1.
Give the definition for these terms. Be sure to set up any notation that is required
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Caesar cipher
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RSA public encryption key
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RSA encryption exponent
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RSA decryption exponent
Exercises 5.5.5 Exercises
2.
Encrypt the message UNCG SPARTANS by translating the letters into numbers, applying the given encryption function, then translating the numbers back into letters.
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\(\displaystyle f(p) = p + 3 \bmod{26}\)
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\(\displaystyle f(p) = p + 22 \bmod{26}\)
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\(\displaystyle f(p) = -3p \bmod{26}\)
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\(\displaystyle f(p) = 5p + 7 \bmod{26}\)
3.
Encrypt the message MIDNIGHT by translating the letters into numbers, applying the given encryption function, then translating the numbers back into letters.
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\(\displaystyle f(p) = p + 17 \bmod{26}\)
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\(\displaystyle f(p) = p - 4 \bmod{26}\)
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\(\displaystyle f(p) = -7p \bmod{26}\)
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\(\displaystyle f(p) = 3p + 12 \bmod{26}\)
4.
Decrypt these messages that were encrypted using the Caesar cipher.
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KHOS
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VSDUWDQV
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VHFUHW
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DEVTXDWXODWH
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VXUUHSWLWLRXV
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DOLFH ORYHV ERE
5.
Decrypt these messages that were encrypted using the encryption function \(f(p) = 5p - 3 \bmod{26}\text{.}\)
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OGERR
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LKYLJLCAR
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XKPKNFPTJ
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CPC APYRJ RYR
6.
Decrypt these messages that were encrypted using the encryption function \(f(p) = p + 10 \bmod{26}\text{.}\)
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LVEO
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LKXKXK
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CYVSNKBSDI
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OFO VYFOC KVSMO
7.
Suppose the cipher text HVS ZONM RCU XIADG CJSF HVS EIWQY PFCKB TCL was produced by encrypting a plain text message using a shift cipher. What is the original plain text message?
8.
9.
Encrypt the message \(M = 253\) using the RSA encryption scheme with public key \((N,e) = (391,17)\text{.}\)
10.
Encrypt the current year using the RSA encryption scheme with public key \((N,e) = (343751,23)\text{.}\)
11.
Show that the RSA public key \((N,e) = (527,13)\) is too small by computing the decryption exponent.
12.
Alice encodes her birthday as an \(8\)-digit number
yyyymmdd. Suppose she encrypts it using the RSA encryption scheme with public key
\begin{equation*}
(N,e) = (25736197, 29),
\end{equation*}
resulting in the cipher text \(C = 8141408\text{.}\) What is her birthday?
