Publicly Verifiable Nominations Committee (NomCom) Random Selection

Internet-Draft	Verifiable Random Selection	June 2023
Eastlake	Expires 25 December 2023	[Page]

Abstract

This document describes a method for making random selections in such a way as to promote public confidence in the unbiased nature of the choice. This method is referred to in this document as "verifiable selection". It focuses on the selection of the voting members of the IETF Nominations Committee (NomCom) from the pool of eligible volunteers; however, similar or, in some cases, identical techniques could be and have been applied to other cases. This document obsoletes RFC 3797.¶

3. Randomness

The crux of the unbiased nature of the selection is that it is based in an exact, predetermined fashion on random information which will be revealed in the future and cannot be known to the person specifying the algorithm. That random information will be used to control the selection. The random information MUST be such that it will be publicly and unambiguously revealed in a timely fashion.¶

3.1. Sources of Randomness

The random sources MUST NOT include anything that a reasonable person would believe to be under the control or influence of the selection administrator. In the case of the IETF NomCom, that includes anything under the control or influence the IETF or its components, such as IETF meeting attendance statistics, numbers of documents issued, or the like.¶

Examples of good information to use are winning lottery numbers for specified runnings of specified public lotteries. Particularly for major government run lotteries, great care is taken to see that they occur on time (or with minimal delay) and produce random quantities. Even in the very unlikely case one was to have been rigged, it would almost certainly be in connection with winning money in the lottery, not in connection with IETF use. Other possibilities are such things as the daily balance in the US Treasury on a specified day, the volume of trading on the New York Stock exchange on a specified day, etc. (However, the example code given below will not handle integers that are too large.) Sporting events can also be used. Experience has indicated that individual stock prices and/or volumes are a poor source of unambiguous data due trading suspensions, company mergers, delistings, splits, multiple markets, etc. In all cases, great care MUST be taken to specify exactly what quantities are being used for randomness and what will be done if their issuance is cancelled, delayed, or advanced.¶

It is important that the last source of randomness, chronologically, produce a substantial amount of the entropy needed. If most of the randomness has come from the earlier of the specified sources, and someone has even limited influence on the final source, they might do an exhaustive analysis and exert such influence so as to bias the selection in the direction they wanted. Thus, it is RECOMMENDED that the last source be an especially strong and unbiased source of a large amount of randomness such as a major government run lottery.¶

It is best not to use too many different sources. Every additional source increases the probability that one or more sources might be delayed, cancelled, or just plain screwed up somehow, calling into play contingency provisions or, worst of all, creating an unanticipated situation. This would either require arbitrary judgment by the selection administrator, defeating the randomness of the selection, or a re-run with a new set of sources, causing much delay in what, for the IETF NomCom, needs to be a time bounded process. Three or four would be a good number of randomness sources. More than five is too many.¶

3.2. Skew

Some of the sources of randomness produce data that is not uniformly distributed. This is certainly true of volumes, prices, and horse race results, for example. However, use of a strong mixing function [RFC4086] will extract the available entropy and produce a hash value whose bits and whose remainder modulo a small divisor, only deviate from a uniform distribution by an insignificant amount.¶

3.3. Entropy Needed

What we are doing is selecting N items without replacement from a population of P items. The number of different ways to do this is as follows, where "!" represents the factorial function:¶


     P!
-------------
N! * (P - N)!

