libntruprime: Internals

This document explains the internal structure of libntruprime, and explains how to add new instruction sets and new implementations. The libntruprime infrastructure is adapted from the infrastructure used in lib25519 and libmceliece.

### Code generation

Portions of the distributed libntruprime package were automatically generated by scripts in the `autogen` directory, using (among other things) source in the `src` directory.

For example, `autogen/src` converts the `src/kem/sntrupP` directory into `crypto_kem/sntrup{653,761,857,953,1013,1277}`, converts the the `src/core/multsntrupP` directory into `crypto_core/multsntrup{653,761,857,953,1013,1277}`, etc. (The `crypto_hash*` directories are not auto-generated.) This structure means that source code is shared across all of the `sntrup` sizes, while allowing per-size specialization of the compiled code, reducing the in-memory code size for the typical case of an application using just one size.

The installation process (`./configure` etc.) does not run the `autogen` scripts. Developers have a choice of two development cycles:

- Cycle 1: Modify files in, e.g., `src/core/multsntrupP`; run `autogen/src`; install; test; repeat.

- Cycle 2: Modify files in, e.g., `crypto_core/multsntrup653`; install; test; repeat. Once `crypto_core/multsntrup653` is working, generalize to `src/core/multsntrupP` and switch to cycle 1.

### Primitives

The `crypto_kem/sntrup*` directories inside libntruprime are intended to compute exactly the KEM primitives defined by the NTRU Prime Sage reference implementation.

Internally, the implementations rely on lower-level subroutines defined in further `crypto_*/*` directories. This structuring provides smaller targets for optimization, testing, and verification.

The subroutines are intended to compute the primitives defined in Python inside libntruprime's `autogen/test` Python script. For example, the `crypto_core/multsntrup*` functions are intended to match the Python function `core_multsntrup`. The `autogen/test` script creates a test program, `ntruprime-test`, which checks libntruprime's subroutines against some outputs of the Python functions and against some SUPERCOP "checksums" (hashes of outputs for various inputs).

As a concrete introduction to the subroutines, the list below describes specifically the primitives used for `sntrup761`. Various numbers appear in these descriptions. The `sntrup761` parameters are p = 761, q = 4591, and w = 286. Related numbers appearing below are (p+3)/4 = 191; (q+2)/3 = 1531; (q−1)/2 = 2295; 1007, the number of bytes produced by the NTRU Prime `Encode` function for `M = 761*[1531]`; 1039 = 1007 + 32; and 1158, the number of bytes produced by `Encode` for `M = 761*[4591]`. The constant 32 is independent of the parameter set, as is the constant 10923 = 32769/3 appearing below. The 1039 and 1158 here are also the ciphertext size and public-key size for `sntrup761`. See `autogen/test` for the `Encode` function and a corresponding `Decode` function; these are copied from Figures 1 and 2 in the NTRU Prime specification.

Here are the primitives:

- `crypto_verify/1039`: `crypto_verify_1039(s,t)` returns 0 when the 1039-byte arrays `s` and `t` are equal, otherwise `-1`.

- `crypto_decode/int16`: `crypto_decode_int16(x,s)`, where `x` is a `uint16[1]` array and `s` is a `uint8[2]` array, sets `x[0]` to the `uint16` whose little-endian encoding is `s[0],s[1]`.

- `crypto_decode/761xint16`: `crypto_decode_761xint16(x,s)`, where `x` is a `uint16[761]` array and `s` is a `uint8[2*761]` array, sets each `x[i]` to the `uint16` whose little-endian encoding is `s[2*i],s[2*i+1]`.

- `crypto_decode/761xint32`: `crypto_decode_761xint16(x,s)`, where `x` is a `uint32[761]` array and `s` is a `uint8[4*761]` array, sets each `x[i]` to the `uint32` whose little-endian encoding is `s[4*i],s[4*i+1],s[4*i+2],s[4*i+3]`.

- `crypto_decode/761x3`: `crypto_decode_761x3(x,s)`, where `x` is a `uint8[761]` array and `s` is a `uint8[191]` array, sets `x[0]` to `(s[0]&3)-1`, sets `x[1]` to `((s[0]>>2)&3)-1`, sets `x[2]` to `((s[0]>>4)&3)-1`, sets `x[3]` to `((s[0]>>6)&3)-1`, sets `x[4]` to `(s[1]&3)-1`, etc.

