dissertacao.pdf
dissertacao.pdf
dissertacao.pdf
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3 Cryptanalysis of RSA 33<br />
3.1 Kind of Attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33<br />
3.2 Some Misuses of RSA . . . . . . . . . . . . . . . . . . . . . . . . 33<br />
3.2.1 Common Modulus Attack . . . . . . . . . . . . . . . . . . 33<br />
3.2.2 Hastad’s Broadcast Attack . . . . . . . . . . . . . . . . . 36<br />
3.2.3 Cycling Attack . . . . . . . . . . . . . . . . . . . . . . . . 39<br />
3.3 Recovering Plain texts Encrypted With Small Public Exponent . 40<br />
3.3.1 Stereotyped Message Attack . . . . . . . . . . . . . . . . . 41<br />
3.3.2 Related Message Attack . . . . . . . . . . . . . . . . . . . 43<br />
3.3.3 Random Padding Attack . . . . . . . . . . . . . . . . . . 44<br />
3.3.4 Leaking Information . . . . . . . . . . . . . . . . . . . . . 45<br />
3.4 Factoring the modulus of RSA with Small Private Exponent d . 46<br />
3.4.1 Wiener’s Continuous Fractions Attack . . . . . . . . . . . 47<br />
3.4.2 Improving Wiener’s Attack . . . . . . . . . . . . . . . . . 48<br />
4 Conclusions 51<br />
5 Bibliography 52<br />
A Implementations of the attacks from section 3.2 56<br />
A.1 Common Modulus Attack . . . . . . . . . . . . . . . . . . . . . . 56<br />
A.2 DeLaurentis Attack . . . . . . . . . . . . . . . . . . . . . . . . . . 57<br />
A.3 Hastad’s Common Plaintext Attack . . . . . . . . . . . . . . . . 57<br />
A.4 Related Plaintext Attack . . . . . . . . . . . . . . . . . . . . . . . 59<br />
B Implementations of the attacks from section 3.3 62<br />
B.1 Stereotyped Message Attack . . . . . . . . . . . . . . . . . . . . . 62<br />
B.2 Related Message Attack . . . . . . . . . . . . . . . . . . . . . . . 63<br />
C Implementation of Wiener’s attack 64<br />
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