A full-featured implementation of of the LMS and HSS Hash Based Signature Schemes from draft-mcgrew-hash-sigs-07.
Switch branches/tags
Nothing to show
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Permalink
Failed to load latest commit information.
Makefile
README
common_defs.h
demo.c
endian.c
endian.h
hash.c
hash.h
hss.c
hss.h
hss_alloc.c
hss_aux.c
hss_aux.h
hss_common.c
hss_common.h
hss_compute.c
hss_derive.c
hss_derive.h
hss_generate.c
hss_internal.h
hss_keygen.c
hss_param.c Initial commit Jul 5, 2017
hss_reserve.c
hss_reserve.h
hss_sign.c
hss_sign_inc.c
hss_sign_inc.h
hss_thread.h
hss_thread_pthread.c
hss_thread_single.c
hss_verify.c
hss_verify.h
hss_verify_inc.c
hss_verify_inc.h
hss_zeroize.c
hss_zeroize.h
license.txt
lm_common.c
lm_common.h
lm_ots.h
lm_ots_common.c
lm_ots_common.h
lm_ots_sign.c
lm_ots_verify.c
lm_ots_verify.h
lm_verify.c
lm_verify.h
programming.notes
read.me
sha256.c
sha256.h
test_h25.c
test_hss.c
test_hss.h
test_keygen.c
test_keyload.c
test_load.c
test_reserve.c Add files via upload Sep 6, 2017
test_sign.c
test_sign_inc.c
test_stat.c
test_testvector.c
test_thread.c
test_verify.c
test_verify_inc.c Initial commit Jul 5, 2017

README

This code attempts to be a usable implementation of of the LMS Hash Based
Signature Scheme from draft-mcgrew-hash-sigs-07.

This is a signature scheme (that is, someone with the private key can sign
messages, someone with the public key can verify sigantures, but cannot
generate signatures) that is based on a hash function (that is, the only
cryptographical assumption is that hash function is secure; in this case,
that you can't find preimages or second preimages).  This particular
scheme is stateful (that is, the signer keeps state that must be updated
for each signature); there are stateless schemes, but they have much larger
signatures.

Here's how to use it: general workflow for the signer:

Step 1: generate a public/private keypair.
  This is the hss_generate_private_key function; you give it the parameter
  set you're interested in (see below for guidelines as to what's
  appropriate here), a function to get randomness, a function to write
  out the private key, a buffer to hold the public key, and the optional
  aux data.

The below step can be repeated as needed (e.g. because of a program reload):

Step 2: load the private key into memory
  This is the hss_load_working_key function; you give the private key,
  a budget of the amount of memory to use, and optionally the aux data
  generated during the hss_generate_private_key.  This memory budget is
  used as a guide for some space/time trade-offs; we'll never fail because
  you haven't authorized enough memory (if you haven't, we'll reduce the
  amount of memory as much as possible, hence passing a 0 will minimize the
  amount of memory, which is appropriate if you'll use the private keys only
  a handful of times).  It turns out minimal space doesn't generate
  signatures that slowly; if you have memory to burn, you could allow it to
  allocate 100k and it would sign faster; if we allow enough space so that we
  can place the entire bottom level LMS tree in memory, the speed up is
  significant in nonthreaded mode (in threaded mode, we generate the
  signature at the same time, and so we don't save as much wallclock time).
  The aux data is optional (the load process will work if you don't provide
  it); it'll be faster if you do (if you don't provide this, this'll
  take at least as long as the original key generation).  Also, the aux data
  is integrity checked (and so if it was modified, this'll ignore it).

     If you just generated a key, and want to sign a message, you'll need to
     load the private key (even if you're not interested in saving the private
     key between reloads).  If this is what you're doing, I suggest you have a
     moderate (e.g. 1k) array that you use to hold the aux data; without that,
     the load process would need to redo almost all the computations that were
     done when initially generating the private key.

Once you've expanded the key, you can use it to, say, actually sign messages.
Here are the steps you an do (and you don't need to reload the key after
every message you've signed):

Step 3: actually generate the signatures
  This is the hss_generate_signature function; you give it the working key,
  a function to update the private key, and the message to sign, and it
  generates the signature.

