Score:2

Crypto

How to calculate/generate the inverse S-box of Kuznyechik block cipher?

phantomcraft

7/21/23, 8:34 AM

Let's suppose I want to modify Kuznyechik block cipher by choosing a random S-box (taken from /dev/random for example).

How can I calculate/generate the inverse S-box?

Does anyone know the formula or algorithm used to do this?

157

0 + 0

s-boxes

block-cipher

Score:2

Crypto

kelalaka

7/21/23, 1:47 PM

Sagemath SBox Package is a friend of SBox learners/designers.

For an invertible SBox;

#         0  1  2  3  4  5  6  7       #index
S = SBox([0, 1, 3, 6, 7, 4, 5, 2])     #output
Sinv = S.inverse()
print(Sinv)

outputs

(0, 1, 7, 2, 5, 6, 3, 4)

Actually, the implementation of the inverse is not hard; just reverse the index-output relation. Remember, invertible SBox is just a permutation.

Note that the source code of SageMath SBox is here and as a good library it first controls the SBox is a permutation or not and returns an SBox oject;

        if not self.is_permutation():
            raise TypeError("S-Box must be a permutation")

        cdef Py_ssize_t i
        cdef list L = [self._S_list[i] for i in range(1 << self.m)]

        return SBox([L.index(i) for i in range(1 << self.m)],
                    big_endian=self._big_endian)

0 + 0

phantomcraft

7/21/23, 11:58 PM

Thanks for the reply. Do you know some similar package/program in C/C++ that does the same of Sagemath SBox package?

kelalaka

7/22/23, 6:40 AM

@phantomcraft I'm not aware of it, however, you can use it in [Python](https://stackoverflow.com/q/61408795/1820553)

phantomcraft

7/23/23, 1:18 AM

I got, thank you.

phantomcraft

7/23/23, 1:22 AM

Sorry, I selected the other question as "useful" because I was interested in a C implementation.

kelalaka

7/23/23, 8:47 AM

@phantomcraft then you are asking on the wrong [so] site. This is not a programming site and you asked `Does anyone know the formula or algorithm used to do this?` so I've given you the easiest way, and the simple algorithm `reverse the index-output relation.`. Without my answer, this question is more to be off-topic side. Have fun.

kelalaka

7/23/23, 9:50 AM

As you can see from the SageMath source code, directly finding inverse is not the correct way to go. Don't blindly trust the SBox that is download from the internet is invertible...

Score:2

Crypto

LightBit

7/22/23, 4:15 PM

Assuming S-boxes are a permutation.

Here is example in Python:

S = (2, 0, 1)
inverse = [0] * len(S)

for i in range(len(S)):
    inverse[S[i]] = i

print(inverse)

Here is example in C:

unsigned int S[256] = {...};
unsigned int inverse[256];

for (int i = 0; i < 256; i++)
{
    inverse[S[i]] = i;
}

0 + 0

phantomcraft

7/23/23, 1:18 AM

Quite simple, I didn't realize that it would be that easy. Thanks!

Elon Musk

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

EN: How to calculate/generate the inverse S-box of Kuznyechik block cipher?

TH: จะคำนวณ / สร้าง S-box ผกผันของรหัสบล็อก Kuznyechik ได้อย่างไร

RO: Cum se calculează/generează cutia S inversă a cifrului bloc Kuznyechik?

RU: Как рассчитать/сгенерировать обратный S-блок блочного шифра Кузнечика?

VI: Làm cách nào để tính toán/tạo hộp S nghịch đảo của mật mã khối Kuznyechik?

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