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Johannes Røsvik 2020-05-23 15:44:21 +02:00
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TTM4135.ipynb
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@ -252,7 +252,7 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"1105 is probable prime\n" "1105 is composite\n"
] ]
} }
], ],
@ -265,7 +265,7 @@
"# times to test for primality\n", "# times to test for primality\n",
"from random import randint\n", "from random import randint\n",
"def fermat_prime(n, k):\n", "def fermat_prime(n, k):\n",
" for x in range(k):\n", " for _ in range(k):\n",
" a = randint(2,n-2)\n", " a = randint(2,n-2)\n",
" # Fermat’s theorem says that if a number p is prime then \n", " # Fermat’s theorem says that if a number p is prime then \n",
" # a^p−1 mod p = 1 for all a with gcd(a,p) = 1.\n", " # a^p−1 mod p = 1 for all a with gcd(a,p) = 1.\n",
@ -299,7 +299,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 23, "execution_count": 8,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
@ -382,7 +382,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": 9,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
@ -429,9 +429,8 @@
"source": [ "source": [
"# Discrete logarithm problem\n", "# Discrete logarithm problem\n",
"Given a prime `p` and an integer `y` with `0 < y < p`, find `x` such that \n", "Given a prime `p` and an integer `y` with `0 < y < p`, find `x` such that \n",
"```\n", "\n",
"y = g^x mod p\n", "> $y = g^{x}\\mod{p}$\n",
"```\n",
"\n", "\n",
"No polynomial algorithims exists, but \"Baby-step giant-step\" is a reasonable one. \n", "No polynomial algorithims exists, but \"Baby-step giant-step\" is a reasonable one. \n",
"\n", "\n",
@ -443,7 +442,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 35, "execution_count": 10,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
@ -520,7 +519,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 10, "execution_count": 11,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {