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2025-04-05 Update From: SLTechnology News&Howtos shulou NAV: SLTechnology News&Howtos > Network Security >
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Scenario: P proves to V that he knows the private key of user S (eMagnedPhoneN)
Proof step (zero knowledge)
1. P ≡ V jointly selects random numbers an and b to satisfy the ab and e mod N.
2. PPerry V produces a random ciphertext C together.
3.P calculation: M ≡ C ^ d mod N Magi X ≡ M ^ a mod N and pass X to V
4.V calculate and judge whether X ^ b mod N = C is valid
Zero knowledge proof is designed to prevent private transmission in the process of proof:
M ≡ C ^ d mod N
C ≡ M ^ e mod N
Convert the second formula above so that V can be decrypted without private d during decryption, so P needs to add a step in the intermediate process: X ≡ M ^ a mod N and pass X to V to receive X to determine whether C = X ^ b mod N is true. In fact, the whole process is still the process of RSA encryption and decryption, only adding a link to replace d, so that V can be decrypted without d.
C ≡ M ^ e mod N = > X ≡ M ^ a mod N (ab ≡ e mod N)
C = X ^ b mod N
Thorough analysis:
The understanding of "≡": the congruence symbol means that the two are the same as dividing by the same remainder.
So 5 ≡ 8 mod3 ≡ 11mod3. Both 5 and 8 are multiples of a difference of 3, so
M ≡ C ^ d mod N, which means M = C ^ d + karma N.
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