Add initial ed25519 notes and example

Signed-off-by: Daniel Bevenius <daniel.bevenius@gmail.com>

Author: danbev

edcurve25519/input.txt

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+bajja

edcurve25519/signature.bin

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+9J�QJ��SϚt1q�\�ŷ��P�<뾷��l�sO/8���`Xc!�:�bޣ�#5�1���

edcurve25519/test.pem

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+-----BEGIN PRIVATE KEY-----
+MC4CAQAwBQYDK2VwBCIEIMa3vX1jnn7GD98BgrTjiY31PJcF+PEFjTk3rDFkQm3F
+-----END PRIVATE KEY-----

edcurve25519/test.pub

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+-----BEGIN PUBLIC KEY-----
+MCowBQYDK2VwAyEAhgxyCkD8+P/7mZSIESrq1Hq0ekaujrDo29f6rzOBPyQ=
+-----END PUBLIC KEY-----

edcurve25519/verify.js

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+const fs = require('fs');
+const crypto = require('crypto');
+const pub = crypto.createPublicKey(fs.readFileSync('test.pub'));
+const input = fs.readFileSync('input.txt');
+const signature = fs.readFileSync('signature.bin');
+console.log('verify successful: ', crypto.verify(null, input, pub, signature));

notes/ed25519.md

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+## Ed25519
+"Normal" Weirstrass curves like NIST P-256, which are used with Elliptic curve
+cryptography have a number of corner/edge cases which can make them slow, and
+also make implementations more difficult which can lead to implementations
+vulnerabilties.
+
+Curve25519 was developed by Daniel J Bernstein in 2006.
+Edward Twisted Curve 25519. There are several benifits to using ed25519 like
+higher performance, smaller private key and public keys, simpler to implemement,
+resistant to timing attacks.
+
+The prime used is 2²⁵⁵-19 (which I think is where the number in the name of this
+curve comes from).
+
+[Curve25519](http://cr.yp.to/ecdh/curve25519-20060209.pdf)
+
+Signatures can fit into 64 bytes.
+
+
+### Creating a key
+```console
+$ openssl genpkey -algorithm ED25519 -out test.pem
+```
+```console
+$  openssl pkey -in test.pem -text
+-----BEGIN PRIVATE KEY-----
+MC4CAQAwBQYDK2VwBCIEIMa3vX1jnn7GD98BgrTjiY31PJcF+PEFjTk3rDFkQm3F
+-----END PRIVATE KEY-----
+ED25519 Private-Key:
+priv:
+    c6:b7:bd:7d:63:9e:7e:c6:0f:df:01:82:b4:e3:89:
+    8d:f5:3c:97:05:f8:f1:05:8d:39:37:ac:31:64:42:
+    6d:c5
+pub:
+    86:0c:72:0a:40:fc:f8:ff:fb:99:94:88:11:2a:ea:
+    d4:7a:b4:7a:46:ae:8e:b0:e8:db:d7:fa:af:33:81:
+    3f:24
+```
+And we can inspect the asn1 format using the following command:
+```console
+$ openssl asn1parse -i -in test.pem 
+    0:d=0  hl=2 l=  46 cons: SEQUENCE          
+    2:d=1  hl=2 l=   1 prim:  INTEGER           :00
+    5:d=1  hl=2 l=   5 cons:  SEQUENCE          
+    7:d=2  hl=2 l=   3 prim:   OBJECT            :ED25519
+   12:d=1  hl=2 l=  34 prim:  OCTET STRING      [HEX DUMP]:0420C6B7BD7D639E7EC60FDF0182B4E3898DF53C9705F8F1058D3937AC3164426DC5
+```
+We can see that the public key is not in there but instead it gets generated by
+the `pkey` command, and if we think back at EC this should just be taking the
+generator point added to it self, private key (integer) number of times.
+The OBJECT :ED25519 is the
+[object identifier](https://oid-rep.orange-labs.fr/get/1.3.101.112), 1.3.101.112.
+
+
+```console
+$ openssl pkey -in test.pem -pubout -out test.pub
+$ cat test.pub 
+-----BEGIN PUBLIC KEY-----
+MCowBQYDK2VwAyEAhgxyCkD8+P/7mZSIESrq1Hq0ekaujrDo29f6rzOBPyQ=
+-----END PUBLIC KEY-----
+$ openssl asn1parse -i -in test.pub 
+    0:d=0  hl=2 l=  42 cons: SEQUENCE          
+    2:d=1  hl=2 l=   5 cons:  SEQUENCE          
+    4:d=2  hl=2 l=   3 prim:   OBJECT            :ED25519
+    9:d=1  hl=2 l=  33 prim:  BIT STRING 
+```
+This is in [spki format](./spki.md).
+
+```console
+$ export LD_LIBRARY_PATH=~/work/security/openssl_build_master/lib64/:$LD_LIBRARY_PATH
+$ ~/work/security/openssl_build_master/bin/openssl pkeyutl -in input.txt -sign -rawin -inkey test.pem > signature.bin
+```
+The signature consists of two 256 bit numbers, R and S
+```console
+$ cat signature.bin | xxd
+00000000: 394a a651 4ac4 d053 cf9a 7431 71d3 5cf3  9J.QJ..S..t1q.\.
+00000010: c5b7 c2d1 1e15 5002 d73c ebbe b7a7 aa6c  ......P..<.....l
+00000020: a218 734f 2f38 c3d9 d860 5863 21ef 3a0f  ..sO/8...`Xc!.:.
+00000030: 1bd9 62de a38c 0323 35b7 31ab 159d 9805  ..b....#5.1.....
+```
+We can verify this (using the public key):
+```console
+$ ~/work/security/openssl_build_master/bin/openssl pkeyutl -verify -sigfile signature.bin -in input.txt -rawin -pubin -inkey test.pub
+Signature Verified Successfully
+```