To do this in a completely random fashion requires as many random bits as the logarithm base 2 of that quantity. Some example approximate calculated number of random bits for the completely random selection of 10 items, such as IETF NomCom members, or 1 item, from various pool sizes are given below:¶

Table 1
Completely Random Selection of One or Ten Items From A Pool
Pool size	60	80	100	125	150	175	200	250
Bits needed to select 1	5.9	6.3	6.6	7.0	7.2	7.4	7.6	8.0
Bits needed to select 10	36	41	44	47	50	52	54	58

Using a smaller number of bits means that not all of the possible selections would be available, for example not all sets of 10 if 10 things are being selected. For a substantially smaller amount of entropy, if multiple things are being selected, there could be a correlation between the selection of two different members of the pool. However, as a practical matter, for pool sizes likely to be encountered in IETF NomCom membership selection, 42 bits of entropy should be adequate to randomly select 10 items as discussed in Appendix B.¶

The current USA Power Ball and Mega Millions lottery drawings have 23.5 bits of entropy each in the five selected regular numbers and about 6 bits of entropy each in the Power Ball / Mega Ball. A four-digit daily numbers game drawing that selects four decimal digits has a bit over 13 bits of entropy.¶

The source code in Section 10 uses the SHA-256 [RFC6234] hash function which has 256 bits of output and therefore can preserve no more than that number of bits of entropy. However, this is very much more than what is likely to be needed for IETF NomCom membership selection.¶

4. A Specific Algorithm for Initial Selection

It is important that a precise algorithm be given for canonicalizing and mixing the random sources being used and making the selection based thereon. Sources suggested above produce either a single positive number (i.e., NY Stock Exchange volume in thousands of shares) or a small set of positive numbers (many lotteries provide 6 numbers in the range of 1 through 70 or the like, a sporting event could produce the scores of two teams, etc.). A suggested precise algorithm is as follows:¶

For each source producing one or more numeric values, each value is canonicalized by representing the value as a decimal number terminated by a period (or with a period separating the whole from the fractional part), without leading zeroes except for a single leading zero if the integer part is zero, and without trailing zeroes on the fractional part after the period. Some examples follow:¶

Table 2
Input	Canonicalized
0	0.
0.0	0.
42	42
7.0	7.
013.	13.
.420	0.42
12.34	12.34
1.2340	1.234

If a source produced multiple values, order those values from smallest to the largest. This sorting is necessary because the same lottery results, for example, are sometimes reported in the order numbers were drawn and sometimes in numeric order and such things as the scores of two sports teams that play a game have no inherent order.¶
If a source produced multiple values, concatenate them and suffix the result with a "/". If a source produced a single number, simply represent it as above with an added "/" suffix.¶
At this point you have a string for each source, say s1/, s2/, ... for source 1, source 2, ... Concatenate these strings in a pre-specified order, the order in which the sources were listed when they were announced if no other order is specified, and represent each character as its ASCII code [RFC0020] producing "s1/s2/.../" as the random seed from which selection is derived.¶
Produce a sequence of random values derived from a mixing of these sources by calculating the SHA-256 hash [RFC6234] of the seed specified in step 4 prefixed and suffixed with an all zeros two-byte sequence for the first value, the string prefixed and suffixed by 0x0001 for the second value, etc., treating the two bytes as a big-endian counter. Treat each of these derived "random" MD5 output values as a positive 128-bit multiprecision big endian integer.¶
Finally, impose a total pseudo-random ordering on the pool of listed items (e.g., NomCom volunteers) as follows: If there are P pool members, select the first by dividing the first derived random value by P and using the remainder plus one as the position of the selectee in the published list. Select the second by dividing the second derived random value by P-1 and using the remainder plus one as the position in the list with the first selected person eliminated. And so on.¶

Any ambiguity in the above procedure is resolved by consulting the example code below.¶

Use of alphanumeric random sources is NOT RECOMMENDED due to the much greater difficulty in canonicalizing them in an independently repeatable fashion; however, if the administrator of the selection process chooses to ignore this advice and use an ASCII or similar Roman alphabet source or sources, all white space, punctuation, accents, and special characters should be removed, and all letters set to upper case. This will leave only an unbroken sequence of letters A-Z and digits 0-9 which can be treated as a canonicalized single number above and suffixed with a "./". The administrator MUST NOT use even more complex and harder to canonicalize quantities such as complex numbers or UNICODE international text.¶

5. Extended NomCom Selection

There may be reasons why one or more of the selected members of the pool need to be eliminated and further selections made. This is particularly true for the IETF NomCom given the strong recommendation above that, in case of doubt or not-yet-resolved eligibility dispute, possible pool members should be left in the pool with the understanding that, in the event they are initially selected, they can be later eliminated should it be decided they are not eligible. For the IETF NomCom, there are two types of reasons for elimination as follows:¶

A.

