Construction of key recovery attack in O(2^(n/2))

Swagata

11/15/22, 10:14 PM

I have to construct a key recovery attack on symmetric key encryption using a publicly known permutation $\Pi$ in $O(2^\frac{n}{2})$ time using $2^\frac{n}{2}$ queries to an encryption oracle.

The encryption is done as $ \Pi ( m \oplus K) \oplus K $, where $K$ is the key. Both $m$ and $K$ belong to ${0, 1}^{n}$

I do not know how I can use the queries to do the key recovery attack in that time. I can check my guesses against the output of the queries for $2^\frac{n}{2}$ of them. But how will I recover the key successfully ?

Really need some help here.

1 + 2

block-cipher

key-recovery

spn

poncho

11/15/22, 11:28 PM

Is this homework?

Swagata

11/15/22, 11:34 PM

@poncho One of the practice problems. Not exactly homework.

Score:1

Crypto

poncho

11/15/22, 11:45 PM

Well, you said that this was a "practice problem"; hence you're supposed to learn from it, so I won't give you the answer.

I will give you a hint: you have $E_k(M) = \Pi(M \oplus K) \oplus K$; suppose you defined $F_k(M) = E_k(M) \oplus E_k(M \oplus 1)$, and further defined $G$ such that $F_k(M) = G( M \oplus K )$ (and yes, such a $G$ exists independent of $K$). How could you use that to do key recovery?

0 + 0

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: Construction of key recovery attack in O(2^(n/2))

TH: การสร้างการโจมตีเพื่อกู้คืนคีย์ใน O(2^(n/2))

RO: Construirea atacului de recuperare cheie în O(2^(n/2))

RU: Построение атаки восстановления ключа за O(2^(n/2))

VI: Xây dựng tấn công khôi phục khóa trong O(2^(n/2))

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