python-hsslms

This is an implementation of Leighton-Micali Hash-Based Signatures in Python according to RFC 8554 <https://www.rfc-editor.org/rfc/rfc8554.html>_. The one time signature keys are generated by using pseudo random generator, which saves a lot of memory to store the private keys in ram and on harddisk.

The implementation is meant as a reference and for educational purposes.

The implementation provides 4 classes:

• LM-OTS One-Time Signatures. These are one-time signatures; each private key MUST be used at most one time to sign a message.
• Leighton-Micali Signatures (LMS). This systemholds a fixed number of one-time signatures, i.e. LM-OTS.
• Hierarchical Signatures (HSS). This system uses a sequence of LMS.
• Persistent Hierarchical Signatures (PersHSS). The same as HSS except that the private key is stored in an encrypted file.

Installation

.. code:: bash

python3 -m pip install hsslms

Example Usage

LM-OTS ^^^^^^

.. code:: python

from os import urandom from hsslms import LM_OTS_Priv

generate a one-time private key

sk = LM_OTS_Priv(LMOTS_ALGORITHM_TYPE.LMOTS_SHA256_N32_W2, urandom(16), 0)

sign a message with the private key

signature = sk.sign(b'abc')

compute the related public key

vk = sk.gen_pub()

verify the signature, if invalid an exception will be raised

vk.verify(b'abc', signature)

LMS ^^^

.. code:: python

from os import urandom from hsslms import LMS_Priv

generate a private key

sk = LMS_Priv(LMS_ALGORITHM_TYPE.LMS_SHA256_M32_H10, LMOTS_ALGORITHM_TYPE.LMOTS_SHA256_N32_W8)

sign a message with the private key, in total 2^10 signatures are available

signature = sk.sign(b'abc')

compute the related public key

vk = sk.gen_pub()

verify the signature, if invalid an exception will be raised

vk.verify(b'abc', signature)

HSS ^^^

.. code:: python

from os import urandom from hsslms import HSS_Priv

generate a private key

sk = HSS_Priv([LMS_ALGORITHM_TYPE.LMS_SHA256_M32_H10]*2, LMOTS_ALGORITHM_TYPE.LMOTS_SHA256_N32_W1)

sign a message with the private key, in total 2^20 signatures are available

signature = sk.sign(b'abc')

compute the related public key

vk = sk.gen_pub()

verify the signature, if invalid an exception will be raised

vk.verify(b'abc', signature)

Performance Measurements

The measurements are done on a Ryzen 5600X, where multiprocessing features are used with 6 cores.

Key Generation ^^^^^^^^^^^^^^

+----------+-----+-----+-----+-----+-------------+------+------+------+-------+ | Key-Type | Time[s] | #Signatures | Size of Signature | +==========+=====+=====+=====+=====+=============+======+======+======+=======+ | w | 1 | 2 | 4 | 8 | | 1 | 2 | 4 | 8 | +----------+-----+-----+-----+-----+-------------+------+------+------+-------+ | H5 | 0.1 | 0.1 | 0.1 | 0.1 | 32 | 8688 | 4464 | 2352 | 1296 | +----------+-----+-----+-----+-----+-------------+------+------+------+-------+ | H10 | 0.3 | 0.2 | 0.2 | 0.7 | 1024 | 8848 | 4624 | 2512 | 1456 | +----------+-----+-----+-----+-----+-------------+------+------+------+-------+ | H15 | 8.0 | 4.6 | 4.3 | 20.2| 32768 | 9008 | 4784 | 2672 | 1616 | +----------+-----+-----+-----+-----+-------------+------+------+------+-------+ | H20 | 293 | 161 | 137 | 643 | 1048576 | 9168 | 4944 | 2832 | 1776 | +----------+-----+-----+-----+-----+-------------+------+------+------+-------+ | H10/H10 | 0.6 | 0.5 | 0.5 | 1.4 | 1048576 | 17748| 9300 | 5076 | 2964 | +----------+-----+-----+-----+-----+-------------+------+------+------+-------+ | H10/H15 | 8.1 | 4.6 | 4.2 | 21.1| 33554432 | 17908| 9460 | 5236 | 3124 | +----------+-----+-----+-----+-----+-------------+------+------+------+-------+ | H15/H15 | 15.7| 10.4| 8.9 | 40.0| 1073741824 | 18068| 9620 | 5396 | 3284 | +----------+-----+-----+-----+-----+-------------+------+------+------+-------+

Performance of Signature Generation: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------+-------+-------+-------+-------+ | Key-Type | Time[s] | +==========+=======+=======+=======+=======+ | w | 1 | 2 | 4 | 8 | +----------+-------+-------+-------+-------+ | H15 | 0.001 | 0.001 | 0.001 | 0.005 | +----------+-------+-------+-------+-------+

Performance of Signature Verification: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------+-------+-------+-------+-------+ | Key-Type | Time[s] | +==========+=======+=======+=======+=======+ | w | 1 | 2 | 4 | 8 | +----------+-------+-------+-------+-------+ | H15 | 0.001 | 0.001 | 0.001 | 0.004 | +----------+-------+-------+-------+-------+

License

MIT <https://opensource.org/licenses/MIT>__