed, making it "strongly secure"
- - Comment on line 240 in ocrypt.c is out of date
- - OmegaCrypt is simple.  ocrypt.c is only 240 lines, though it does
depend on external ChaCha and CubeHash
- - I respect good coders.  I have to respect this author.

After initializing ChaCha with input data, memory is initialized by
copying the input data to the start, and then XORing ChaCha data over
all of it.  This should make memory cryptographically pseudo-random.

For the t_cost loop, he iterates this main loop many times:

loop 2^17*(1 << t_cost) times:
  switch(rand32() & 3)":
    0) state_array[rand32() & m_array_mask] += carry
       carry ^= rand64()
    1) state_array[((rand32() ^ 0x0a1b2c3d) & m_array_mask] ^= carry
       carry += rand64()
    2) state_array[(rand32() ^ 0xfedc0123) & m_array_mask] ^= rand64()
       state_array[(rand32() ^ 0xfedc0123) & m_array_mask] += rand64()
^ carry
       carry ^= state_array[carry & m_array_mask]
    3) state_array[state_array[(rand32() ^ 0x76543210) & m_array_mask]
& m_array_mask] += carry ^ rand64()
       carry += state_array[(rand32() ^ 0x7654321) & m_array_mask] ^

Rand32() and rand64() return ChaCha data.

One thing to note is that there is no need for XORing ChaCha data with
constants to generate pseudo-random addresses.  This does not make it
any more random, but does slow down the defender.

Like several entries, OmegaCrypt XORs and ADDs over memory, but
probably should use the read memory first, since it's read anyway.
This would make it more TMTO resistant with little computation
penalty.  Lyra2 does this, for example.

ASIC Hardness
- -------------

A significant problem that the author may not realize is that
OmegaCrypt does not benefit from it's unpredictable addressing nearly
as much as bcrypt-like entries.

The data from the ChaCha stream *is* predictable in the sense that I
can pre-compute as much of it as I want at about 32 bytes per ns in my
high-end ASIC.  This allows me to pre-compute which cases will execute
in each loop, as well as most addresses that will accessed, so that
they can be put in the pipeline before their data is needed.  The only
effectively unpredictable memory accesses are in case 2 and 3, one
each.  The read from memory indexed by carry in case 2 depends on the
value of carry computed in the previous loop iteration.  The
unpredictable memory access in case 3 is the read from an address
loaded from a predictable memory location.  Unfortunately, there is no
sequential dependence, and the case 3 addresses can call be
pre-computed in advance as well.

Only case 2 offers a strong benefit from unpredictable addressing.
However, it only executes every 4 loops on average, so 3/4ths of these
loops will execute in 1 cycle at the full ASIC clock speed of 3.4GHz
(same as my CPU).  Case 2 should take 3 clocks, like the typical
average unpredictable write on my CPU.  The average is 1.5 clocks per
iteration, consuming an average of 14 bytes of ChaCha data every 1.5
clocks, or about 28 bytes every three clocks, which is just below my
ChaCha stream generator's speed, meaning ChaCha data generation is not
the bottleneck.  Initializing it with a constant rather than password
and salt should not harm the ASIC hardness.

Filling memory with ChaCha data will be very fast.  My cache does
writes in 0.065ns per byte for sequential writes.  The final read for
CubeHash is even faster at 0.05ns per byte.  The first and last passes
combined will only require 1us.  With t_cost == 0, with the carry
dependency, I have to slow down to one clock per loop, accept for case
2, which requires 3, for an average of 1.5 clocks/iteration.  The
benchmarks below were for t_cost == 0, or 2^17 iterations.  My ASIC
should do that in 1.5*2^17 clocks, or 58us.

The entire hash can be done in about 60us, compared to 124ms in the
benchmark below.  That's a factor of over 2,000X with no required
external memory.  This is weak ASIC hardness for a memory-hard
algorithm, but typical of the more "mathematical" defense algorithms
in the Catena-like category.

TMTO Resistance
- ---------------

I see no major holes in OmegaCrypt's TMTO resistance.  With higher
t_cost than m_cost, it's defense increases.  With t_cost == m_cost, it
should do better than Scrypt because of it's unpredictable writes.
However, if OmegaCrypt becomes a cache-timing resistant algorithm like
Catena, then it will suffer the usual time*memory cost reduction due
to the usual TMTOs that can be made when we know the addressing
pattern.  Cache-timing resistant algorithms, when all else is equal,
are typically 3X-ish worse on TMTO defense, because an attacker can
carefully place his pebbles where he knows they will be needed rather
than distributing them were they might be needed.  This typically
results in a 2X to 3X reduction in pebble moves on  the data
dependency graph.  Note that the graph continues to grow even as data
is over-written, meaning memory is not increasing, which is why TMTO
resistance grows as over-write passes increase.

OmegaCrypt should also be modified to make use of the data read when
doing the += and ^= operations to memory.  This creates more edges in
the data dependency graph, making it harder to pebble.  Lyra2 benefits
from this.

- ----------

8MiB hash:

PHC> time ./phs-omegacrypt 0 3

85 dc 3d fc bf de 9a 60
09 dc 24 dd 1e b1 f2 bb
38 9a d5 07 79 60 d8 20
0f 2f 9f e5 dd 17 cb 59      32 (octets)

real	0m0.124s
user	0m0.122s
sys	0m0.001s

1GiB hash:

PHC> time ./phs-omegacrypt 0 10

dc 99 9a e6 b6 0b 65 82
bf 3b 83 8a 68 f9 39 80
3b 25 ed d6 20 06 a3 40
1d bb c5 b3 b2 2b 41 8d      32 (octets)

real	0m13.910s
user	0m13.846s
sys	0m0.068s

The runtimes, like the Catena-like algorithms, are too high for
authentication servers, even with small cache-bound hashing.  They are
also too high for external 1GiB hashing, and so do not compete well
with Scrypt.  Also, I ran this with t_cost == 0, which did only 2^17
loop iterations, potentially creating a TMTO vulnerability, since most
data in memory remains simply the ChaCha output to the end.

OmegaCrypt is simply too slow and has too weak ASIC resistance to be a
competitive algorithm in the field of "practical" bcrypt-like and
Scrypt-like entries.  It would do better if it were tweaked to compete
in the Catena-like category instead.

I think that there are enough of these more mathematical security
minded people people in the competition to have a Catena-like
category, and maybe even announce a winner for them, so long as that
does not preclude having a bcrypt successor and Scrypt successor which
provide more practical defense.

Every factor of 10 counts.  However, we have closer to 100X difference
between the Catena-like entries and the bcrypt and Scrypt-like entries
in terms of time*memory defense (how much memory an attacker will have
to use times how long he will have to use it).  TwoCats hashes 1GiB in
external DRAM in 0.155s, compared to 0.124s for 8MiB for OmegaCrypt.
A 0.155 1GiB hash costs an attacker 128X the memory in 25% more
memory.  The defense goes as the square of the runtime, so the ratio
of the defense of these two hashes is
(0.124/0.155)^2*(0.155*2^30)/(0.124*2^23) = 101X.

100X difference in time*memory cost seems to be about average when
comparing the mathematical defense entries (Catena-like) to the
practical defense entries (becrypt and Scrypt-like).

Version: GnuPG v1


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