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Script updating gh-pages from 9a73ae2. [ci skip]
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16 changes: 8 additions & 8 deletions cjpatton/257/draft-irtf-cfrg-vdaf.html
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</tr></thead>
<tfoot><tr>
<td class="left">Barnes, et al.</td>
<td class="center">Expires 22 February 2025</td>
<td class="center">Expires 23 February 2025</td>
<td class="right">[Page]</td>
</tr></tfoot>
</table>
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<dd class="internet-draft">draft-irtf-cfrg-vdaf-latest</dd>
<dt class="label-published">Published:</dt>
<dd class="published">
<time datetime="2024-08-21" class="published">21 August 2024</time>
<time datetime="2024-08-22" class="published">22 August 2024</time>
</dd>
<dt class="label-intended-status">Intended Status:</dt>
<dd class="intended-status">Informational</dd>
<dt class="label-expires">Expires:</dt>
<dd class="expires"><time datetime="2025-02-22">22 February 2025</time></dd>
<dd class="expires"><time datetime="2025-02-23">23 February 2025</time></dd>
<dt class="label-authors">Authors:</dt>
<dd class="authors">
<div class="author">
Expand Down Expand Up @@ -1118,7 +1118,7 @@ <h2 id="name-status-of-this-memo">
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."<a href="#section-boilerplate.1-3" class="pilcrow"></a></p>
<p id="section-boilerplate.1-4">
This Internet-Draft will expire on 22 February 2025.<a href="#section-boilerplate.1-4" class="pilcrow"></a></p>
This Internet-Draft will expire on 23 February 2025.<a href="#section-boilerplate.1-4" class="pilcrow"></a></p>
</section>
</div>
<div id="copyright">
Expand Down Expand Up @@ -5335,15 +5335,15 @@ <h4 id="name-overview-2">
C(x) = x * (x-1)
</pre><a href="#section-7.3.1-6" class="pilcrow"></a>
</div>
<p id="section-7.3.1-7">This circuit contains one subtraction gate (<code>x -1</code>) and one multiplication
gate (<code>x * (x -1)</code>). Observe that <code>C(x) = 0</code> if and only if <code>x in range(2)</code>.<a href="#section-7.3.1-7" class="pilcrow"></a></p>
<p id="section-7.3.1-7">This circuit contains one subtraction gate (<code>x - 1</code>) and one multiplication
gate (<code>x * (x - 1)</code>). Observe that <code>C(x) = 0</code> if and only if <code>x in range(2)</code>.<a href="#section-7.3.1-7" class="pilcrow"></a></p>
<p id="section-7.3.1-8">Our goal is to allow each Aggregator, who holds a secret share of <code>x</code>, to
correctly compute a secret share of <code>C(x)</code>. This allows the Aggregators to
determine validity by combining their shares of the output.<a href="#section-7.3.1-8" class="pilcrow"></a></p>
<p id="section-7.3.1-9">Suppose for a moment that the validity circuit <code>C</code> is affine, meaning its only
operations are addition, subtraction, and multiplication-by-constant. (The
circuit above is non-affine because it contains a multiplication gate with
non-constant inputs.) Then each Aggregator can compute its share locally, since<a href="#section-7.3.1-9" class="pilcrow"></a></p>
two non-constant inputs.) Then each Aggregator can compute its share locally, since<a href="#section-7.3.1-9" class="pilcrow"></a></p>
<div class="alignLeft art-text artwork" id="section-7.3.1-10">
<pre>
C(x_shares[0] + ... + x_shares[SHARES-1]) =
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</div>
<p id="section-7.3.1-11">(Note that, for this equality to hold, it is necessary to scale any addition of
a constant in the circuit by <code>1/SHARES</code>.) However, this is not the case if <code>C</code>
contains multiplication gates with non-constant inputs. Thus our goal is to
contains multiplication gates with two non-constant inputs. Thus our goal is to
transform these multiplication gates into computations on secret shared data
that each Aggregator can perform locally.<a href="#section-7.3.1-11" class="pilcrow"></a></p>
<p id="section-7.3.1-12">The key idea is to have the prover construct a polynomial <code>p</code> such that <code>p(j)</code>
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16 changes: 8 additions & 8 deletions cjpatton/257/draft-irtf-cfrg-vdaf.txt
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CFRG R. L. Barnes
Internet-Draft Cisco
Intended status: Informational D. Cook
Expires: 22 February 2025 ISRG
Expires: 23 February 2025 ISRG
C. Patton
Cloudflare
P. Schoppmann
Google
21 August 2024
22 August 2024


Verifiable Distributed Aggregation Functions
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time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."

This Internet-Draft will expire on 22 February 2025.
This Internet-Draft will expire on 23 February 2025.

Copyright Notice

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C(x) = x * (x-1)

This circuit contains one subtraction gate (x -1) and one
multiplication gate (x * (x -1)). Observe that C(x) = 0 if and only
This circuit contains one subtraction gate (x - 1) and one
multiplication gate (x * (x - 1)). Observe that C(x) = 0 if and only
if x in range(2).

Our goal is to allow each Aggregator, who holds a secret share of x,
Expand All @@ -3312,15 +3312,15 @@ Table of Contents
Suppose for a moment that the validity circuit C is affine, meaning
its only operations are addition, subtraction, and multiplication-by-
constant. (The circuit above is non-affine because it contains a
multiplication gate with non-constant inputs.) Then each Aggregator
can compute its share locally, since
multiplication gate with two non-constant inputs.) Then each
Aggregator can compute its share locally, since

C(x_shares[0] + ... + x_shares[SHARES-1]) =
C(x_shares[0]) + ... + C(x_shares[SHARES-1])

(Note that, for this equality to hold, it is necessary to scale any
addition of a constant in the circuit by 1/SHARES.) However, this is
not the case if C contains multiplication gates with non-constant
not the case if C contains multiplication gates with two non-constant
inputs. Thus our goal is to transform these multiplication gates
into computations on secret shared data that each Aggregator can
perform locally.
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