Step 3a: reserve N signatures
  This is the hss_reserve_signature function; this allows you to advance
  the 'current counter' in private RAM by N (and so the update_private_key
  function won't need to be called for the next N signature generations).
  Of course, if the application exits without using all those N signatures,
  those will still be considered used.


The workflow for the verifier is easy: you pass the message, the public key
and the signature to hss_validate_signature; that returns 1 if the signature
validates, 0 if it doesn't.  We provide APIs both to sign/validate the
signature in one shot (hss_generate_signature/hss_validate_signature), and
also init/update/finalize routines in case we have the message in multiple
pieces (see hss_sign_inc, hss_validate_inc for the details of those APIs).

The makefile generates three .a files; hss_lib.a, which includes the above
routines; hss_lib_threaded.a, which is the same, but with threading enabled
(and so -lpthread is required to link), and hss_verify.a, which just includes
the verification logic (nonthreaded; threading speeds up verification only
somewhat; if you want a threaded verification code, it should be fairly
obvious how to make it yourself).



Now, the practical problems that a (stateful) hash based signature has are:
- Statefulness; each signature effectively has a nonce, which must not be
  used to sign two different messages.  If we use a private key over reboots,
  that means that we need to track the state in longterm storage somehow.
- Size of the signature; depending on the parameter set, the signatures might
  be several k long
- There's an upper bound on the number of signatures that can be generated
  with a specific public key.
This package tries to address all of them, as follows:

Statefulness; we do several things to mitigate this issue:
  - Everytime we need to update the state (either during initial key
    generation, signature generation or reservation (see below)), we have
    the application provide a function that is supposed to write the new
    state to secure storage; the signature is not released to the application
    (actually, not even generated) unless that function claims success.
  - There's quite a lot of state involved with this package.  However, instead
    of writing all that to secure storage, what we do is write a summary.
    On a program reload, we read ("load") that summary back into memory,
    reconstruct the full state, and continue on.  Because this summary is
    short, this makes it easier to store, and we have less to worry about
    partial updates (say, if we crashed in the middle of an update).
  - If writing the state to secure storage is expensive, what we can do is
    "reserve" a number of signatures; that will update the state on secure
    storage; however, if we reserve N signatures, that means that for the
    next N signature operations, we won't have to actually perform the
    update.  Hence, we can move much of the work to time where we would have
    been idle. 
Signature size; we can't actually do anything about the signature format
(that's fixed in the draft), however what we can do is try to make selecting
a parameter set with a short signature reasonable:
  - Efficiency; we try to make it efficient; efficiency allows you to use
    more aggressive parameter sets (chiefly, ones with W=8, and relatively few
    Merkle levels), which makes the signature shorter.
  - We support multithreading; that is, during the key generation and key
    reload procedures, we can use multiple threads to speed things up.
    Speeding these up allows up to use considerably larger trees (and hence
    fewer of them).
  - We support 'auxiliary data' for the top level Merkle tree.  Our model is
    that you don't mind spending quite a bit of time during key gemeration (as
    that is a rate event); you are far more sensitive to the operation
    operations (such as the key reload, which you might do whenever you
    restart the program).  What the aux data allows you program to do is
    generate the top level Merkle tree once (and store some intermediate
    nodes); this means that we can practically use a very large top level
    Merkle tree, without costing much (other than ken gen time).  In fact,
    if you're happy with 1-30 million signatures maximum, you could go with
    a single level Merkle tree, which yields relatively short (<2k) signatures
  - After the initial key gen and load, we compute everything incrementally.
    That means that, just because we have a level 20 tree, we never have to
    sit down and compute 2**20 operations at once; we spread that work over
    the time we spent generating the signatures from the previous tree.
Upper bound on signatures; again, we're stuck with the upper limit on any
parameter set; however we try to make it reasonable to select a parameter set
with a large number of signatures.  We gave most of the efficiency features
above; we give a table below listing various parameter sets that are
reasonably efficient, and have large upper signature bounds.  For example,
if 1 billion signatures are enough, then a 20/10 parameter set might be
reasonable.