Elimination due to simple rule enforcement by the administrator. Examples would be someone that did not meet the eligibility requirements or whose inclusion would violate the rule limiting the number of voters with the same sponsor or all but one occurrence of someone included multiple times due to a name change or similar confusion. When there are such eliminations in the initial selectees, the administrator simply goes further down the ordered list produced with the initial randomness sources until there are the desired number of selectees who are not eliminated by such decisions. The administrator SHOULD announce who has been eliminated and the reason for the administrator's decision to eliminate them.¶

B.

Eliminations due to a selectee, that is, agreement from the selectee to serve cannot be obtained by the administrator before a deadline established by the administrator. For example, either the selectee declines to serve or, despite reasonable efforts, the selectee is not adequately contactable.¶

(The elimination of someone due to non-contactability may work a hardship for that individual if it was due to no fault of their own and they wanted to serve. But there is no reasonable alternative if a NomCom voting membership of volunteers with a confirmed agreement to serve is to be finalized in a timely manner. Since someone so eliminated will, as provided below, be replaced by another randomly selected pool member, there is no problem from the point of view of NomCom composition.)¶

It will frequently be the case that, after the initial selection from the pool and the handling of any Type A eliminations as above, there will be a small number of Type B eliminations. If no further actions were taken, there will be an insufficient number of people selected and not eliminated. If selection were extended in this case by just going further down the ordered list, as with Type A eliminations, this would give initially selected persons the ability to, by declining to serve, in effect, transfer their voting NomCom membership to a known different person since the entire initial ordered list is, at that point, publicly known. Some perceive this as a problem, so it is resolved by the administrator iteratively using what is essentially a miniature version of the initial selection to re-randomize the remaining pool members as follows:¶

The administrator, when or before the algorithm is announced, determines a secret random number R possibly using the techniques given in Section 4 using secret sources of randomness which MUST be different from those publicly announced for the initial selection. The administrator MUST record this secret random number and SHOULD record its randomness source(s). The administrator then calculates and records a hash chain using the SHA-256 [RFC6234] hash function, denoted as H, as follows: denote H(R) as H[1](R), H(H(R)) = H(H[1](R)) as H[2](R), H(H(H(R))) = H(H[2](R)) as H[3](R), ... H(H[N-1](R))) as H[N](R), where N is a number chosen by the administrator as the maximum number of times it might be necessary to extend selection due to Type B eliminations. It would always be safe to set N to the size of the pool minus the number of people to be selected but, as a practical matter for IETF NomCom selection, an N or 25 should be a very generous allowance.¶
The new pool consists of the initial pool in the same order without any selectees who have agreed to serve and without any pool members eliminated by any earlier Type A or B eliminations.¶
The new randomness is the next earlier value in the hash chain, that is H[N - 1](R). This random source is treated as an additional source added to the initially announced list of random sources as the last source and is processed as specified resulting in it being suffixed to the seed produced by the initial randomness sources. (See worked example and the example code below.)¶
The administrator publicly announces the selectees who were not eliminated, how many additional selections are needed, and H[N - 1](R). Since H[N(R) was previously made public, anyone can check that the administrator has correctly announced H[N - 1](R) by calculating H(H[N - 1](R)) and comparing it with H[N](R). The administrator announces the extended selections and any further extension of the extended selections due to Type A eliminations as above.¶
The administrator still needs to check for Type B eliminations among the new Extended Selection selectees. At this point in the process, the time constraints are likely to be very tight so contacting extensions selectees to be sure they are still willing to serve MUST be done urgently and with a very tight deadline. Since there may be further Type B eliminations among the extended selectees, more than one cycle of Extended Selection may be needed. If so, steps 2 through 5 are repeated with minor modifications as follows: For Step 2, those in the pool before the next extension are all those from the pool who have not been selected or been subject to Type A or Type B elimination so far. In particular, note that because they have been previous eliminated and to avoid various complex disputes and timing race conditions, someone who was uncontactable or declined to serve in an earlier round does NOT become eligible for later rounds even if they later become contactable or change their mind about declining. For Step 3, the next earlier hash in the hash chain is used as the additional randomness; when multiple selection extensions have to be run, the additional randomness does not pile up making the pseudo-random seed longer and longer but rather each extension's additional randomness hash value is used with the initial random sources. In Step 4 the hash chain value announced is H[N-E](R) where this is the Eth Selection Extension.¶

