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@ -1,12 +1,5 @@ |
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{ |
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"cells": [ |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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"metadata": {}, |
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"outputs": [], |
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"source": [] |
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}, |
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{ |
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"cell_type": "markdown", |
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"metadata": {}, |
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@ -713,7 +706,7 @@ |
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"3. Select $e$ randomly with $gcd(e, \\varphi(n)) = 1$.\n", |
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"4. Compute $d = e−1 \\mod \\varphi(n)$.\n", |
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"5. The public key is the pair $n$ and $e$.\n", |
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"6. The private key consists of the values $p$, $q$ and $d$.\n", |
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"6. The private key consists of the values $p$, $q$ (or $n = pq$) and $d$.\n", |
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"\n", |
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"### Encryption\n", |
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"\n", |
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@ -723,13 +716,13 @@ |
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"\n", |
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"### Decryption\n", |
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"\n", |
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"The private key for decryption is KD = d (values p and q are not used here).\n", |
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"1. Compute D(C,KD) = Cd mod n = M." |
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"The private key for decryption is $KD = d$ (values $p$ and $q$ are not used here).\n", |
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"1. Compute $D(C,KD) = Cd \\mod n = M$." |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": 24, |
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"execution_count": 14, |
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"metadata": {}, |
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"outputs": [ |
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{ |
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@ -785,15 +778,13 @@ |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": 22, |
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"execution_count": 15, |
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"metadata": {}, |
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"outputs": [ |
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{ |
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"name": "stdout", |
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"output_type": "stream", |
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"text": [ |
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"C = M^e (mod n) = 50^102900819 (mod 604604729) = 2488\n", |
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"\n", |
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"Ciphertext: 2488\n" |
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] |
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} |
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@ -809,28 +800,25 @@ |
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"\n", |
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"M = 50\n", |
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"C = rsa_encrypt(M, rsa_keys)\n", |
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"print(f\"C = M^e (mod n) = {M}^{e} (mod {n}) = {C}\\n\")\n", |
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"print(f\"Ciphertext: {C}\")" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": 23, |
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"execution_count": 16, |
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"metadata": {}, |
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"outputs": [ |
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{ |
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"name": "stdout", |
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"output_type": "stream", |
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"text": [ |
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"M = C^d (mod n) = 2488^1 (mod 604604729) = 50\n", |
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"\n", |
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"Message: 50\n" |
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] |
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} |
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], |
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"source": [ |
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"def rsa_decrypt(C, rsa_keys):\n", |
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" # private key\n", |
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" # Private key\n", |
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" p = rsa_keys['p']\n", |
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" q = rsa_keys['q']\n", |
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" d = rsa_keys['d']\n", |
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@ -840,7 +828,6 @@ |
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" return square_and_multiply(C,d,n)\n", |
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"\n", |
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"M = rsa_decrypt(C, rsa_keys)\n", |
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"print(f\"M = C^d (mod n) = {C}^{d} (mod {n}) = {M}\\n\")\n", |
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"print(f\"Message: {M}\")" |
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] |
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} |
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