Now, here is another listing of the features of this package (in a
feature-centric order, rather than a problem-centric one:

- It tries to deal with state management.  It does not assume that the
  signing computer will be running without a reboot for the entire time that
  the private key is valid, and it does not assume that we're able to do a
  large scale update of secret state to disk (which would cause problems if we
  rebooted in the middle of an update).  It addresses this by dividing the
  private key into three parts:
  - A short section which is meant to be saved in secure storage (and this is
    the part which is referred to as the 'private key'; this includes the
    number of signatures generated so far.  It's currently 48 bytes long
    (with the part that needs to be actually updated only 8 bytes), we assume
    that it is updated atomically.  These 48 bytes consist of an 8 byte count
    of the number of sigantures generated so far, 8 bytes of a compressed
    version of the parameter set, and 32 bytes of 'seed' (a random value that
    is used to derive every secret)
  - A longer section (the "working key") that resides in memory; we assume
    that this is private, but need not be saved into long term (nonvolatile)
    storage.  This section include the Merkle tree contents (actually, a
    subsection, as below we implement a time/memory trade-off), the next
    Merkle tree contents (incremental computation), I values, signatures for
    internal public keys; for most parameter sets, this easily fits into
    10-30k (time/memory trade-offs will allow it to be larger to give better
    signing performannce).  For example, a level 20/10 tree (maximum of 2**30
    signatures), we can use as little as 16kbytes of ephemeral state (and the
    time isn't all that bad after the working key has been regenerated).

The idea by the above split is that we keep the short permament key somewhere
safe (and which would survive a restart should we need to); at any time (for
example, after a restart), we can regenerate the longer section, which we
would keep in memory.  We use the version of memory to actually generate the
signatures (and update the short section as needed).  If we restart, we
regenerate the large working section, and carry on.  In addition, by using
reservations (see below), we don't actually need to update the secure storage
every time.

By keeping the short section short, that means that we don't have to worry
about partial updates (which we would if that the private part was a
multikilobyte explicit tree); we can also use limited private space (e.g. HSM).

We also have an optional third section to the private key:

  - Auxiliary data; this is an optional section that contains the node values
    of parts of the top level Merkle tree; this is generated at keygen time,
    and is read-only thereafter; the point of this is to speed up the process
    of loading the private key into memory.  This aux data is (usually)
    persistent, but need not be secret.
     - For a level 20 top level tree, 10916 bytes of aux data allows us to
       regen the top level tree in circa a second.  That means that, for a
       20/10 level tree, generating the private key is expensive (3 minutes
       on my test machine), but restarts after that can be done in a second
       or two.
     - We also authenticate the auxiliary data; that means that an adversary
       who can corrupt the auxiliary data can increase the time it takes for
       us to load the working key; however they don't get any other advantage.
     - I did say that the auxiliary data is usually persistent.  However, if
       we can't store it permamently, it still can be used to speed up the
       initial program load (that is, immediately after the private key
       generation); we'd use a moderate (several k) temp array to both
       the key generation and first reload; if we need to do a reload
       afterwards, we would not pass the aux array (as we wouldn't save it).
       This'll speed up the initial load process (as it wouldn't have to redo
       most of the computations that the key generation did); it won't speed
       up the later reloads, however at least we got some benefit from it.

- We include a function that takes the short section, and recreate the working
  portion, we refer to this as 'loading the private key into memory'.  This is
  meant to be called on a reload, and (assuming that you use the aux data) can
  be significantly faster than generating the key in the first place.

- We incrementally compute the next trees (so we don't hit a bump when we
  generate the 1025th signature)

- Time/memory trade-offs available (so we don't need so much memory for the
  loaded private key)
   - The 'load the private key' function (hss_load_private_key) takes a
     parameter while means "try to limit the memory used to X bytes"; this
     allows some flexibility in designing the trade-off (although less than I
     expected when I first designed the API; the 'use as little memory as
     possible' option isn't that slow, and the 'd*mn-the-memory-
     full-speed-ahead' mode doesn't use that much memory (unless the bottom
     level Merkle tree is huge).  Yes, there's a delta, but not a big one.

- For any function that can update the private key, we have the application
  (the program that is using the package to sign messages) pass a function
  ("update_private_key") and a context pointer.  If this is non-NULL, then
  when we update the private key, we call this function, what this function is
  expected to do is write the private key into secure storage (and pass
  nonzero on success); if you pass a NULL function pointer, then we assume
  that passed context pointer is actually the pointer to the private key.

- Explicit implementation of the reservation primitive.  Right now, we have
  an API that states "make sure that we have N signatures reserved (so that
  we won't have to update the private key for the next N signature operations).

- We can also perform operations in parallel (pthread's); do get this, you
  use the hss_lib_thread.a library (and include -lpthread on the link); if
  you use the hss_lib.a library, then everything is done in the main thread.
  Using multiple threads speeds up the key generation and key loading process
  significantly (15x in my experience, assuming you have enough CPU cores);
  we also can use it during the signing and verification process, however the
  speed up there is less radical (perhaps 2x).

- I believe the code is fully compliant C99 (that is, it should work on any
  C99 implementation that can handle the program/data size; even silly ones
  with 13 bit chars and 26 bit int's and things like that); in fact, the
  private keys should be portable to different architectures.  I haven't
  tested out either of these claims, though.


I've included a simple program (demo.c) that uses the above facility to
sign files, and verify them.  I've also included a test harness (test_hss) to
do regression testing of HSS; however I would rather advise you not to look
at how those regression tests use the library as best practice; they are
designed to push the library's corner cases, and so sometimes do things that
real applications really ought not do.


General notes:

- Advice about parameter sets: while this supports all the HSS parameter sets
  currently allowed in draft-mcgrew-hash-sigs-07, some work better than others
  The general recommendation is to use a few large trees (that is, with lots
  of levels), rather than using a number of levels of smaller trees; this
  package tries to make large trees not that costly (and reducing the number
  of trees certainly cuts down on the signature size).  If you have a
  reasonable amount of auxiliary data available (and ideally, multithreading),
  then making the top level tree H=20 (or even H=25) is doable; the main cost
  is the time to do the initial key generation (which in most cases is a rare
  event).  On my test machine, I can generate a key with a H=20 tree on top
  (with W=8) in 3 minutes (multithreaded); loading that key into memory (with
  10k of aux data, with a single H=10 tree below it) takes 1-2 seconds.  An
  H=25 tree on top took 1.5 hours; loading that key into memory (with 1Meg of
  aux data) took a second.  Increasing the lower tree to H=15 makes loading
  take 6 seconds (without affecting the key generation time).  Those parameter
  sets give reasonable speed, with 3.3-3.7k signatures, and allow 1 billion to
  1 trillion signatures per private key (which I expect should be sufficient
  for most uses; at 1000 signatures per second, that's enough to last you
  either 10 days (top H=20, bottom H=14), a year, or 3 decades (top H=25,
  bottom H=15).
      Here's a table that goes through a list of various parameter sets.
  They all have W=8 (which minimizes signature sizes, while increasing time),
  and were measured on my test platform (with threading enabled; times would
  be considerably larger without threading).  These are here to give a
  guideline as to what's possible; for the computational time, your mileage
  may vary, depending on the computing resources you have.  The machine I
  have does not have the SHA-256 extensions; you could possibly do
  significantly better.