- `crypto_decode/761x1531`: `crypto_decode_761x1531(x,s)`, where `x` is an `int16[761]` array and `s` is a `uint8[1007]` array, applies `Decode` to convert `s` into 761 integers between 0 and 1530 (i.e., the `M` input to the function is `761*[1531]`), and then multiplies each integer by 3 and subtracts 2295 to obtain `x`.

- `crypto_decode/761x4591`: `crypto_decode_761x4591(x,s)`, where `x` is an `int16[761]` array and `s` is a `uint8[1158]` array, applies `Decode` to convert `s` into 761 integers between 0 and 4590 (i.e., the `M` input to the function is `761*[4591]`), and then subtracts 2295 from each integer to obtain `x`.

- `crypto_encode/int16`: `crypto_encode_int16(s,x)`, where `s` is a `uint8[2]` array and `x` is a `uint16[1]` array, sets `s[0],s[1]` to the little-endian encoding of `x[0]`.

- `crypto_encode/761x3`: `crypto_encode_761x3(s,x)`, where `s` is a `uint8[191]` array and `x` is a `uint8[761]` array, sets `s[0]` to `(x[0]+1)+4*(x[1]+1)+16*(x[2]+1)+64*(x[3]+1)`, sets `s[1]` to `(x[4]+1)+4*(x[5]+1)+16*(x[6]+1)+64*(x[7]+1)`, ..., sets `s[189]` to `(x[756]+1)+4*(x[757]+1)+16*(x[758]+1)+64*(x[759]+1)`, and sets `s[190]` to `x[760]+1`.

- `crypto_encode/761xfreeze3`: `crypto_encode_761xfreeze3(s,x)`, where `s` is a `uint8[761]` array and `x` is an `int16[761]` array, sets each `s[i]` to `x[i]-3*((10923*x[i]+16384)>>15)`.

- `crypto_encode/761x1531`: `crypto_encode_761x1531(s,x)`, where `s` is a `uint8[1007]` array and `x` is an `int16[761]` array, sets `s` to `Encode(R,M)`, where `M` is `761*[1531]` and `R[i]` is `(((x[i]+2295)&16383)*10923)>>15`. (The way this is used in `sntrup761` has `R[i]` below `M[i]`; however, tests include larger `R[i]`.)

- `crypto_encode/761x1531round`: `crypto_encode_761x1531round(s,x)`, where `s` is a `uint8[1007]` array and `x` is an `int16[761]` array, is the same as `crypto_encode_761x1531(s,y)`, where `y[i] = 3*((10923*x[i]+16384)>>15)`.

- `crypto_encode/761x4591`: `crypto_encode_761x4591(s,x)`, where `s` is a `uint8[1158]` array and `x` is an `int16[761]` array, sets `s` to `Encode(R,M)`, where `M` is `761*[4591]` and `R[i]` is `(x[i]+2295)&16383`. (The way this is used in `sntrup761` has `R[i]` below `M[i]`; however, tests include larger `R[i]`.)

- `crypto_sort/int32`: `crypto_sort_int32(x,n)` sorts the `int32` values `x[0]`, `x[1]`, ..., `x[n-1]`.

- `crypto_sort/uint32`: `crypto_sort_uint32(x,n)` sorts the `uint32` values `x[0]`, `x[1]`, ..., `x[n-1]`.

- `crypto_core/inv3sntrup761`: `crypto_core_inv3sntrup761(h,f,0,0)` sets polynomial `h` to the reciprocal of polynomial `f` modulo x761−x−1 modulo 3. The polynomial `f` is expressed as a `uint8[761]` array where bytes that reduce to 0, 1, 2, 3 modulo 4 are interpreted as the small integers 0, 1, 0, −1 respectively; these integers in {−1,0,1} are then interpreted as the coefficients of x0, x1, etc. in that order. Coefficients −1, 0, 1 in `1/f` modulo 3 are converted to bytes 255, 0, 1 in array `h`. There is then a final byte 0 indicating that the reciprocal exists, so `h` is a `uint8[762]` array. If `f` does not have a reciprocal then the `h` array is instead set to 761 bytes 0 followed by final byte 255.

