# hw2 - E n,e,d m = m e mod n For ciphertext c ∈ Z n the...

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Homework 2 Due in Class on Feb 28 1 Another Property of Euler’s Totient Function Show that, for any n , d | n φ ( d ) = n . 2 Modular Inverse Calculate the inverse of 256 with respect to modulus 625 . 3 Using RSA as Block Cipher Recall that the only difference between a public key cryptosystem and a private key cryptosystem is that the former’s decryption key is different from the encryption key. So we can try to convert RSA into a block cipher as follows: Use the RSA key generation algorithm to generate public key ( n,e ) and private key ( n,d ) . Then we deﬁne K = ( n,e,d ) and use K as the key of our block cipher. For cleartext m Z * n , the ciphertext is
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Unformatted text preview: E ( n,e,d ) ( m ) = m e mod n . For ciphertext c ∈ Z * n , the cleartext is D ( n,e,d ) ( c ) = c d mod n . Is the above block cipher as secure as a typical block cipher (like AES)? Why or why not? 4 Sharing RSA Modulus A company needs to set up the keys for its employees. So the company chooses an RSA modulus n and multiple pairs of encryption/decryption exponents ( e 1 ,d 1 ) ,..., ( e k ,d k ) . Then for each i , the i th employee uses the public key ( n,e i ) and the private key ( n,d i ) . What is the security problem of such a key setup? 1...
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