assignment thread #201527

This assignment question keeps haunting me, and the professor stubbornly refuses to give us any hint.

Given a cipher mode (here referred to as "DBC", or double block chaining) as shown in the diagrams located at the bottom of my post, a function DBC-encrypt(E,IV,p) which encrypts plaintext p using initialization vector IV and symmetric cipher E, and a function DBC-decrypt(D,IV,c) which decrypts ciphertext c using initialization vector IV and symmetric cipher D (where D is the inverse of E for a given key), prove that the following authenticated encryption scheme is not secure, given that the underlying cipher E/D is secure and IVs are unique:

AE-DBC-encrypt(E,IV,m)
    EIV <- E(IV)
    c <- DBC-encrypt(E, EIV, m || IV)
    return (EIV, c)

AE-DBC-decrypt-and-authenticate(E,EIV,c)
    plaintext <- DBC-decrypt(D, EIV, c)
    m <- all-but-last-block(plaintext)
    checksum <- last-block(plaintext)
    if checksum == D(EIV) then
        return m
    else
        return null
    end

Note that IV is not transmitted, only E(IV).


Diagrams:
data:image/png;base64,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

data:image/png;base64,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

Actually there is no "hard limit", if we consider that each post can represent a link to multiple posts(or posts ranges like 1-200) in multiple threads from entire shiichan like 1,2,3,76,http://dis.4chan.org/read/prog/1321898094/1-3 which can be downloaded and combined into single file, but this would take a bit more time. Shiichan stores ~19k threads each 10MB max would be about 190000mb or 190GB if used to the maximum storage capacity(if shiichan was used exclusively for this).