- `crypto_core/invsntrup761`: `crypto_core_invsntrup761(h,f,0,0)` sets polynomial `h` to the reciprocal of `3f` modulo x761−x−1 modulo 4591. The input polynomial `f` is expressed as an `int8[761]` array; the array entries in {−128,...,127} are interpreted as the coefficients of x0, x1, etc. in that order. Each coefficient of the reciprocal of `3f` is reduced modulo q to the range −(q−1)/2 through (q−1)/2 and then encoded as 2 bytes in little-endian form in `h`. There is then a final byte 0 indicating that the reciprocal exists, so `h` is a `uint8[2*761+1]` array. If `3f` does not have a reciprocal then the `h` array is instead set to `2*761` bytes 0 followed by final byte 255.

- `crypto_core/mult3sntrup761`: `crypto_core_multsntrup761(h,f,g,0)` sets `h` to the product of two small-coefficient polynomials `f` and `g` modulo x761−x−1 modulo 3. The polynomial `f` is expressed as a `uint8[761]` array where bytes that reduce to 0, 1, 2, 3 modulo 4 are interpreted as the small integers 0, 1, 0, −1 respectively; these integers in {−1,0,1} are then interpreted as the coefficients of x0, x1, etc. in that order. The polynomial `g` is expressed the same way. Each coefficient of the product modulo x761−x−1 is reduced modulo 3 to the range −1, 0, 1, and then stored in the `uint8[761]` array `h` as byte 255, 0, 1 respectively.

- `crypto_core/multsntrup761`: `crypto_core_multsntrup761(h,f,g,0)` sets `h` to the product of a polynomial `f` and a small-coefficient polynomial `g` modulo x761−x−1 modulo q. The polynomial `f` is expressed as a `uint8[2*761]` array storing 761 `int16` values in little-endian form. The polynomial `g` is expressed as a `uint8[761]` array, where bytes that reduce to 0, 1, 2, 3 modulo 4 are interpreted as the small integers 0, 1, 0, −1 respectively. Each coefficient of the product modulo x761−x−1 is reduced modulo q to the range −(q−1)/2 through (q−1)/2, and then encoded as 2 bytes in little-endian form in `h`, which is a `uint8[2*761]` array.

- `crypto_core/scale3sntrup761`: `crypto_core_scale3sntrup761(h,f,0,0)` transforms a polynomial `f` to a polynomial `h`. Each polynomial is expressed as a `uint8[2*761]` array storing 761 `int16` values in little-endian form. Each `f` coefficient is transformed to the corresponding `h` coefficient with the following sequence of `int16` operations (all intermediate results reduced to `int16`): multiply by 3; subtract 2296; if negative, add 4591; if negative, add 4591; subtract 2295.

- `crypto_core/weightsntrup761`: `crypto_core_weightsntrup761(y,x,0,0)`, where `y` is a `uint8[2]` array and `x` is a `uint8[761]` array, sets `y[0],y[1]` to the little-endian encoding of the sum of the 761 bits `x[0]&1,...,x[760]&1`.

- `crypto_core/wforcesntrup761`: `crypto_core_wforcesntrup761(y,x,0,0)`, where `y` is a `uint8[761]` array and `x` is a `uint8[761]` array, sets `y` to a copy of `x` if the little-endian encoding of the sum of the 761 bits `x[0]&1,...,x[760]&1` is 286. Otherwise it sets `y` to 286 bytes equal to `1` followed by 761−286 bytes equal to `0`.

- `crypto_hashblocks/sha512`: `crypto_hashblocks_sha512(h,x,xlen)` updates an intermediate SHA-512 hash `h` using all of the full 128-byte blocks at the beginning of the `xlen`-byte array `x`, and returns the number of bytes left over, namely `xlen` mod 128.

- `crypto_hash/sha512`: `crypto_hash_sha512(h,x,xlen)` computes the SHA-512 hash `h` of the `xlen`-byte array `x`.

