Received-SPF: pass (google.com: best guess record for domain of linux-crypto-owner@vger.kernel.org designates 209.132.180.67 as permitted sender) client-ip=209.132.180.67;
Subject: Re: aes_expandkey giving wrong expanded keys over
 crypto_aes_expand_key(older deprecated implementation under aes_generic)
To:     Ard Biesheuvel <ard.biesheuvel@linaro.org>
CC:     "open list:HARDWARE RANDOM NUMBER GENERATOR CORE" 
        <linux-crypto@vger.kernel.org>, "Kristo, Tero" <t-kristo@ti.com>,
        Herbert Xu <herbert@gondor.apana.org.au>
References: <de5768f5-8c56-bec0-0c73-04aa4805c749@ti.com>
 <CAKv+Gu-XNFE+=griwBJCNooyoV7BR81hkqQ9jV3PDb-P6ghYxg@mail.gmail.com>
 <82a75666-3cb7-e33d-d873-1aad5581a13c@ti.com>
 <CAKv+Gu9H9wFbAZwA5Gt6TaqBVEQheryP+kG+y5FsmNmf8FE5_Q@mail.gmail.com>
 <2a124fcf-9bdc-7305-1d0b-6482ffffe3c5@ti.com>
 <CAKv+Gu8kr-n0D8r17a4RXNO_VfNRGNjvwdCMazE9rb9OSthzbg@mail.gmail.com>
From:   Keerthy <j-keerthy@ti.com>
Message-ID: <fe664bd4-40f4-7848-5c18-e92c4a96b466@ti.com>
Date:   Wed, 11 Dec 2019 11:52:41 +0530
User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:68.0) Gecko/20100101
 Thunderbird/68.2.1
MIME-Version: 1.0
In-Reply-To: <CAKv+Gu8kr-n0D8r17a4RXNO_VfNRGNjvwdCMazE9rb9OSthzbg@mail.gmail.com>
Content-Type: multipart/mixed;
        boundary="------------FF35AB608D0C104CC8B86B70"
Content-Language: en-US
Sender: linux-crypto-owner@vger.kernel.org
Precedence: bulk

--------------FF35AB608D0C104CC8B86B70
Content-Type: text/plain; charset="utf-8"
Content-Transfer-Encoding: quoted-printable


On 10/12/19 7:23 pm, Ard Biesheuvel wrote:
> On Tue, 10 Dec 2019 at 12:04, Keerthy <j-keerthy@ti.com> wrote:
>>
>>
>>
>> On 10/12/19 3:37 pm, Ard Biesheuvel wrote:
>>> On Tue, 10 Dec 2019 at 11:06, Keerthy <j-keerthy@ti.com> wrote:
>>>>
>>>>
>>>>
>>>> On 10/12/19 3:31 pm, Ard Biesheuvel wrote:
>>>>> Hello Keerthy,
>>>>>
>>>>> On Tue, 10 Dec 2019 at 10:35, Keerthy <j-keerthy@ti.com> wrote:
>>>>>>
>>>>>> Hi Ard,
>>>>>>
>>>>>> I am not sure if am the first one to report this. It seems like
>>>>>> aes_expandkey is giving me different expansion over what i get wit=
h the
>>>>>> older crypto_aes_expand_key which was removed with the below commi=
t:
>>>>>>
>>>>>> commit 5bb12d7825adf0e80b849a273834f3131a6cc4e1
>>>>>> Author: Ard Biesheuvel <ard.biesheuvel@linaro.org>
>>>>>> Date:   Tue Jul 2 21:41:33 2019 +0200
>>>>>>
>>>>>>     crypto: aes-generic - drop key expansion routine in favor of l=
ibrary
>>>>>> version
>>>>>>
>>>>>> The key that is being expanded is from the crypto aes(cbc) testsui=
te:
>>>>>>
>>>>>>   }, { /* From NIST SP800-38A */
>>>>>>                 .key    =3D "\x8e\x73\xb0\xf7\xda\x0e\x64\x52"
>>>>>>                           "\xc8\x10\xf3\x2b\x80\x90\x79\xe5"
>>>>>>                           "\x62\xf8\xea\xd2\x52\x2c\x6b\x7b",
>>>>>>                 .klen   =3D 24,
>>>>>>
>>>>>>
>>>>>> The older version crypto_aes_expand_key output that passes the cbc=
(aes)
>>>>>> decryption test:
>>> ...
>>>>>>
>>>>>> The difference is between 52nd index through 59.
>>>>>>
>>>>>> Any ideas if this is expected?
>>>>>>
>>>>>
>>>>> Yes, this is expected. This particular test vector uses a 192 bit k=
ey,
>>>>> so those values are DC/ignored.
>>>>
>>>> Thanks for the quick response. However with the new implementation
>>>> decryption test case fails for me with wrong result.
>>>
>>> Can you share more details please? Platform, endianness, etc ..
>>
>> Ard,
>>
>> I am trying to get aes working on a yet to be upstream TI HW crypto
>> Accelerator SA2UL. It is little endian.
>>
>> I had posted a series earlier this year:
>>
>> https://lkml.org/lkml/2019/6/28/20
>>
>> The device expects the inverse key for decryption.
>>
>=20
> Could you elaborate? There is no such thing as an inverse *key*, only
> an inverse *key schedule* which is used for the Equivalent Inverse
> Cipher.