    ParmSet  KeyGenTime  KeyLoadTime   AuxSize   SigSize   KeyLifetime
     15         6 sec       3 sec         100      1616     30 seconds
     20         3 min       1 sec       10916      1776     16 minutes
     25      1.5 hour      18 sec       21860      1936     9 hours
    15/10       6 sec       1 sec         356      3172     9 hours
    15/15       6 sec      10 sec         356      3332     12 days
    20/10       3 min       2 sec       10916      3332     12 days
    20/15       3 min      10 sec        2724      3492     1 year
    25/10    1.5 hour       7 sec       87396      3492     1 year
    25/10    1.5 hour       1 sec      349540      3492     1 year
    25/15    1.5 hour      13 sec       87396      3652     34 years

  ParmSet: this is the height of the Merkle tree(s); parameter sets listed as
      a single integer consists of a single Merkle tree of that height; 
      parameter sets that consist of two trees are listed as x/y, with
      x being the height of the top level Merkle tree, and y being the
      bottom level.
  KeyGenTime: the measured key generation time; this is the operation that is
     done once per private key.
  KeyLoadTime: the measured key load time (assuming the auxsize of the
     specified amount); this is the operation that is done on program reload
     to continue using an existing private key.
  AuxSize: the size of the aux data that was used to test load time, the value
     listed for AuxSize is in bytes.  You can use smaller sizes, however that
     would increase the key load time (as can be seen by the two different
     KeyLoadTimes given for ParmSet 25/10)
  SigSize: the size of a signature (in bytes)
  KeyLifetime: the lifetime of a key, assuming we generated 1000 signatures
     per second.  In practice, we're not likely to get anywhere close to
     1000 signatures per second sustained; if you have a more appropriate
     figure for your scenario, this column is pretty easy to recompute.

  As for signature generation or verification times, those are moderately
  insensitive to the above parameter settings (except for the Winternitz
  setting, and the number of Merkle trees for verification). Tests on the same
  machine (without multithreading) gave approximately 4msec to sign a short
  message, 2.6msec to verify (for this test, we gave the working key lots of
  memory; if you skimp on that, the parameter sets with the larger bottom
  trees slow down somewhat more than the ones with less; we also used a two
  level ParmSet; a single level would approximately halve the verification
  time).  All times can be significantly improved (by maybe a factor of 8) by
  using a parameter set with W=4; however that also about doubles the
  signature size.  In addition, we allow you to adjust the amount of
  threading on a per-call basis (byte the hss_extra_info parameter);
  I suspect that typically you'll run with the defaults.

- Portability of the private keys: I believe that the private keys are
  portable to different CPU architectures (that is, picking up a private
  key on one CPU and moving it to another will work)
  However, I don't currently promise that private keys generated by this
  version of the package will work on future versions; we reserve the right
  to make changes that break current created private keys.  Eventually, we'll
  need to preserve this (possibly by including a version flag in the private
  key); however, I don't believe that this package is mature enough yet.
  After all, essentially everything involved with signing (with the sole
  exception of the bottom C signature randomizer) must be derived in the exact
  same way from the top level seed; once we start doing versioning, that means
  we must forever support that way of deriving internal values from the secret
  seed.

- Same thing with the API; eventually, we'll need to stabilize the API;
  however, I don't believe we're there yet (although with the extra_info
  structure, we may be getting close; any new parameter where most 
  applications are happy with a reasonable default can be placed into the
  extra_info structure); I don't want to lock us in to what we have right now.

- Note that there is a MUST statement in the draft that this implementation
  does not comply to:

      These key pairs, and their identifiers, MUST be generated
      independently.  All of the information of the leaf level L-1,
      including the private key, MUST NOT be stored in nonvolatile memory.

  Actually, we generate everything (including data from level L-1) from the
  secret seed, which is stored in secure nonvolatile storage as a part of the
  private key.  We do this because our model is that we might restart at any
  time, and on a restart, we reload the private key, which recreates the tree
  structure from scratch).  If we generated the bottom level randomly, that
  would mean the next level OTS signature would sign two different messages.
  Now, we could autoadvance to the next L-1 tree, however that would use up
  signatures for no good reason.

- This package will allow at most 18446744073709551615 signatures per private
  key (that's 2**64-1), even if the parameter set would allow more.  If you
  think you need more signatures than that, well, dude, what are you smoking?

