encryption - Prove the decryption by counter mode is correct -

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as review question have prove decryption process of counter mode correct. how prove it? no other information given.

encryption: cj = e(k, counter + j -1) ⊕ pj  decryption: pj = e(k, counter + j -1) ⊕ cj 

pj = e(k, counter + j -1) ⊕ cj

replace cj = e(k, counter + j -1) ⊕ pj 

cj = e(k, counter + j -1) ⊕ e(k, counter + j -1) ⊕ pj

since x⊕x=0 (the encrypted counter xored itself) , 0⊕x=x

pj = 0 ⊕ pj  pj = pj

qed


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