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Some fixes/extensions
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@teschlg
teschlg committed Jun 26, 2024
1 parent 92d9993 commit 6452fbc
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99 changes: 79 additions & 20 deletions doc/kryptools.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -359,7 +359,6 @@
],
"source": [
"from fractions import Fraction\n",
"\n",
"from kryptools import cf, convergents\n",
"\n",
"cf(Fraction(18, 23))"
Expand Down Expand Up @@ -411,7 +410,7 @@
{
"data": {
"text/plain": [
"-1"
"1"
]
},
"execution_count": 13,
Expand All @@ -422,7 +421,7 @@
"source": [
"from kryptools import jacobi_symbol\n",
"\n",
"jacobi_symbol(3, 7)"
"jacobi_symbol(4, 7)"
]
},
{
Expand Down Expand Up @@ -493,7 +492,7 @@
"id": "76fb4f61-d902-4432-92c9-7383c4e068cd",
"metadata": {},
"source": [
"To compute the order of a element of the [multiplicative group of integers modulo $n$](https://en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n), $\\mathbb{Z}_n^*$, use"
"To compute the order of an element of the [multiplicative group of integers modulo $n$](https://en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n), $\\mathbb{Z}_n^*$, use"
]
},
{
Expand Down Expand Up @@ -1558,6 +1557,14 @@
" return Poly(c, ring = gf, modulus = kyber(n))"
]
},
{
"cell_type": "markdown",
"id": "49847633-a975-4537-9ddd-9fc49b898dce",
"metadata": {},
"source": [
"The matrix"
]
},
{
"cell_type": "code",
"execution_count": 47,
Expand All @@ -1577,12 +1584,21 @@
}
],
"source": [
"Matrix(\n",
"A = Matrix(\n",
" [\n",
" [PolyKyber([randint(0, p - 1) for _ in range(n)]) for i in range(k)]\n",
" for j in range(k)\n",
" ]\n",
")"
")\n",
"A"
]
},
{
"cell_type": "markdown",
"id": "2fdfe1e9-2cd4-4725-afa7-08b195d3b1c6",
"metadata": {},
"source": [
"The small solution"
]
},
{
Expand All @@ -1594,7 +1610,8 @@
{
"data": {
"text/plain": [
"[ x^3 + x + 96, 96 x^2 + x + 1 ]"
"[ x^3 + x + 96 ]\n",
"[ 96 x^2 + x + 1 ]"
]
},
"execution_count": 48,
Expand All @@ -1603,7 +1620,16 @@
}
],
"source": [
"Matrix([[PolyKyber([randint(-1, 1) for _ in range(n)]) for i in range(k)]])"
"s = Matrix([ PolyKyber([randint(-1,1) for _ in range(n)]) for i in range(k)])\n",
"s"
]
},
{
"cell_type": "markdown",
"id": "ce0eed66-9270-4a04-871b-13578cbde26f",
"metadata": {},
"source": [
"The error"
]
},
{
Expand All @@ -1615,7 +1641,8 @@
{
"data": {
"text/plain": [
"[ 96 x^3 + x + 95, 2 x ]"
"[ 96 x^3 + x + 95 ]\n",
"[ 2 x ]"
]
},
"execution_count": 49,
Expand All @@ -1625,7 +1652,39 @@
],
"source": [
"q = p // (4 * k * n)\n",
"Matrix([[PolyKyber([binomialvariate(2 * q) - q for _ in range(n)]) for i in range(k)]])"
"e = Matrix([PolyKyber([binomialvariate(2 * q) - q for _ in range(n)]) for i in range(k)])\n",
"e"
]
},
{
"cell_type": "markdown",
"id": "684f101f-e79f-4a30-90a5-f5dd3a0557eb",
"metadata": {},
"source": [
"The inhomogenous vector"
]
},
{
"cell_type": "code",
"execution_count": 50,
"id": "fabcbecf-cf96-4211-a1e3-ad0f5a337a09",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[ 47 x^3 + 63 x^2 + 60 x + 38 ]\n",
"[ 47 x^3 + 30 x^2 + 42 x + 47 ]"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b = A * s + e\n",
"b"
]
},
{
Expand All @@ -1646,7 +1705,7 @@
},
{
"cell_type": "code",
"execution_count": 50,
"execution_count": 51,
"id": "9b566550-f23c-4fbc-8b7c-63bbee8e0c72",
"metadata": {},
"outputs": [
Expand Down Expand Up @@ -1685,7 +1744,7 @@
},
{
"cell_type": "code",
"execution_count": 51,
"execution_count": 52,
"id": "55c29e0c-e0c2-409a-af23-6590fd9cc545",
"metadata": {},
"outputs": [
Expand All @@ -1695,7 +1754,7 @@
"(113, 91)"
]
},
"execution_count": 51,
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -1717,7 +1776,7 @@
},
{
"cell_type": "code",
"execution_count": 52,
"execution_count": 53,
"id": "2a3d8e7d-71b3-4a93-b6cc-803f00432c56",
"metadata": {},
"outputs": [
Expand All @@ -1727,7 +1786,7 @@
"129"
]
},
"execution_count": 52,
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -1747,7 +1806,7 @@
},
{
"cell_type": "code",
"execution_count": 53,
"execution_count": 54,
"id": "bb93b5fc-99c9-4977-8299-9342b84e143d",
"metadata": {},
"outputs": [],
Expand All @@ -1767,7 +1826,7 @@
},
{
"cell_type": "code",
"execution_count": 54,
"execution_count": 55,
"id": "41e18357-da42-4cd7-bd4e-1c3355f1c69d",
"metadata": {},
"outputs": [],
Expand All @@ -1790,7 +1849,7 @@
},
{
"cell_type": "code",
"execution_count": 55,
"execution_count": 56,
"id": "af81d5f2-a524-4555-8e74-06a0c9a7ea08",
"metadata": {},
"outputs": [
Expand All @@ -1801,7 +1860,7 @@
" 0x02449ef2ed30a8deb96e584a08c329adbf1be87ce40f1a0e7b4e86178682c41a9c)"
]
},
"execution_count": 55,
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
Expand Down Expand Up @@ -1837,7 +1896,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.2"
"version": "3.12.1"
}
},
"nbformat": 4,
Expand Down
41 changes: 36 additions & 5 deletions kryptools/poly.py
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Original file line number Diff line number Diff line change
Expand Up @@ -83,7 +83,12 @@ def map(self, func):

