add libsecp256k1 docs

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diff --git a/docs/libraries.rst b/docs/libraries.rst
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--- a/docs/libraries.rst
+++ b/docs/libraries.rst
@@ -682,6 +682,89 @@ NSS
 libsecp256k1
 ============
 
+| Version: ``v0.4.0``
+| Repository: https://github.com/bitcoin-core/secp256k1
+| Docs: 
+
+Primitives
+----------
+
+Supports ECDSA, ECDH and Schnorr signatures over secp256k1.
+
+ECDH
+^^^^
+
+KeyGen:
+ - Short-Weierstrass
+ - `Fixed findow with full precomputation <https://github.com/bitcoin-core/secp256k1/blob/v0.4.0/src/ecmult_gen_impl.h#L45>`__ via ``secp256k1_ec_pubkey_create -> secp256k1_ec_pubkey_create_helper -> secp256k1_ecmult_gen``. Window of size 4.
+ - Uses scalar blinding.
+ - `Jacobian version of add-2002-bj <https://github.com/bitcoin-core/secp256k1/blob/v0.4.0/src/group_impl.h#L670>`__  (via ``secp256k1_gej_add_ge``).
+ - No doubling.
+
+
+Derive:
+ - Uses GLV decomposition and `interleaving with width-5 NAFs <https://github.com/bitcoin-core/secp256k1/blob/v0.4.0/src/ecmult_const_impl.h#L133>`__ via ``secp256k1_ecdh -> secp256k1_ecmult_const``.
+ - Addition same as in Keygen.
+ - `DBL <https://github.com/bitcoin-core/secp256k1/blob/v0.4.0/src/group_impl.h#L406>`__ (via ``secp256k1_gej_double``)::
+     
+    Z3 = Y1*Z1
+    S = Y1^2
+    L = X1^2
+    L = 3*L
+    L = L/2
+    T = -S
+    T = T*X1
+    X3 = L^2
+    X3 = X3+T
+    X3 = X3+T
+    S = S^2
+    T = T+X3
+    Y3 = T*L
+    Y3 = Y3+S
+    Y3 = -Y3
+
+ECDSA
+^^^^^
+
+Keygen:
+ - Same as ECDH.
+
+Sign:
+ - Same as Keygen via ``secp256k1_ecdsa_sign -> secp256k1_ecdsa_sign_inner -> secp256k1_ecdsa_sig_sign -> secp256k1_ecmult_gen``.
+
+Verify:
+ - Split both scalars using GLV and then interleaving with width-5 NAFS on 4 scalars via ``secp256k1_ecdsa_verify -> secp256k1_ecdsa_sig_verify -> secp256k1_ecmult -> secp256k1_ecmult_strauss_wnaf``.
+ - DBL same as in ECDH DERIVE. Two formulas for addition are implemented. For the generator part, same addition as in Keygen is used. For public key, the following::
+    
+    assume iZ2 = 1/Z2
+    az = Z_1*iZ2
+    Z12 = az^2
+    u1 = X1
+    u2 = X2*Z12
+    s1 = Y1 
+    s2 = Y2*Z12
+    s2 = s2*az
+    h = -u1
+    h = h+u2
+    i = -s2
+    i = i+s1
+    Z3 = Z1*h
+    h2 = h^2
+    h2 = -h2
+    h3 = h2*h
+    t = u1*h2
+    X3 = i^2
+    X3 = X3+h3
+    X3 = X3+t
+    X3 = X3+t
+    t = t+X3
+    Y3 = t*i
+    h3 = h3*s1
+    Y3 = Y3+h3
+
+ - Before the addition the Jacobian coordinates are mapped to an isomorphic curve. 
+
+
 Nettle
 ======