Sorry i was a bit unclear.

>=20
> AES-192 expands the 24 byte key to 13 round keys consisting of 4
> 32-bit words each, and so the algorithm does not actually use the
> contents of slots 52 and up in this case.
>=20
>> In the earlier working version i was copying the ctx.key_enc[48] to
>> ctx.key_enc[53] index of the ctx.key_enc array as the 24 bytes of
>> decryption key to my hardware.
>>
>> Now as told earlier the 52nd & 53rd words are changed and hence i end =
up
>> in wrong result.
>>
>> Fail:
>>
>> ctx.key_dec[48] =3D 0xf7b0738e & ctx.key_enc[48] =3D 0x6fa08be9
>> ctx.key_dec[49] =3D 0x52640eda & ctx.key_enc[49] =3D 0x3c778c44
>> ctx.key_dec[50] =3D 0x2bf310c8 & ctx.key_enc[50] =3D 0x472cc8e
>> ctx.key_dec[51] =3D 0xe5799080 & ctx.key_enc[51] =3D 0x2220001
>> ctx.key_dec[52] =3D 0x13eaf950 & ctx.key_enc[52] =3D 0x13eaf850
>> ctx.key_dec[53] =3D 0xffff8000 & ctx.key_enc[53] =3D 0xffff8000
>>
>> Pass:
>>
>> ctx.key_dec[48] =3D 0xf7b0738e & ctx.key_enc[48] =3D 0x6fa08be9
>> ctx.key_dec[49] =3D 0x52640eda & ctx.key_enc[49] =3D 0x3c778c44
>> ctx.key_dec[50] =3D 0x2bf310c8 & ctx.key_enc[50] =3D 0x472cc8e
>> ctx.key_dec[51] =3D 0xe5799080 & ctx.key_enc[51] =3D 0x2220001
>> ctx.key_dec[52] =3D 0x105127e8 & ctx.key_enc[52] =3D 0x68342d29
>> ctx.key_dec[53] =3D 0xffff8000 & ctx.key_enc[53] =3D 0xddd31195
>>
>=20
> The old code does the following for AES-192
>=20
> #define loop6(i)       do {            \
>        t =3D ror32(t, 8);                \
>        t =3D ls_box(t) ^ rco_tab[i];     \
>        t ^=3D ctx->key_enc[6 * i];               \
>        ctx->key_enc[6 * i + 6] =3D t;            \
>        t ^=3D ctx->key_enc[6 * i + 1];           \
>        ctx->key_enc[6 * i + 7] =3D t;            \
>        t ^=3D ctx->key_enc[6 * i + 2];           \
>        ctx->key_enc[6 * i + 8] =3D t;            \
>        t ^=3D ctx->key_enc[6 * i + 3];           \
>        ctx->key_enc[6 * i + 9] =3D t;            \
>        t ^=3D ctx->key_enc[6 * i + 4];           \
>        ctx->key_enc[6 * i + 10] =3D t;           \
>        t ^=3D ctx->key_enc[6 * i + 5];           \
>        ctx->key_enc[6 * i + 11] =3D t;           \
> } while (0)
>=20
> case AES_KEYSIZE_192:
>         ctx->key_enc[4] =3D get_unaligned_le32(in_key + 16);
>         t =3D ctx->key_enc[5] =3D get_unaligned_le32(in_key + 20);
>         for (i =3D 0; i < 8; ++i)
>                 loop6(i);
>         break;
>=20
> so while it happens to populate slots 52 and 53 as well (when i =3D=3D =
7),
> the AES spec does not actually cover this, given that those values are
> not actually used in the computation (and I am at a loss understanding
> why it should make a difference in your case).
>=20
> In any case, you can work around this by calculating the missing
> values in your driver's expand_key() routine,
>=20
> ctx.key_enc[52] =3D ctx.key_enc[51] ^ ctx.key_enc[46];
> ctx.key_enc[53] =3D ctx.key_enc[52] ^ ctx.key_enc[47];

Thanks a lot for the detailed explanation.

Thanks a lot Ard. The above work around gets it working on my hardware
for 24 byte keys. I will dig more details on that.

Best Regards,
Keerthy

>=20

--------------FF35AB608D0C104CC8B86B70
Content-Type: application/pgp-keys; name="pEpkey.asc"
Content-Transfer-Encoding: quoted-printable
Content-Disposition: attachment; filename="pEpkey.asc"

-----BEGIN PGP PUBLIC KEY BLOCK-----
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3D
=3DNfsW
-----END PGP PUBLIC KEY BLOCK-----

--------------FF35AB608D0C104CC8B86B70--