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<!DOCTYPE html>
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<title>The ristretto255 and decaf448 Groups</title>
<meta content="Henry de Valence" name="author">
<meta content="Jack Grigg" name="author">
<meta content="Mike Hamburg" name="author">
<meta content="Isis Lovecruft" name="author">
<meta content="George Tankersley" name="author">
<meta content="Filippo Valsorda" name="author">
<meta content="
This memo specifies two prime-order groups, ristretto255 and decaf448,
suitable for safely implementing higher-level and complex
cryptographic protocols. The ristretto255 group can be implemented
using Curve25519, allowing existing Curve25519 implementations to be
reused and extended to provide a prime-order group. Likewise, the
decaf448 group can be implemented using edwards448.
This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF.
" name="description">
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width: 25%;
margin: 0;
padding: 0 1em;
z-index: 1;
}
#toc h2 {
border-top: none;
border-bottom: 1px solid #ddd;
font-size: 1em;
font-weight: normal;
margin: 0;
padding: 0.25em 1em 1em 0;
}
#toc nav {
display: block;
height: calc(90vh - 84px);
bottom: 0;
padding: 0.5em 0 0;
overflow: auto;
}
img { /* future proofing */
max-width: 100%;
height: auto;
}
}
/* pagination */
@media print {
body {
width: 100%;
}
p {
orphans: 3;
widows: 3;
}
#n-copyright-notice {
border-bottom: none;
}
#toc, #n-introduction {
page-break-before: always;
}
#toc {
border-top: none;
padding-top: 0;
}
figure, pre {
page-break-inside: avoid;
}
figure {
overflow: scroll;
}
.breakable pre {
break-inside: auto;
}
h1, h2, h3, h4, h5, h6 {
page-break-after: avoid;
}
h2+*, h3+*, h4+*, h5+*, h6+* {
page-break-before: avoid;
}
pre {
white-space: pre-wrap;
word-wrap: break-word;
font-size: 10pt;
}
table {
border: 1px solid #ddd;
}
td {
border-top: 1px solid #ddd;
}
}
/* This is commented out here, as the string-set: doesn't
pass W3C validation currently */
/*
.ears thead .left {
string-set: ears-top-left content();
}
.ears thead .center {
string-set: ears-top-center content();
}
.ears thead .right {
string-set: ears-top-right content();
}
.ears tfoot .left {
string-set: ears-bottom-left content();
}
.ears tfoot .center {
string-set: ears-bottom-center content();
}
.ears tfoot .right {
string-set: ears-bottom-right content();
}
*/
@page :first {
padding-top: 0;
@top-left {
content: normal;
border: none;
}
@top-center {
content: normal;
border: none;
}
@top-right {
content: normal;
border: none;
}
}
@page {
size: A4;
margin-bottom: 45mm;
padding-top: 20px;
/* The following is commented out here, but set appropriately by in code, as
the content depends on the document */
/*
@top-left {
content: 'Internet-Draft';
vertical-align: bottom;
border-bottom: solid 1px #ccc;
}
@top-left {
content: string(ears-top-left);
vertical-align: bottom;
border-bottom: solid 1px #ccc;
}
@top-center {
content: string(ears-top-center);
vertical-align: bottom;
border-bottom: solid 1px #ccc;
}
@top-right {
content: string(ears-top-right);
vertical-align: bottom;
border-bottom: solid 1px #ccc;
}
@bottom-left {
content: string(ears-bottom-left);
vertical-align: top;
border-top: solid 1px #ccc;
}
@bottom-center {
content: string(ears-bottom-center);
vertical-align: top;
border-top: solid 1px #ccc;
}
@bottom-right {
content: '[Page ' counter(page) ']';
vertical-align: top;
border-top: solid 1px #ccc;
}
*/
}
/* Changes introduced to fix issues found during implementation */
/* Make sure links are clickable even if overlapped by following H* */
a {
z-index: 2;
}
/* Separate body from document info even without intervening H1 */
section {
clear: both;
}
/* Top align author divs, to avoid names without organization dropping level with org names */
.author {
vertical-align: top;
}
/* Leave room in document info to show Internet-Draft on one line */
