document.write( "Question 1207737: Carlos wants to send Cecil a message encrypted with RSA. Cecil has published his public encryption exponent $4$ and his public modulus $15$. When Carlos encrypts the number $11$ with this system, what is the result? \n" ); document.write( "

Algebra.Com's Answer #845878 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "I did a little research on cryptography. RSA stands for Rivest=Shamir-Adleman,\r\n" );
document.write( "the cryptographers who came up with the RSA cryptographic algorithm in 1977.\r\n" );
document.write( "It's a cookbook formula.\r\n" );
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document.write( "Carlos wants to send Cecil a message encrypted with RSA. Cecil has published his\r\n" );
document.write( "public encryption exponent $4$ and his public modulus $15$. When Carlos encrypts\r\n" );
document.write( "the number $11$ with this system, what is the result?\r\n" );
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document.write( "Cecil has published his public encryption exponent as 4 and his public modulus\r\n" );
document.write( "as 15.\r\n" );
document.write( "Carlos wants to encrypt the number 11 using this RSA public key.\r\n" );
document.write( "The formula for RSA encryption is: \r\n" );
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document.write( ", where:\r\n" );
document.write( "C = the ciphertext (the encrypted message)\r\n" );
document.write( "M = the plaintext message (in this case, 11)\r\n" );
document.write( "e = the public encryption exponent (4)\r\n" );
document.write( "n = the public modulus (15)\r\n" );
document.write( "Plugging in the values:\r\n" );
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document.write( "      976 \r\n" );
document.write( " 15)14641\r\n" );
document.write( "    135\r\n" );
document.write( "     114\r\n" );
document.write( "     105\r\n" );
document.write( "       91\r\n" );
document.write( "       90\r\n" );
document.write( "        1\r\n" );
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document.write( "The remainder is 1,\r\n" );
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document.write( "so  \r\n" );
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document.write( "Therefore, the result of encrypting the number 11 with Cecil's public key (exponent 4, modulus 15) is 1.\r\n" );
document.write( "So the encrypted message that Carlos would send to Cecil is the number 1.\r\n" );
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document.write( "Edwin

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