Display MoreMathematical Proof proving the leaked chats of mhj are edited, doctored, and not legitimate:-
The principles below define the core aspects of authentic and unaltered communication records:
Principle 1 (P1): Every original message (OM) is transmitted through a secure channel (SC).
Principle 2 (P2): Every OM is accompanied by a unique digital signature (DS).
Principle 3 (P3): A message (M) without its corresponding DS is deemed suspicious (SM).
Principle 4 (P4): If an alteration (A) occurs post-transmission, the DS will not match the OM.
Principle 5 (P5): Any subset (S) of communication records that meets P1-P4 can be considered authentic (A).
Definitions and Recursive Functions
Define the verification of messages recursively:
Definition 1: Let M be a message. If M is an original message with DS, then verify(M) = true. If M has been altered, then verify(M) = false.
Definition 2: Let DS be a digital signature. DS(M) uniquely identifies the authenticity of M.
Theorem: Leaked Chats (LC) of mhj are Doctored if They Fail Verification
Proof:
Step 1: Assume M1 is an OM sent by mhj at time T1 with digital signature DS1.
Step 2: Let M1' be a message purportedly sent by mhj at T1 but accompanied by DS2.
Step 3: By P2, DS1 should match M1 if and only if M1 is authentic.
Step 4: By P3, if DS2 does not match M1, then M1' has been altered (AM).
Step 5: M1' fails verify(M1') and thus is doctored by P4.
Recursive Verification and Application
Definition 3: Let V be the verification function. If V(M) = true, M is authentic. If V(M) = false, M is doctored.
Definition 4: The set LC contains messages M1, M2, ..., Mn purportedly from mhj. Each Mi must pass verification to be considered authentic.
Theorem: If Any Message in LC Fails Verification, the Set Contains Doctored Messages
Proof:
Assumption: LC = {M1, M2, ..., Mn} purportedly from mhj.
Step 1: Apply V to each message Mi in LC.
Step 2: If ∃ Mi ∈ LC such that V(Mi) = false, then Mi is doctored.
Step 3: By P4, if V(Mi) = false for any Mi, LC contains doctored messages.
Practical Approach to Message Verification for mhj
Principle of Least Tampering (PLT): Any alteration in a message without corresponding changes in DS indicates tampering.
Verification Function V: Define V as a function that checks the integrity of messages against their digital signatures.
V(M) = true if and only if M matches its DS.
V(M) = false if M does not match its DS.
Case Study: Verifying a Set of Messages Purportedly from mhj
Consider the following set of leaked chats LC = {M1, M2, ..., Mn} purportedly from mhj. For each Mi:
Digital Signature Check (DSC): Verify that DS(Mi) matches Mi.
Verification Steps:
Step 1: For each Mi in LC, compute V(Mi).
Step 2: If V(Mi) = true for all i, LC is authentic.
Step 3: If V(Mi) = false for any i, mark Mi as doctored.
Applying the Proof to a Practical Scenario Involving mhj
Original Message Example:
OM1: "Meeting at 10 AM." sent by mhj with DS1 = SHA256("Meeting at 10 AM.").
Doctored Message Example:
DM1: "Meeting at 11 AM." purportedly sent by mhj with DS1 ≠ SHA256("Meeting at 11 AM.").
Using V, we get:
V(OM1) = true
V(DM1) = false
By P4 and the recursive nature of V, DM1 is identified as doctored.
Conclusion:
Thus, the leaked chats of mhj are edited, doctored, and not legitimate.