- The API has an optional struct hss_extra_info* parameter; this is to allow
  you to convey information that typically is not needed (but on occasion,
  might be).  You can always pass a NULL pointer (in which the package uses
  reasonable defaults); the current parameters that are exchanged:
  - num_threads; this allows the application to tell this packet about the
      number of concurrent threads that it is allowed to use; 1 means not to
      use threading at all; 2-16 means that many threads, and 0 means the
      default.
  - last_signature; if the signature generation routine detects that it has
      just signed the last signature it is allowed to, it'll set this flag.
      Hence, if the application cares about that, then it can pass an
      extra info structure, and on return, test this flag.
  - error_code: if some operation fails, the field is set to a value that
      indicates why it failed (similar to errno, except not a global).
      Hence, if the application cares about that, then it can pass an extra
      info structure, and on failure return, test this flag.

  Just a word of warning; if you do pass in an hss_extra_info structure,
  the fields must be initialized, passing in a structure containing random
  stack garbage is begging Murphy to perform his magic.  You can do this
  by either:
      struct hss_extra_info info = { 0 };
  or
      struct hss_extra_info info;
      hss_init_extra_info( &info );

Future ideas; I'm not against future ideas, but this package is getting
sufficiently complex that I'm not likely to do anything that adds even more
complexity unless someone has a real need.  If you do have a real need (for
one of the below ideas, or something else), plesae tell me; otherwise, I'm 
likely not to implement it:

- It feels like the reservation primitive, as implemented, isn't ideal, as it
  doesn't give any feedback to the application (and so it doesn't know how
  close we are to the limit).
  One possibility would be to have the signature algorithm automatically
  advance the reservation count by N (rather than 1) when it uses up the last
  reserveration; this means that the application doesn't need to do anything
  (other than specify N at load time) to do a private key update once every
  N'th signature; however it does mean that when we do write to secure
  storage, we do it during signature time.

- Extend multithreading to generate the higher level Merkle signatures when we
  step to the next lower level Merkle tree.  We do multithreading for most of
  the expensive operations, but not this one; when we need to generate a
  nonbottom signature, that's done by the main thread (while none of the other
  threads are doing anything).  It's about half the cost of creating an OTS
  public key, but it's still not free.  We do this only rarely (once every
  1024 signatures of the bottom level tree is of height 10), however it does
  increase the worse-case time (which can be significant for some
  applications).  One issue is that we can't sign the NEXT tree until we've
  completed building all of the subtrees; if one of the tasks is finiahing
  that up, well, we might be stuck.

- Perhaps we can have support for SIMD hash implementations (e.g. AVX) that
  can, in parallel, compute N independent hashes.  I suspect that it wouldn't
  be that difficult to add it to the Winternitz routines (which is where the
  bulk of the time is spent anyways).  However, it would appear that Intel's
  SHA-256 instructions would be faster than AVX (and doesn't add any
  complexity; recent versions of OpenSSL already include it); hence this would
  be of interest only for CPUs with AVX but not SHA-256-NI; currently, that's
  common, but I expect that'd change over time; it's not clear that this
  amount of code would be warrented for a short term fix.  On the other hand,
  if we can get support for a GPU, well, that'd be a really big win (albeit
  at a significantly higher complexity cost)

- Q: restarting at some points (say, at the start of a Merkle tree) is
  cheaper than restarting in the middle, or near the end.  Should we do an
  auto-reserve if we're getting close to the end (so that, if we do restart,
  that's cheaper)?  One the other hand, with parallel processing on the load
  function, loading anywhere is already fairly cheap.

- We might want to explicitly support a block-type interface (with read/writes)
  to handle the aux data, rather than insist that it fits into a contiguous
  memory segment; this may make it easier for an implementation to use a
  significant sized aux data.  My major complaints about this is "yet more
  code complexity?  Don't we have enough?" and "yet another nonobvious API to
  document".  On the other hand, except for H=25, we never really need more
  than 10k or so of aux data; would this (code and documentation) complexity
  actually be worth it?

- The hss_load_private_key takes the 'memory budget' as a parameter, which 
  allows the user to select the time/memory trade-off.  It might be considered
  sporting to give the user some context as to what the trade-offs actually
  are; perhaps a way of generating a table of memory-size vs. hash compression
  operations (or OTS public key generations) expected per signature; it
  depends on the parameter set, and so we can't just publish a table (although
  a table for typical parameter sets on a typical compiler might not be that
  hideous).

