Why in cryptography it is common to use the SAME key for all the group?

Question

I believe that it is safer that each member should have his or her encryption and decryption keys that no one else knows. IN this case a message $m$ is sent as $m^{e_1}$ the receiver sends $t$ back as $m^{e_1e_2}$ the sender decrypts his/her by $m^{e_1e_2d_1}$ and the final decryption is $m^{e_1e_2d_1d_2}=m$ by Fermat little theorem.

Thank you for your help

For Shamir three-pass protocol, I thought $e_2$ and $d_2$ are both private to the receiver. — peterwhy, Dec 14 '14 at 08:04

score 1 · Answer 1 · answered Dec 14 '14 at 08:07

1

You're using the Shamir three-pass protocol. Here both $e_1,d_1$ are only known to the sender, and $e_2,d_2$ only to the receiver. So I don't understand what your problem is. Or are you describing another protocol?

answered Dec 14 '14 at 08:07

Henno Brandsma

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Why in cryptography it is common to use the SAME key for all the group?

1 Answers1