1 files changed, 124 insertions, 0 deletions

diff --git a/docs/libraries.rst b/docs/libraries.rst
new file mode 100644
index 0000000..292d4bc
--- /dev/null
+++ b/docs/libraries.rst
@@ -0,0 +1,124 @@
+================
+ECC in Libraries
+================
+
+BouncyCastle
+============
+
+| Version: ``1.76`` (tag r1rv76)
+| Repository: https://github.com/bcgit/bc-java/
+| Docs: https://bouncycastle.org/docs/docs1.8on/index.html
+
+Primitives
+----------
+
+Supports short-Weierstrass curves for the usual (ECDSA, ECDH).
+Supports X25519, Ed25519.
+Also more exotic stuff like ECMQV, GOST key exchange and signatures
+and lots of others.
+
+Lots of `scalarmults <https://github.com/bcgit/bc-java/tree/r1rv76/core/src/main/java/org/bouncycastle/math/ec>`_ available:
+ - `Comb <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/FixedPointCombMultiplier.java>`_
+ - `GLV <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/GLVMultiplier.java>`_
+ - `Window NAF L2R <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/WNafL2RMultiplier.java>`_
+ - `Window "tau" NAF <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/WTauNafMultiplier.java>`_
+
+Several `coordinate systems <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/ECCurve.java#L27>`_ supported:
+ - Affine
+ - Projective (Homogenous)
+ - Jaobian
+ - Jacobian-Chudnovsky
+ - Jacobian-Modified
+ - Lambda-Affine? (binary-field curves only)
+ - Lambda-Projective? (binary-field curves only)
+ - Skewed? (binary-field curves only)
+
+Some curve-custom code in:
+https://github.com/bcgit/bc-java/tree/r1rv76/core/src/main/java/org/bouncycastle/math/ec/custom/sec
+Specifically, fast-prime modular reduction for SECG curves, and (weirdly) a short-Weierstrass implementation of Curve25519.
+
+Ed25519 based on `Mike Hamburg's work <https://eprint.iacr.org/2012/309.pdf>`_.
+
+ECDH
+^^^^
+
+KeyGen:
+ - Short-Weierstrass
+ - `Comb <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/crypto/generators/ECKeyPairGenerator.java#L94>`_ via ``ECKeyPairGenerator.generateKeyPair -> ECKeyPairGenerator.createBasePointMultiplier``.
+ - `Jacobian-Modified <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/ECCurve.java#L676>`_ via ``ECCurve.FP_DEFAULT_COORDS``.
+   SECP curves use Jacobian, SECT curves use Lambda-Projective.
+ - Formulas unknown.
+
+Derive:
+ - Short-Weierstrass
+ - `GLV if possible, else Window NAF <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/ECCurve.java#L154>`_ via ``ECDHBasicAgreement.calculateAgreement -> ECPoint.multiply -> ECCurve.getMultiplier -> ECCurve.createDefaultMultiplier``.
+ - `Jacobian-Modified <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/ECCurve.java#L676>`_ via ``ECCurve.FP_DEFAULT_COORDS``.
+   SECP curves use Jacobian, SECT curves use Lambda-Projective.
+ - Formulas unknown.
+
+ECDSA
+^^^^^
+
+KeyGen:
+ - Short-Weierstrass
+ - `Comb <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/crypto/generators/ECKeyPairGenerator.java#L94>`_ via ``ECKeyPairGenerator.generateKeyPair -> ECKeyPairGenerator.createBasePointMultiplier``.
+ - `Jacobian-Modified <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/ECCurve.java#L676>`_ via ``ECCurve.FP_DEFAULT_COORDS``.
+   SECP curves use Jacobian, SECT curves use Lambda-Projective.
+ - Formulas unknown.
+
+Sign:
+ - Short-Weierstrass
+ - `Comb <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/crypto/signers/ECDSASigner.java#L237>`_ via
+   ``ECDSASigner.generateSignature -> ECDSASigner.createBasePointMultiplier``.
+ - `Jacobian-Modified <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/ECCurve.java#L676>`_ via ``ECCurve.FP_DEFAULT_COORDS``.
+   SECP curves use Jacobian, SECT curves use Lambda-Projective.
+ - Formulas unknown.
+
+Verify:
+ - Short-Weierstrass
+ - `Multi-scalar GLV if possible, else multi-scalar Window NAF with Shamir's trick <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/ECAlgorithms.java#L72>`_ via ``ECDSASigner.verifySignature -> ECAlgorithms.sumOfTwoMultiples``.
+ - `Jacobian-Modified <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/ECCurve.java#L676>`_ via ``ECCurve.FP_DEFAULT_COORDS``.
+   SECP curves use Jacobian, SECT curves use Lambda-Projective.
+ - Formulas unknown.
+
+X25519
+^^^^^^
+
+KeyGen:
+ - Twisted-Edwards
+ - `Comb <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/rfc8032/Ed25519.java#L92>`_ via
+   ``X25519.generatePublicKey -> X25519.scalarMultBase -> Ed25519.scalarMultBaseYZ -> Ed25519.scalarMultBase``.
+ - Many coordinate systems: Extended, half-Niels, affine.
+ - Some HWCD formulas are used.
+
+Derive:
+ - Montgomery
+ - `Ladder <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/rfc7748/X25519.java#L93>`_ via
+   ``X25519.calculateAgreement -> X25519.scalarMult``.
+ - `xz <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/rfc7748/X25519.java#L68>`_.
+ - `dbl-1987-m-3 <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/rfc7748/X25519.java#L73>`_ and
+   some `ladd-1987 <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/rfc7748/X25519.java#L111>`_ formula.
+
+Ed25519
+^^^^^^^
+
+KeyGen:
+ - Twisted-Edwards
+ - `Comb <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/rfc8032/Ed25519.java#L92>`_  via
+   ``Ed25519.generatePublicKey -> Ed25519.scalarMultBaseEncoded -> Ed25519.scalarMultBase``.
+ - Many coordinate systems: Extended, half-Niels, affine.
+ - Some HWCD formulas are used.
+
+Sign:
+ - Twisted-Edwards
+ - `Comb <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/rfc8032/Ed25519.java#L92>`_ via
+   ``Ed25519.sign -> Ed25519.implSign -> Ed25519.scalarMultBaseEncoded -> Ed25519.scalarMultBase``.
+ - Many coordinate systems: Extended, half-Niels, affine.
+ - Some HWCD formulas are used.
+
+Verify:
+ - Twisted-Edwards
+ - `Multi-scalar Window-NAF with Straus's trick <https://github.com/bcgit/bc-java/blob/r1rv76/core/src/main/java/org/bouncycastle/math/ec/rfc8032/Ed25519.java#L1329>`_ via
+   ``Ed25519.verify -> Ed25519.implVerify -> Ed25519.scalarMultStraus128Var``.
+ - Many coordinate systems: Extended, half-Niels, affine.
+ - Some HWCD formulas are used.