- Could we make this package valid C++ as well?  One issue is the malloc's
  (which aren't casted), we could insert the "extern "C" {" markers (to say
  these functions use the C ABI), are there other issues?

  - As for going the other way (making this valid C89), well the biggest issue
    there is the 64 bit int's we use (sequence_t); we do use VLAs, but those
    shouldn't be that hard to remove.  Yes, we could program around the 64 bit
    int's, however I don't see the point unless someone really needs this.

- The logic to distribute updates to the upper level trees (which does the
  work when we're close to the end of the current bottom level tree, when the
  bottom level tree runs out of BUILDING_TREEs to update) rather assumes that
  an upper level OTS is about the same cost as a bottom level OTS.  This is
  actually true if we use the same OTS parameter set (Winternitz parameter)
  everywhere; however if the upper levels use a costlier one (e.g. the bottom
  level tree uses W=4, the upper level trees use W=8), it's less true.  It
  might make sense to try to potentially split up the work of updating the
  upper level tree into more signature operations; at least, in this case
  (and it'd be an ideal way to add even more complexity into this package).
  Of course, we'd have to ask: how common are these mixed-winternitz settings
  anyways?

- Another thing that I could see being useful in some scenarios is providing
  a way to safely share the same private key between multiple signers.
  Here are two ways to do this:
  1. There'd be a master holder of the private key (which would hold the real
     private key); a secondary signer would ask for the permission to sign N
     signatures; the master would pass it a 'subkey' that would give it
     permission to sign using sequence numbers X and X+N-1 (where X is the
     current private key value), and the master would increment its copy of X
     by N.  The client would load the subkey and we're good to go.  It's not
     clear how the master would advance its working key by N; a first cut may
     be that the master does a fresh hss_generate_working_key; there are more
     efficient ways to do it, but there are lots of corner cases that would
     require testing to make sure we've covered everything.  The subkey we
     send to the client would be the private key plus one parameter (the
     allowed maximum); we might want to modify our private key format to
     include this maximum if we're serious about this (so that the secondary
     signer could run the standard HSS code).  There are likely a number of
     gotcha's involved; however less than the below idea.
  2. We'd also have a master holder, but instead of giving the entire secret
     key to the secondary signer (and tell him "please only use sequence
     numbers from X to X+N-1"), we instead gave him an entire subtree (without
     giving him enough information to sign outside that subtree). Note that we
     can construct a subtree of size 2**n, for any n (given a tree-based
     method to derive OTS keys; that would help with side channel resistance);
     it need not be an entire Merkle tree; such a method would waste up to
     2**n - 1 sequence numbers of the main tree (as it assumes that the
     initial sequence number we give to the secondary server is a multiple of
     2**n), unless the master tried something tricky and remember those
     weren't used yet).  This approach would not prevent an attacker who
     obtains that subkey from signing anything he wants for as many times as
     he wants; we assume that valid signers will not repeat sequence numbers,
     but an attacker might not feel so constrained.  It would allow us, given
     such a breach, to figure out who leaked their subkey; would that be
     considered enough of an advantage to make up for the extra complexity?
     For this to be a reasonable alternative, we'd need a facility to log who
     we gave what (otherwise, what's the point?)

- Should we worry about implementations that don't support malloc?  Or, have
  a 'secure_malloc' that reserves memory that is never paged out (and we'd
  prefer placing our keying data there)?  The candidates for doing a secure
  malloc would be the hss_working_key and the merkle_level (because they
  both contain seeds); no other malloc'ed data structure contain any
  secret data.  On the other hand, there doesn't appear to be a great deal
  of point in doing a secure malloc unless we know that the automatic
  data is also secure (or we move all keying data out of automatic data;
  could be problematic).

- Should the verifier cache previous successful verifications (at least, the
  top level trees)?  I personally don't think it's worth the bother (or the
  complexity).

