From f8013f56eaba9eb0ea269fc74191a4d8075679ff Mon Sep 17 00:00:00 2001
From: Vasudev Kamath
Date: Tue, 28 Aug 2018 20:22:52 +0530
Subject: Some updation.
---
content/development/golang_spake2_edwards.rst | 18 +++++++++++-------
1 file changed, 11 insertions(+), 7 deletions(-)
diff --git a/content/development/golang_spake2_edwards.rst b/content/development/golang_spake2_edwards.rst
index 4e95f51..5b0ca19 100644
--- a/content/development/golang_spake2_edwards.rst
+++ b/content/development/golang_spake2_edwards.rst
@@ -1,7 +1,7 @@
SPAKE2 in Golang: ECDH, SPAKE2 and Curve Ed25519
################################################
-:date: 2018-08-28 11:38 +0530
+:date: 2018-08-28 20:25 +0530
:slug: golang_spake2_4
:tags: go, golang, spake2, cryptography, ecc
:author: copyninja
@@ -42,6 +42,8 @@ share a shared secret now.
s = B^a \bmod{p} = g^{ba} \bmod{p} = A^b \bmod{p} = g^{ab} \bmod{p}
+Since group is Abelian :math:`g^{ba} \bmod{p} = g^{ab} \bmod{p}` and hence both
+side will come to same shared key.
Now in ECC,
@@ -128,18 +130,20 @@ Curve Ed25519 Group
Now that we have seen the SPAKE2 protocol, we will next see the use of Elliptic
Curve groups in it and see how it varies.
-SPAKE2 uses *Abelian Group* with large number of "elements". `Brian Warner
-`_ has choosen elliptic curve group *Ed25519* (some
-times also referred as X25519) as default group in *python-spake2*
+SPAKE2 uses *Abelian Group* with large number of "elements". We know that
+Elliptic curve groups are Abelian groups, so we can fit them in SPAKE2. `Brian
+Warner `_ has choosen elliptic curve group *Ed25519*
+(some times also referred as X25519) as default group in *python-spake2*
implementation. This is the same group which is used in *Ed25519 signature
scheme*. The difference between multiplicative integer group modulo p and
elliptic curve group is that, element in integer group is just a number but in
elliptic curve group its a point. (represented by 2 co-ordinates).
-Curve Ed25519 is a *twisted Edwards curve*, defined in affine form as
-:math:`ax^2 + y^2 = 1 + dx^2y^2` where :math:`d \in k\{0,1\}`.
+Curve Ed25519 which is actually called Edwards25519 is a *twisted Edwards
+curve*, defined in affine form as :math:`ax^2 + y^2 = 1 + dx^2y^2` where
+:math:`d \in k\{0,1\}`.
-* :math:`q = 2^{255} - 19` is the order of curve group
+* :math:`q = 2^{255} - 19` is the order of curve groups
* :math:`l = 2^{252} + 27742317777372353535851937790883648493` is the order of
curve subgroup.
* :math:`a = -1`
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