[cryptography] deniable store and forward with integrity protection?

Jeffrey Walton noloader at gmail.com
Tue Feb 15 21:28:32 EST 2011


Hi James,

Off topic:

> I am pretty sure I it can be done in half a round trip using pairing
> based cryptography, that is to say, a bilinear map,
Are you aware of any C++ implementations of PBC? I have a need, but
have only found Ben Lynn's stuff over at Standford. Last time I looked
at it, I felt it best to pass on the implementation.

Jeff

On Tue, Feb 15, 2011 at 4:03 PM, James A. Donald <jamesd at echeque.com> wrote:
> On 2011-02-15 8:05 PM, Daniel Silverstone wrote:
>>
>> On Tue, Feb 15, 2011 at 01:13:43PM +1000, James A. Donald wrote:
>>>
>>> It is fairly easy to design a protocol that achieves this
>>> result without a round trip requirement, (authentication
>>> without round trips or signature), but has such a protocol
>>> already been published and examined?
>>
>> The closest I can think of is The Wrestlers Protocol[1] but I don't think
>> it
>> fits all your requirements.
>
> The wrestlers protocol is two round trips, or one and a half round trips
> followed by a final trip for the message, for a total of two round trips. I
> am pretty sure I it can be done in half a round trip using pairing based
> cryptography, that is to say, a bilinear map, but do not recall seeing that
> procedure studied in the literature, nor a proof of security claimed for it,
> even though it seems to me the simplest and most obvious application of
> pairing based cryptography.
>
> Indeed, one of the big benefits of pairing based crypography is a reduction
> in round trips
>
> Ann and Bob have well known public keys, and are identified by those keys,
> but do not yet have any shared secret.  If they have a shared secret, then
> standard symmetric cryptography gives them authenticated, encrypted, but
> deniable messages.  Trouble is, however, that establishing the shared secret
> from public keys is not necessarily deniable (which problem the Wrestler's
> protocol addresses.
>
> And if we do not care about contact deniability, and we probably don't,
> since likely adversaries to whom the recipient might rat us out probably
> have message tracing, we do care about round trips.
>
> We would like to send an authenticated encrypted message without a round
> trip to establish a shared secret from shared keys.
>
> Ann constructs a message which must contain a large random value that cannot
> be guessed by adversaries, or else it will be possible for an adversary to
> verify guesses of what her message is. She constructs a hash of this
> message, her public key, and Bob's public key.
>
> She constructs from this hash an elliptic point Q, by treating part of the
> hash as a compressed point.
>
> Ann has secret key a, public key aG, Bob has secret key b, Public key bG
>
> Ann calculates the pairing e(aQ,bG), which will be the shared secret.
>
> She encrypts her message using this shared secret.  She then sends Bob the
> encrypted message, the ellliptic point Q, her public key or something that
> identifies her public key, and Bob's public key, or something that
> identifies his public key.
>
> Bob then calculates the pairing e(aG,bQ), uses it as shared secret to
> decrypt the message.  He then calculates the hash, and verifies that the
> hash does in fact yield Q, which shows that the message did indeed come from
> Ann.
>
> The message he received from Ann must contain what is now a strong shared
> secret, which can be used for subsequent messages.
>



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