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From: Eric Lombrozo <elombrozo@gmail.com>
In-Reply-To: <CAAS2fgTGDzPFDP=ii08VXcXYpWr2akYWxqJCNHW-ABuN=ESc8A@mail.gmail.com>
Date: Wed, 5 Mar 2014 14:14:20 -0800
Message-Id: <7E50E1D6-3A9F-419B-B01E-50C6DE044E0F@gmail.com>
References: <CANEZrP25N7W_MeZin_pyVQP5pC8bt5yqJzTXt_tN1P6kWb5i2w@mail.gmail.com>
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	<CAAS2fgTGDzPFDP=ii08VXcXYpWr2akYWxqJCNHW-ABuN=ESc8A@mail.gmail.com>
To: Gregory Maxwell <gmaxwell@gmail.com>
Cc: Bitcoin Development <bitcoin-development@lists.sourceforge.net>
Subject: Re: [Bitcoin-development] New side channel attack that can recover
	Bitcoin keys
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Everything you say is true.

However, branchless does reduce the attack surface considerably - if =
nothing else, it significantly ups the difficulty of an attack for a =
relatively low cost in program complexity, and that might still make it =
worth doing.

As for uniform memory access, if we avoided any kind of heap allocation, =
wouldn't we avoid such issues?

Anyhow, without having gone into the full details of this particular =
attack, it seems the main attack point is differences in how squaring =
and multiplication (in the case of field exponentiation) or doubling and =
point addition (in the case of ECDSA) are performed. I believe using a =
branchless implementation where each phase of the operation executes the =
exact same code and accesses the exact same stack frames would not be =
vulnerable to FLUSH+RELOAD.

"To be able to recover the sequence of point additions and doublings, =
the spy program should distinguish
between consecutive doubling operations and must be able to order them =
with respect to point additions.
Our spy program achieves this by setting the time slot to less than half =
the length of the group operations.
With the selected curve, group add operations take 7,928 cycles on =
average, while group double operation
take 7,601 cycles. Setting the time slot to 3,000 cycles ensures that =
there is an empty time slot within any
group operation, allowing our spy to correctly distinguish consecutive =
doubles"

The approach I've suggested makes doubling operations indistinguishable =
from point additions from the perspective of cache access.

On Mar 5, 2014, at 1:44 PM, Gregory Maxwell <gmaxwell@gmail.com> wrote:

> On Wed, Mar 5, 2014 at 1:31 PM, Eric Lombrozo <elombrozo@gmail.com> =
wrote:
>> If we don't mind sacrificing some performance when signing, there's a =
fairly
>> simple way to implement a constant-time constant-cache-access-pattern
>> secp256k1.
>> It is based on the idea of branchless implementations of the field =
and group
>> operations.
>=20
> Do take care that branchless doesn't mean side-channel free: On
> non-trivial hardware you must have uniform memory accesses too.
>=20
> (and that itself isn't enough for sidechannel freeness against an
> attacker that can do power analysis... then you star worrying about
> the internal structure your primitive adders and the hamming weight of
> your numbers, and needing to build hardware that uses differential
> logic, and yuck yuck yuck:  This is why you still shouldn't reuse
> addresses, and why a blinding approach may still be sensible, even if
> you believe your implementation is hardened against side-channels)


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