Add purpose section to README; update package descriptions and docstr…

…ings.

README.rst

@@ -2,7 +2,7 @@
 sophiegermain
 =============
 
-Pure-Python library that provides a selection of `Sophie Germain primes <https://en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes>`__.
+Pure-Python library that provides a selection of `Sophie Germain primes <https://en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes>`__ that are organized by representation size.
 
 |pypi| |readthedocs| |actions| |coveralls|
 
@@ -22,6 +22,10 @@ Pure-Python library that provides a selection of `Sophie Germain primes <https:/
    :target: https://coveralls.io/github/nillion-oss/sophiegermain?branch=main
    :alt: Coveralls test coverage summary.
 
+Purpose
+-------
+Some cryptographic protocols involve the use of `Sophie Germain and safe primes <https://en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes>`__. In such cases, it is often useful to choose a Sophie Germain or safe prime based on the range of values (*i.e.*, `congruence classes of integers <https://en.wikipedia.org/wiki/Modular_arithmetic>`__ or `finite field <https://en.wikipedia.org/wiki/Finite_field>`__ elements) that an instantiation of a protocol must accommodate. This library provides immediate access to the smallest Sophie Germain prime for each possible binary representation length (up to and including 1025 bits).
+
 Installation and Usage
 ----------------------
 This library is available as a `package on PyPI <https://pypi.org/project/sophiegermain>`__:

pyproject.toml

@@ -2,7 +2,8 @@
 name = "sophiegermain"
 version = "0.1.0"
 description = """\
-    Pure-Python library that provides a selection of Sophie Germain primes.
+    Pure-Python library that provides a selection of Sophie Germain primes
+    that are organized by representation size.
     """
 license = {text = "MIT"}
 authors = [

src/sophiegermain/sophiegermain.py

@@ -1,5 +1,6 @@
 """
-Pure-Python library that provides a selection of Sophie Germain primes.
+Pure-Python library that provides a selection of Sophie Germain primes
+that are organized by representation size.
 """
 # pylint: disable=too-many-lines
 from __future__ import annotations
@@ -1036,8 +1037,9 @@
 
 def sophiegermain(bit_length: int) -> int:
     """
-    Return the smallest Sophie Germain prime that can be represented using
-    the specified number of bits.
+    Return the smallest
+    `Sophie Germain prime <https://en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes>`__
+    the representation of which requires the specified number of bits.
     
     >>> sophiegermain(2)
     2
@@ -1052,8 +1054,8 @@ def sophiegermain(bit_length: int) -> int:
     >>> sophiegermain(1025).bit_length()
     1025
 
-    The result returned by :obj:`sophiegermain` can always be represented
-    using the specified number of bits.
+    The result returned by :obj:`sophiegermain` can be represented using the
+    specified number of bits.
     
     >>> all([sophiegermain(k).bit_length() == k for k in range(2, 1026)])
     True