3 \equiv m\cdot 19+s \pmod{26} \def\pps{ ++(0pt,10pt) -- ++(5pt,-10pt) -- ++(5pt,10pt) ++(5pt,-10pt)} In this paper, we extend this concept in the encryption core of our proposed cryptosystem. \end{equation*}, \begin{equation*} \mbox{ Decryption involves matrix computations such as matrix inversion, and arithmetic calculations such as modular inverse. c+x=t,\ j+w=m,\ f+y=k,\ -f=y,\ -y=f,\ etc.\\ 5\cdot 11+16\equiv 19\pmod{26}\text{,} 10 \amp 11 \amp 00 \amp 01 \amp 00 \\ \hline Therefore it is reasonable to assume that DZY is the, Y is e, and D is t. So when this was enciphered we have to of had, Subtracting the second expression from the first we get, Looking at the multiplication table modulo 26 we can see that \(m=9\) since \(9\cdot 11\equiv 21\pmod{26}\text{. Look back at Example 6.1.3 and write down the pairs of additive and multiplicative inverses. with subscripts prime to 26, as âprimaryâ letters, we make the assertion, easily proved: If \(\alpha\) is any primary letter and \(\beta\) is any letter, there is exactly one letter \(\gamma\) for which \(\alpha\gamma=\beta\text{.}\). Hill cipher is one of the techniques to convert a plain text into ciphertext and vice versa. \end{equation*}, \begin{equation*} The cipher we will focus on here, Hill's Cipher, is an early example of a cipher based purely in the mathematics of number theory and algebra; the areas of mathematics which now dominate all of modern cryptography. }\), Substitute your value for \(m\) into the first equation and use it to find \(s\text{.}\). M.K. Hill cipher is it compromised to the known-plaintext attacks. In this section of text Hill has introduced us to the idea of modular arithmetic and modular equivalence, in particular the idea of equivalence modulo 26. \amp 00 \amp 01 \amp 10 \amp 11 \\ \hline 24-10\equiv s \pmod{26} Why do you think all the remainders come out this way? a\cdot 1\equiv a\pmod{n}\text{.} 19(0+22)\equiv 2\pmod{26} A hard question: 350-500 points 4. The proposed method increases the security of the system because it involves two or more digital signatures under modulation of prime number. \def\ppd{-- ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) ++(15pt,-10pt)} \def\pph{ ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(15pt,0pt)} so that \(s=14\text{. h�b```���l�B ��ea�� ��0_Ќ�+��r�b���s^��BA��e���⇒,.���vB=/���M��[Z�ԳeɎ�p;�)
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According to the definition in wikipedia, in classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Note that the multiplier \(m\) must be relatively prime to the modulus so that it has a multiplicative inverse. \def\ppo{-- ++(10pt,0pt) ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)} \end{gather*}, \begin{gather*} A very hard question: 550-700 points In the case of a tie, select questions predetermined by the event supervisor wil… \def\ppw{ ++(0pt,10pt) -- ++(5pt,-10pt) -- ++(5pt,10pt) ++(-5pt,-5pt) node {$\cdot$} ++(10pt,-5pt)} h�bbd```b``v��A$��d�f[�Hƹ`5�`����� L� �����+`6X=�[�.0�"s*�$c�{F.���������v#E���_ ?�X
01 \amp 10 \amp 00 \amp 01 \amp 11 \\ \hline }\) Note that \(m^{-1}\equiv 19\pmod{26}\) and \(-s\equiv 22\pmod{26}\text{. %%EOF
}\), Decipher the message RXGTM CHUHJ CFWM which was enciphered using the key \(m=3\) and \(s=7\text{.}\). }\) Alternately, we can observe that \(36-8=28\) and \(28=2\cdot(14)\) is divisible by \(n=14\text{.}\). To decrypt, as opposed to just decipher, an affine cipher you can use the techniques we learned in Chapter 2 since they are a type of monoalphabetic substitution cipher. It also make use of Modulo Arithmetic (like the Affine Cipher). 19(9+22)\equiv 17\pmod{26} }\), (3) Given any letter \(\alpha\text{,}\) we can find exactly one letter \(\beta\text{,}\) dependent on \(\alpha\text{,}\) such that \(\alpha+\beta=a_0\text{. After you write down the tables write down the pairs of multiplicative and additive inverses. numbers you can multiply them by in order to get 1? }\), Thinking about your previous answers, what are the values of the following: \(j+z\text{,}\) \(nf\text{,}\) \(au+j\text{,}\) and \(bv+jw\text{.}\). 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