def __add__(self, other: "Poly") -> "Poly":
if not isinstance(other, self.__class__):
raise NotImplementedError(f"Cannot add {self} and {other}.")
try:
tmp = self.coeff[:]
tmp[0] += other
return self.__class__(tmp, modulus=self.modulus)
except:
return NotImplemented
ls, lo = len(self.coeff), len(other.coeff)
if ls < lo:
scoeff = self.coeff + (lo - ls) * [0]
Expand All @@ -98,12 +103,27 @@ def __add__(self, other: "Poly") -> "Poly":
modulus = other.modulus
return self.__class__([s + o for s, o in zip(scoeff, ocoeff)], modulus=modulus)

def __radd__(self, other: "Poly") -> "Poly":
if not isinstance(other, self.__class__):
try:
tmp = self.coeff[:]
tmp[0] += other
return self.__class__(tmp, modulus=self.modulus)
except:
pass
return NotImplemented

def __neg__(self) -> "Poly":
return Poly([-s for s in self.coeff], modulus=self.modulus)

def __sub__(self, other: "Poly") -> "Poly":
if not isinstance(other, self.__class__):
raise NotImplementedError(f"Cannot subtract {self} and {other}.")
try:
tmp = self.coeff[:]
tmp[0] -= other
return self.__class__(tmp, modulus=self.modulus)
except:
return NotImplemented
ls, lo = len(self.coeff), len(other.coeff)
if ls < lo:
scoeff = self.coeff + (lo - ls) * [0]
Expand All @@ -118,11 +138,22 @@ def __sub__(self, other: "Poly") -> "Poly":
modulus = other.modulus
return self.__class__([s - o for s, o in zip(scoeff, ocoeff)], modulus=modulus)

def __rsub__(self, other: "Poly") -> "Poly":
if not isinstance(other, self.__class__):
try:
tmp = self.coeff[:]
tmp[0] -= other
return self.__class__(tmp, modulus=self.modulus)
except:
pass
return NotImplemented

def __mul__(self, other: "Poly") -> "Poly":
if isinstance(other, int):
return Poly([other * s for s in self.coeff])
if not isinstance(other, self.__class__):
raise NotImplementedError(f"Cannot multiply {self} and {other}.")
try:
return Poly([other * s for s in self.coeff])
except:
return NotImplemented
ls, lo = len(self.coeff), len(other.coeff)
coeff = [0] * (ls + lo - 1)
for k in range(ls + lo - 1):
Expand Down

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