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Add the curve25519 curve (#124)

Browse Source 
* add ed25519 curve

* changelog

* curve info

* fix

* edit

* update

* add more explanation

* Update curve25519/src/curves/mod.rs

* Update curve25519/src/curves/mod.rs

* fixed the comment

* Update curve25519/src/curves/mod.rs

Co-authored-by: onewayfunc <onewayfunc@gmail.com>
This commit is contained in:
Weikeng Chen
2022-10-29 19:55:35 -07:00
committed by GitHub
parent a7d266f73d
commit db03d405b5
17 changed files with 450 additions and 0 deletions
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91
curve25519/scripts/fr.ipynb Normal file
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "04264893",
"metadata": {},
"outputs": [],
"source": [
"r = 7237005577332262213973186563042994240857116359379907606001950938285454250989"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1603b293",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2^2 * 3 * 11 * 198211423230930754013084525763697 * 276602624281642239937218680557139826668747"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"factor(r - 1)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "425ceac7",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"7237005577332262213973186563042994240857116359379907606001950938285454250988\n",
"1570463851528226261927580272323658009530148727742783848239914322803198255651\n",
"4908983020090465803374304318106080751443647916949975825112097080460587568629\n",
"7119675135705137915307919240607293966034195415655343409829245710729128040338\n",
"2975531125133123119648879457563281269120703404158613135195788908093573672641\n"
]
}
],
"source": [
"gen = 2\n",
"print(pow(gen, (r - 1) / 2, r))\n",
"print(pow(gen, (r - 1) / 3, r))\n",
"print(pow(gen, (r - 1) / 11, r))\n",
"print(pow(gen, (r - 1) / 198211423230930754013084525763697, r))\n",
"print(pow(gen, (r - 1) / 276602624281642239937218680557139826668747, r))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f4c58ca4",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.2",
"language": "sage",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

162
curve25519/scripts/g1.ipynb Normal file
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "f890e69f",
"metadata": {},
"outputs": [],
"source": [
"q = pow(2,255) - 19"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d90a7f0b",
"metadata": {},
"outputs": [],
"source": [
"A = 486662\n",
"B = 1"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "1b2aebc5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"486664\n",
"486660\n"
]
}
],
"source": [
"a = (A + 2) * 1\n",
"d = (A - 2) * 1\n",
"print(a)\n",
"print(d)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "aae2f8bf",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"9"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"u = 9\n",
"u"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "ea9a4d90",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"14781619447589544791020593568409986887264606134616475288964881837755586237401"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v = mod(u^3 + A * u^2 + u, q).sqrt()\n",
"v"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "95895004",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"38213832894368730265794714087330135568483813637251082400757400312561599933396"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"u * pow(v, -1, q) % q"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "1134cf74",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"46316835694926478169428394003475163141307993866256225615783033603165251855960"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(u - 1) * pow(u + 1, -1, q) % q"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ec089e21",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.2",
"language": "sage",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}