- `crypto_kem/sntrup761`: `crypto_kem_sntrup761_keypair(pk,sk)` is key generation for `sntrup761`, and is provided by the stable API as `sntrup761_keypair`. Similar comments apply to `enc` and `dec`.

The functions `crypto_sort_int32(x,n)` and `crypto_sort_uint32(x,n)` take time that depends on `n` but not on the contents of the `x` array. Similarly, the `crypto_hash*` functions take time that depends on input length but not on input contents. All other subroutines take constant time. There is one use of "declassification" in `crypto_kem/sntrup`: a rejection-sampling loop at the beginning of key generation enforces invertibility mod 3.

As in SUPERCOP and NaCl, array lengths intentionally use `long long`, not `size_t`. In libntruprime, as in lib25519 and libmceliece, array lengths are signed.

### Implementations

A single primitive can, and usually does, have multiple implementations. Each implementation is in its own subdirectory. The implementations are required to have exactly the same input-output behavior, and to some extent this is tested, although it is not yet formally verified (except for some components such as `crypto_sort`).

Different implementations typically offer different tradeoffs between portability, simplicity, and efficiency. For example, `crypto_core/inv3sntrup761/bits64` is portable; `crypto_core/inv3sntrup761/avx` is faster and less portable.

Each unportable implementation has an `architectures` file. Each line in this file identifies a CPU instruction set (and ABI) where the implementation works. For example, `crypto_core/inv3sntrup761/avx/architectures` has two lines

    amd64 avx2
    x86 avx2

meaning that the implementation works on CPUs that have the Intel/AMD 64-bit or 32-bit instruction sets with the AVX2 instruction-set extension. The top-level `compilers` directory shows (among other things) the allowed instruction-set names such as `avx2`.

At run time, libntruprime checks the CPU where it is running, and selects an implementation where `architectures` is compatible with that CPU. Each primitive makes its own selection once per program startup, using the compiler's `ifunc` mechanism (or `constructor` on platforms that do not support `ifunc`). This type of run-time selection means, for example, that an `amd64` CPU without AVX2 can share binaries with an `amd64` CPU with AVX2. However, correctness requires instruction sets to be preserved by migration across cores via the OS kernel, VM migration, etc.

The compiler has a `target` mechanism that makes an `ifunc` selection based on CPU architectures. Instead of using the `target` mechanism, libntruprime uses a more sophisticated mechanism that also accounts for benchmarks collected in advance of compilation.

### Compilers

libntruprime tries different C compilers for each implementation. For example, `compilers/default` lists the following compilers:

    clang -Wall -fPIC -fwrapv -Qunused-arguments -O2
    gcc -Wall -fPIC -fwrapv -O3

Sometimes `gcc` produces better code, and sometimes `clang` produces better code.

As another example, `compilers/amd64+sse3+ssse3+sse41+sse42+popcnt+avx+bmi1+bmi2+avx2+fma` lists the following compilers:

    clang -Wall -fPIC -fwrapv -Qunused-arguments -O2 -mmmx -msse -msse2 -msse3 -mssse3 -msse4.1 -msse4.2 -mavx -mbmi -mbmi2 -mpopcnt -mavx2 -mfma -mtune=skylake
    gcc -Wall -fPIC -fwrapv -O3 -mmmx -msse -msse2 -msse3 -mssse3 -msse4.1 -msse4.2 -mavx -mbmi -mbmi2 -mpopcnt -mavx2 -mfma -mtune=skylake

The `-mavx2` option tells these compilers that they are free to use the AVX2 instruction-set extension.

Code compiled using the compilers in `compilers/amd64+sse3+ssse3+sse41+sse42+popcnt+avx+bmi1+bmi2+avx2+fma` will be considered at run time by the libntruprime selection mechanism if the `supports()` function in `compilers/amd64+sse3+ssse3+sse41+sse42+popcnt+avx+bmi1+bmi2+avx2+fma.c` returns nonzero. This function checks whether the run-time CPU supports AVX2 (and SSE3 and so on, and OSXSAVE with XMM/YMM being saved; https://gcc.gnu.org/bugzilla/show_bug.cgi?id=85100 says that all versions of gcc until 2018 handled this incorrectly in `target`). Similar comments apply to other `compilers/*` files.