#identifiers dt {
width: 8em;
}
/* Don't waste quite as much whitespace between label and value in doc info */
#identifiers dd {
margin-left: 1em;
}
/* Give floating toc a background color (needed when it's a div inside section */
#toc {
background-color: white;
}
/* Make the collapsed ToC header render white on gray also when it's a link */
@media screen and (max-width: 1023px) {
#toc h2 a,
#toc h2 a:link,
#toc h2 a:focus,
#toc h2 a:hover,
#toc a.toplink,
#toc a.toplink:hover {
color: white;
background-color: #444;
text-decoration: none;
}
}
/* Give the bottom of the ToC some whitespace */
@media screen and (min-width: 1024px) {
#toc {
padding: 0 0 1em 1em;
}
}
/* Style section numbers with more space between number and title */
.section-number {
padding-right: 0.5em;
}
/* prevent monospace from becoming overly large */
tt, code, pre {
font-size: 95%;
}
/* Fix the height/width aspect for ascii art*/
.sourcecode pre,
.art-text pre {
line-height: 1.12;
}
/* Add styling for a link in the ToC that points to the top of the document */
a.toplink {
float: right;
margin-right: 0.5em;
}
/* Fix the dl styling to match the RFC 7992 attributes */
dl > dt,
dl.dlParallel > dt {
float: left;
margin-right: 1em;
}
dl.dlNewline > dt {
float: none;
}
/* Provide styling for table cell text alignment */
table td.text-left,
table th.text-left {
text-align: left;
}
table td.text-center,
table th.text-center {
text-align: center;
}
table td.text-right,
table th.text-right {
text-align: right;
}
/* Make the alternative author contact information look less like just another
author, and group it closer with the primary author contact information */
.alternative-contact {
margin: 0.5em 0 0.25em 0;
}
address .non-ascii {
margin: 0 0 0 2em;
}
/* With it being possible to set tables with alignment
left, center, and right, { width: 100%; } does not make sense */
table {
width: auto;
}
/* Avoid reference text that sits in a block with very wide left margin,
because of a long floating dt label.*/
.references dd {
overflow: visible;
}
/* Control caption placement */
caption {
caption-side: bottom;
}
/* Limit the width of the author address vcard, so names in right-to-left
script don't end up on the other side of the page. */
address.vcard {
max-width: 30em;
margin-right: auto;
}
/* For address alignment dependent on LTR or RTL scripts */
address div.left {
text-align: left;
}
address div.right {
text-align: right;
}
/* Provide table alignment support. We can't use the alignX classes above
since they do unwanted things with caption and other styling. */
table.right {
margin-left: auto;
margin-right: 0;
}
table.center {
margin-left: auto;
margin-right: auto;
}
table.left {
margin-left: 0;
margin-right: auto;
}
/* Give the table caption label the same styling as the figcaption */
caption a[href] {
color: #222;
}
@media print {
.toplink {
display: none;
}
/* avoid overwriting the top border line with the ToC header */
#toc {
padding-top: 1px;
}
/* Avoid page breaks inside dl and author address entries */
.vcard {
page-break-inside: avoid;
}
}
/* Tweak the bcp14 keyword presentation */
.bcp14 {
font-variant: small-caps;
font-weight: bold;
font-size: 0.9em;
}
/* Tweak the invisible space above H* in order not to overlay links in text above */
h2 {
margin-top: -18px; /* provide offset for in-page anchors */
padding-top: 31px;
}
h3 {
margin-top: -18px; /* provide offset for in-page anchors */
padding-top: 24px;
}
h4 {
margin-top: -18px; /* provide offset for in-page anchors */
padding-top: 24px;
}
/* Float artwork pilcrow to the right */
@media screen {
.artwork a.pilcrow {
display: block;
line-height: 0.7;
margin-top: 0.15em;
}
}
/* Make pilcrows on dd visible */
@media screen {
dd:hover > a.pilcrow {
visibility: visible;
}
}
/* Make the placement of figcaption match that of a table's caption
by removing the figure's added bottom margin */