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Date:   Tue, 23 Oct 2018 07:40:34 -0300
From:   Ard Biesheuvel <>
To:     Eric Biggers <>
        linux-arm-kernel <>,
        Linux Kernel Mailing List <>,
        Herbert Xu <>,
        Paul Crowley <>,
        Greg Kaiser <>,
        Michael Halcrow <>,
        "Jason A . Donenfeld" <>,
        Samuel Neves <>,
        Tomer Ashur <>
Subject: Re: [RFC PATCH v2 11/12] crypto: adiantum - add Adiantum support

On 20 October 2018 at 15:12, Eric Biggers <> wrote:
> Hi Ard,
> On Sat, Oct 20, 2018 at 12:17:58PM +0800, Ard Biesheuvel wrote:
>> On 16 October 2018 at 01:54, Eric Biggers <> wrote:
>> > From: Eric Biggers <>
>> >
>> > Add support for the Adiantum encryption mode.  Adiantum was designed by
>> > Paul Crowley and is specified by our paper:
>> >
>> >     Adiantum: length-preserving encryption for entry-level processors
>> >     (
>> >
>> > See our paper for full details; this patch only provides an overview.
>> >
>> > Adiantum is a tweakable, length-preserving encryption mode designed for
>> > fast and secure disk encryption, especially on CPUs without dedicated
>> > crypto instructions.  Adiantum encrypts each sector using the XChaCha12
>> > stream cipher, two passes of an ε-almost-∆-universal (εA∆U) hash
>> > function, and an invocation of the AES-256 block cipher on a single
>> > 16-byte block.  On CPUs without AES instructions, Adiantum is much
>> > faster than AES-XTS; for example, on ARM Cortex-A7, on 4096-byte sectors
>> > Adiantum encryption is about 4 times faster than AES-256-XTS encryption,
>> > and decryption about 5 times faster.
>> >
>> > Adiantum is a specialization of the more general HBSH construction.  Our
>> > earlier proposal, HPolyC, was also a HBSH specialization, but it used a
>> > different εA∆U hash function, one based on Poly1305 only.  Adiantum's
>> > εA∆U hash function, which is based primarily on the "NH" hash function
>> > like that used in UMAC (RFC4418), is about twice as fast as HPolyC's;
>> > consequently, Adiantum is about 20% faster than HPolyC.
>> >
>> > This speed comes with no loss of security: Adiantum is provably just as
>> > secure as HPolyC, in fact slightly *more* secure.  Like HPolyC,
>> > Adiantum's security is reducible to that of XChaCha12 and AES-256,
>> > subject to a security bound.  XChaCha12 itself has a security reduction
>> > to ChaCha12.  Therefore, one need not "trust" Adiantum; one need only
>> > trust ChaCha12 and AES-256.  Note that the εA∆U hash function is only
>> > used for its proven combinatorical properties so cannot be "broken".
>> >
>> So what happens if the part of the input covered by the block cipher
>> is identical between different generations of the same disk block
>> (whose sector count is used as the 'outer' IV). How are we not in the
>> same boat as before when using stream ciphers for disk encryption?
> This is the point of the hash step.  The value encrypted with the block cipher
> to produce the intermediate value C_M (used as the stream cipher nonce) is
> H(T, P_L) + P_R.  (T is the tweak a.k.a the IV, P_L is the plaintext except the
> last 16 bytes, P_R is the last 16 bytes.)  A collision in this value occurs iff:
>         H(T1, P1_L) + P1_R = H(T2, P2_L) + P2_R
> i.e.
>         H(T1, P1_L) - H(T2, P2_L) = P2_R - P1_R
> If (T1, P1_L) = (T2, P2_L) then P1_R != P2_R so the equation has no solutions
> (since we don't consider queries where the whole input is the same; those
> unavoidably produce the same ciphertext).  Otherwise (T1, P1_L) != (T2, P2_L),
> and since the hash function H is ε-almost-∆-universal over integers mod 2^128,
> the equation is true for at most a very small proportion 'ε' of hash keys.
> But, the hash key is chosen at random and is unknown to the attacker.
> The same applies in the other direction, for chosen ciphertext attacks.
> Basically, it's very difficult for an attacker to cause the intermediate value
> C_M to be reused, and the outputs will appear random until they do.
> Of course, all this is explained much more precisely and comprehensively in our
> paper.  See section 5, "Security reduction".

Thanks for the explanation. I saw that the result of the AES
encryption was used as the XChaCha nonce, but I failed to spot that
the result of the nhpoly1305 pass is added/subtracted to/from that
particular block first.

In any case, this looks good to me: as far as I can tell, the code
implements the algorithm as described in the paper, and the plumbing
into the crypto API looks correct to me as well.

Reviewed-by: Ard Biesheuvel <>

Whether the paper is correct is a different matter: it looks
convincing to me but IANAC.

The only request I have is to add a speed test to tcrypt as well so we
can easily benchmark it.

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