- This might end up being used as the bottom half of a hybrid signature
  system.  The biggest change that the current hybrid proposal would need is
  'partial trees', that is, trees were some of the authentication path is
  artificial (that is, arbitrary values that don't correspond to OTS public
  values).  To do this, we'd probably end up having a 'current level' setting
  on the merkle_level structure, and a bunch of changes to initialize and
  respect it; we'd also add a partial_tree parameter to the hss_extra_info
  (which would tell hss_generate_working_key to generate such a structure).

- We could design a signature format that's somewhat shorter; (although the
  proof may need fiddling in some cases):
  - Not having the intermediate root hashes in the signature
  - A C randomizer of 32 bytes is overkill (with 16 bytes, we still make the
    'guess C, generate a collision based on that' attack as difficult as a
    second preimage attack)
  - We don't really need explicit intermediate C randomizers for the message
    hashing (as an attacker can't select that message value in advance)
  - We could have the lower level I values a determanistic function of the top
    level I (rather than expressing them in the signature)
  - We don't need to express the parameter types for the top level signature
    in the signatures
  - We can omit L from the signature, and shorten q
  These ideas would (for a 2 level parm set) reduce the siganture size by
  about 112 bytes (we could drop 3 bytes from the public key; probably not
  worth doing).  Should we have an API for this alternative format?
  With a bit of cleverness, we can support both (all signatures would be in a
  form that's compatible with the short format; we'd be able to express them
  in either format as required).  On the other hand, with the current format,
  a 15/10 W=8 parm set has a pk+signature length of 3184 bytes total (pk is
  60 bytes, sig is 3124 bytes); this would reduce this total to 3072 bytes.
  Is a <4% space reduction really worth the effort?  This idea gave more
  impressive savings back when we have 64 byte I values...

- Some of our internal functions have fairly generic names (e.g.
  get/put_bigendian).  We should go through, and give them names that are less
  likely to conflict with other functions we're linked with.  This is one
  place where C++ namespaces would be nice...

- Some of the computation for a signing operation could be precomputed; we
  could implement an API that says "call this during idle time, and your
  next siggen will be cheaper".  I personally wouldn't expect a lot of call
  (pun intended!) for this sort of thing (and, in any case, we can't
  precompute the OTS signature of the message, hence there are limits to how
  much benefit we can give).  And, maxing out the memory allowed in a working
  key gives most of the same benefit...

- We have starting building some regression tests; we should do more

- We support incremental signing; there is a potential security problem.  If
  the caller plays games, he can cause bad things to happen; a) if he modifies
  the signature between init and final, he could trick us into reusing an OTS
  signature index, and b) if he copies the context, he could trick us in using
  the same index to sign two different messages.  The first would be fairly
  easy to block (generate a MAC of the parts of the signature we care about,
  and store that in the ctx); the second is harder.  The only thing I can
  think of to block it would be to have the working_key track those signature
  indicies it has issued incremental signatures for, and are still pending
  (this would block the first attack as well).  That would likely require
  dynamic memory allocation (unless we put a tight cap on the maximum number
  of contexts that could be pending). My question is: should we go to that
  extent?  After all, we already need to trust the application already (as we
  allow them to sign anything they want, using the API).

- Should we have better protection against the application accidentally
  passing in an uninitialized/freed buffer as a hss_working_key, or a
  hss_*_inc context structure?  Right now, the value we use to say 'this is a
  good structure' is 0 (hss_error_none), which is far too likely a value to
  be seen in an uninitialized buffer.  Should we also include a magic value
  as well, for some simple validity checking?  Something like that certainly
  wouldn't be fool-proof; however it might catch some simple mistakes.
 
- Right now, we pass the update_private_key to every hss_generate_signature
  operation.  Would it make more sense to pass it instead when we
  hss_load_private_key, and just store it in the working_key?  Would it
  make sense to use the same context for read_private_key and 
  update_private_key?

- Right now, hss_extra_info has a last_signature flag.  Would it be more
  useful to have a 'signatures_remaining' count instead (and when it hits
  0, that'd mean we just wrote the last signature)?