If some compilers fail (for example, clang is not installed, or the compiler version is too old to support the compiler options used in libntruprime), the libntruprime compilation process will try its best to produce a working library using the remaining compilers, even if this means lower performance.

### Trimming

By default, to reduce size of the compiled library, the libntruprime compilation process trims the library down to the implementations that are selected by libntruprime's selection mechanism.

For example, if the selection mechanism decides that CPUs with AVX2 should use `invsntrup761/avx` with `clang` and that other CPUs should use `invsntrup761/portable` with `gcc`, then trimming will remove `invsntrup761/avx` compiled with `gcc` and `invsntrup761/portable` compiled with `clang`.

This trimming is handled at link time rather than compile time to increase the chance that, even if some implementations are broken by compiler "upgrades", the library will continue to build successfully.

To avoid this trimming, pass the `--no-trim` option to `./configure`. All implementations that compile are then included in the library, tested by `ntruprime-test`, and measured by `ntruprime-speed`. You'll want to avoid trimming if you're adding new instruction sets or new implementations (see below), so that you can run tests and benchmarks of code that isn't selected yet.

### How to recompile after changes

If you make changes under `crypto_*`, the fully supported recompilation mechanism is to run `./configure` again to clean and repopulate the build directory, and then run `make` again to recompile everything.

This can be on the scale of seconds if you have enough cores, but maybe you're developing on a slower machine. Three options are currently available to accelerate the edit-compile cycle:

- There is an experimental `--no-clean` option to `./configure` that, for some simple types of changes, can produce a successful build without cleaning.

- Running `make` without `./configure` can work for some particularly simple types of changes. However, not all dependencies are currently expressed in `Makefile`, and some types of dependencies that `./configure` understands would be difficult to express in the `Makefile` language.

- You can disable the implementations you're not using by setting sticky bits on the source directories for those implementations: e.g., `chmod +t crypto_*/*/avx`.

Make sure to reenable all implementations and do a full clean build if you're collecting data to add to the source `benchmarks` directory.

### How to add new instruction sets

Adding another file `compilers/amd64+foo`, along with a `supports()` implementation in `compilers/amd64+foo.c`, will support a new instruction set. Do not assume that the new `foo` instruction set implies support for older instruction sets (the idea of "levels" of instruction sets); instead make sure to include the older instruction sets in `+` tags, as illustrated by `compilers/amd64+sse3+ssse3+sse41+sse42+popcnt+avx+bmi1+bmi2+avx2+fma`.

In the compiler options, always make sure to include `-fPIC` to support shared libraries, and `-fwrapv` to switch to a slightly less dangerous version of C.

The `foo` tags don't have to be instruction sets. For example, if a CPU has the same instruction set but wants different optimizations because of differences in instruction timings, you can make a tag for those optimizations, using, e.g., CPU IDs or benchmarks in the corresponding `supports()` function to decide whether to enable those optimizations. Benchmarks tend to be more future-proof than a list of CPU IDs, but the time taken for benchmarks at program startup has to be weighed against the subsequent speedup from the resulting optimizations.

To see how well libntruprime performs with the new compilers, run `ntruprime-speed` on the target machine and look for the `foo` lines in the output. If the new performance is better than the performance shown on the `selected` lines:

- Copy the `ntruprime-speed` output into a file on the `benchmarks` directory, typically named after the hostname of the target machine.

- Run `./prioritize` in the top-level directory to create `priority` files. These files tell libntruprime which implementations to select for any given architecture.

- Reconfigure (again with `--no-trim`), recompile, rerun `ntruprime-test`, and rerun `ntruprime-speed` to check that the `selected` lines now use the `foo` compiler.

If the `foo` implementation is outperformed by other implementations, then these steps don't help except for documenting this fact. The same implementation might turn out to be useful for subsequent `foo` CPUs.

### How to add new implementations

Taking full advantage of the `foo` instruction set usually requires writing new implementations. Sometimes there are also ideas for taking better advantage of existing instruction sets.

Structurally, adding a new implementation of a primitive is a simple matter of adding a new subdirectory with the code for that implementation. Most of the work is optimizing the use of `foo` intrinsics in `.c` files or `foo` instructions in `.S` files. Make sure to include an `architectures` file saying, e.g., `amd64 avx2 foo`.

