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From: "Russell O'Connor" <roconnor@blockstream.io>
To: Peter Todd <pete@petertodd.org>,
	 Bitcoin Protocol Discussion
	<bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] A Method for Computing Merkle Roots of Annotated Binary Trees
Date: Sat, 27 May 2017 18:07:07 -0400	[thread overview]
Message-ID: <CAMZUoKmAsxZFaLoOeAQT-YwCJBZ4z+qWJtRHPOXKTyqG7EAsfw@mail.gmail.com> (raw)
In-Reply-To: <CAMZUoKkS8azx7Gooo3D+H_gdGdTNiNtwwNVbvU0u7HzOfdUSBg@mail.gmail.com>

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On May 28, 2017 06:09, "Russell O'Connor" <roconnor@blockstream.io> wrote:



On May 28, 2017 03:16, "Peter Todd" <pete@petertodd.org> wrote:

On Mon, May 22, 2017 at 06:32:38PM -0400, Russell O'Connor wrote:
> On May 22, 2017 23:05, "Peter Todd" <pete@petertodd.org> wrote:
>
> On Mon, May 22, 2017 at 03:05:49AM -0400, Russell O'Connor via bitcoin-dev
> wrote:
> >     MerkleRoot := SHA256(SHA256(LeftRoot ⋅ RightRoot))
> >     sha256Compress : Word256 × Word512 -> Word256
>
> To be clear, what math operations do you mean by "⋅" and "×"?
>
>
> By "⋅", I usually mean concatenation (though I also use it for function
> composition in one instance).   By "×", I mean the Cartesian product.

Cartesian product can mean a lot of things.

What specifically do you mean by "cartesian product" here?


Oops, I forgot to reply all.  Below is my reply.

Given two types A and B, then A × B is the type of pairs of A and B in the
sense of type theory as used in Standard ML or Haskell or other typed
languages.


To follow up, by "sha256Compress : Word256 × Word512 -> Word256" I mean
that sha256Compress is a function that takes two arguments, the first being
a 256 bit word and the second being a 512 bit word, and returns a 256 bit
word (or equivalently sha256Compress is a function that takes a pair as
input, the first component being a 256 bit word and the second component
being a 512 bit word, and returns a 256 bit word).

sha256Compress is meant to be the compression function defined by the
SHA256 standard, though nothing here depends on anything more that its type
signature.

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  parent reply	other threads:[~2017-05-27 22:07 UTC|newest]

Thread overview: 11+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2017-05-22  7:05 [bitcoin-dev] A Method for Computing Merkle Roots of Annotated Binary Trees Russell O'Connor
2017-05-22 14:05 ` Peter Todd
2017-05-22 22:32   ` Russell O'Connor
2017-05-27 17:41     ` Peter Todd
     [not found]       ` <CAMZUoKkS8azx7Gooo3D+H_gdGdTNiNtwwNVbvU0u7HzOfdUSBg@mail.gmail.com>
2017-05-27 22:07         ` Russell O'Connor [this message]
2017-05-23  6:06 ` Bram Cohen
2017-05-28  8:26 ` Peter Todd
2017-05-29 14:55   ` Russell O'Connor
2017-05-29 16:10     ` Peter Todd
2017-06-01 15:10       ` Russell O'Connor
2017-06-27  4:13     ` Peter Todd

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