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RSA??????

RSA????????????????????????????????????RSA??????????????

• ??????????????????????????????????????

• ?????????????????????

RSA??

RSA?????????????????

[ \text{??} = \text{??}^E \mod N ]

?????RSA???????E?????N????????????E?N????????RSA???????E?N?RSA??????????E?N???????????(E,N)??????

??E?N???????????????????????????????E????Encryption??????N????Number??????

RSA??

RSA?????????????????

[ \text{??} = \text{??}^D \mod N ]

??????????D?????N???????????RSA???????D?N????????????D?N???????????(D,N)???

????????RSA????????????????????E???mod N???????D???mod N??

?????

?????(E,D,N)????

[ L = \text{lcm}(p?1?q?1) ]

3. ?E?E?????????

   • 1 < E < L
   • [ \text{gcd}(E?L) = 1 ]

   E?L???

4. ?D??D???E?????????

   • 1 < D < L
   • [ E \times D \mod L = 1 ]

????

????????????RSA????????????????????????????????

5.1 ?N

????????????

• p = 17
• q = 19
• N = p ? q = 323

5.2 ?L

L = lcm(p?1? q?1) = lcm(16?18) = 144

144?16?18???????

5.3 ?E

?E?????2????

• 1 < E < 144
• [ \text{gcd}(E?144) = 1 ]

E?144?????5??????2?????E = 5

????=(E?N)? ?5?323?

5.4 ?D

?D?????2????

• 1 < D < 144
• [ 5 \times D \mod 144 = 1 ]

???D?29??????????

1 < 29 < 144

5 ? 29 mod 144 = 145 mod 144 = 1

??????D?N???29?323?

5.5 ??

?????123

?????^E mod N?123^5 mod 323=225

???????123?

????????????????RSA???????????????????????????