Names of implementation directories can use letters, digits, dashes, and underscores. Do not use two implementation names that are the same when dashes and underscores are removed.

All `.c` and `.S` files in the implementation directory are compiled and linked. There is no need to edit a separate list of these files. You can also use `.h` files via the C preprocessor.

If an implementation is actually more restrictive than indicated in `architectures` then the resulting compiled library will fail on some machines (although perhaps that implementation will not be used by default). Putting unnecessary restrictions into `architectures` will not create such failures, but can unnecessarily limit performance.

Some, but not all, mistakes in `architectures` will produce warnings from the `checkinsns` script that runs automatically when libntruprime is compiled. Running the `ntruprime-test` program tries all implementations, but only on the CPU where `ntruprime-test` is being run; also, `ntruprime-test` does not guarantee code coverage.

`amd64` implies little-endian, and implies architectural support for unaligned loads and stores. Beware, however, that the Intel/AMD vectorized `load`/`store` intrinsics (and the underlying `movdqa` instruction) require alignment; if in doubt, use `loadu`/`storeu` (and `movdqu`). The `ntruprime-test` program checks unaligned inputs and outputs, but can miss issues with unaligned stack variables.

To test your implementation, compile everything, check for compiler warnings and errors, run `ntruprime-test` (or just `ntruprime-test xof` to test a `crypto_xof` implementation), and check for a line saying `all tests succeeded`. To use AddressSanitizer (for catching, at run time, buffer overflows in C code), add `-fsanitize=address` to the `gcc` and `clang` lines in `compilers/*`; you may also have to add `return;` at the beginning of the `limits()` function in `command/limits.inc`.

To see the performance of your implementation, run `ntruprime-speed`. If the new performance is better than the performance shown on the `selected` lines, follow the same steps as for a new instruction set: copy the `ntruprime-speed` output into a file on the `benchmarks` directory; run `./prioritize` in the top-level directory to create `priority` files; reconfigure (again with `--no-trim`); recompile; rerun `ntruprime-test`; rerun `ntruprime-speed`; check that the `selected` lines now use the new implementation.

### How to handle namespacing

As in SUPERCOP and NaCl, to call `crypto_sort_int32()`, you have to include `crypto_sort_int32.h`; but to write an implementation of `crypto_sort_int32()`, you have to instead include `crypto_sort.h` and define `crypto_sort`. Similar comments apply to other primitives.

The function name that's actually linked might end up as, e.g., `libntruprime_sort_int32_avx2_C2` where `avx2` indicates the implementation and `C2` indicates the compiler. Don't try to build this name into your implementation.

If you have another global symbol `x` (for example, a non-`static` function in a `.c` file, or a non-`static` variable outside functions in a `.c` file), you have to replace it with `CRYPTO_NAMESPACE(x)`, for example with `#define x CRYPTO_NAMESPACE(x)`.

For global symbols in `.S` files and `shared-*.c` files, use `CRYPTO_SHARED_NAMESPACE` instead of `CRYPTO_NAMESPACE`. For `.S` files that define both `x` and `_x` to handle platforms where `x` in C is `_x` in assembly, use `CRYPTO_SHARED_NAMESPACE(x)` and `_CRYPTO_SHARED_NAMESPACE(x)`; `CRYPTO_SHARED_NAMESPACE(_x)` is not sufficient.

libntruprime includes a mechanism to recognize files that are copied across implementations (possibly of different primitives) and to unify those into a file compiled only once, reducing the overall size of the compiled library and possibly improving cache utilization. To request this mechanism, include a line

    // linker define x

for any global symbol `x` defined in the file, and a line

    // linker use x

for any global symbol `x` used in the file from the same implementation (not `crypto_*` subroutines that you're calling, `randombytes`, etc.). This mechanism tries very hard, perhaps too hard, to avoid improperly unifying files: for example, even a slight difference in a `.h` file included by a file defining a used symbol will disable the mechanism.

Typical namespacing mistakes will produce either linker failures or warnings from the `checknamespace` script that runs automatically when libntruprime is compiled.

Version: This is version 2026.06.11 of the "Internals" web page.