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I know hill cipher is a block chipher ,We produce decryption key by inverse of key matirx but we still use different key for decryption. Therefore Can we say that Hill cipher is asymmetric chipher?

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  • $\begingroup$ Think of the inverse key as the output of a block cipher key schedule, the same way AES uses InvMixColumns to generate decryption subkeys in the Equivalent Inverse version of the cipher $\endgroup$ – Richie Frame Jun 2 '15 at 10:13
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No, because matrix inversion can be done efficiently. Namely, if encryption is multiplication by a matrix $A$, then you can define decryption with $A$ as first computing the inverse of $A$ and then multiplying.

An essential property of public-key cryptosystems is that it should not be possible to efficiently derive the (private) decryption key from the (public) encryption key. In the Hill cipher, the matrix must be kept secret.

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