The use of a hash chain, as in step 1 above, is a well known technique that first appeared in [Lamport] and is used in [RFC1760]. Because the hash function H is assumed to be non-invertible, the public announcement of H[N](R) or any other value in the chain does not reveal any earlier values in the hash chain. While the administrator could try various values of R and could thus influence the value of H[N](R) or other H[*](R), this does not provide any control over the selections because the hash chain value is combined with the output of the pre-specified public randomness sources.¶

Multiple extension cycles may be required so the selection administration should allow enough time for at least 5 or so of them. For example, in the selection of the 2022/2023 NomCom, 3 extensions would have been required: The pool was, by historical standards, huge, with 267 members, the largest ever. In the initial selection, one of the 10 potential selectees was Type B eliminated because confirmation of their willingness to serve could not be obtained in a timely fashion. In the 1st Extended Selection, the 11th potential selectee was Type B eliminated because they declined to serve and the 12th was Type A eliminated because there were already two selectees with the same sponsor. In the 2nd Extended Selection, the 13th potential selected also declined to serve. In the 3rd Extended Selection, the 14th potential selectee became the final voting member of the Nomcom when they confirmed their willingness to serve.¶

6. Handling Real World Problems

In the real world, problems can arise in following the steps and flow outlined in the sections above. Some problems that have actually arisen are described below with recommendations for handling them.¶

6.1. Uncertainty as to the Pool

Every reasonable effort should be made to see that the published pool, from which selection is made, is of certain and eligible persons. However, especially with compressed schedules or perhaps someone whose claim that they volunteered and/or are eligible has not been resolved by the deadline, or a determination that someone is not eligible which occurs after the publication of the pool, or the like, there may still be uncertainties.¶

The best way to handle this is to maintain the announced schedule in so far as possible, INCLUDE in the published pool all those whose eligibility is uncertain and to keep the published pool list numbering IMMUTABLE after it is frozen. If one or more people in the pool are later selected by the algorithm and random input but it has been determined they are ineligible, they can be skipped and subsequently selected persons used. (This is referred to above as a Type A elimination.) Thus, the uncertainty only effects one selection and in general no more than a maximum of U selections where there are U uncertain pool members.¶

Other courses of action are far worse. Actual insertion or deletion of entries in the pool after its publication changes the length of the list and scrambles who is selected. Even if done before the random numbers are known, such dinking with the list after its publication looks bad. To avoid schedule slips, there MUST be clear fixed firm public deadlines and someone who challenges their absence from the pool after the published deadline MUST have their challenge automatically denied for tardiness even if their delay is not the fault of the challenger.¶

6.2. Randomness Ambiguities

The best good faith efforts have been made to specify precise and unambiguous sources of randomness. These sources have been made public in advance and there has not been objection to them. However, it has happened that when the time comes to actually get and use this randomness, the real world has thrown a curve ball and it isn't quite clear what data to use. Problems have particularly arisen in connection with individual stock prices, volumes, and financial exchange rates or indices. If volumes that were published in thousands are published in hundreds, you have a rounding problem. Prices that were quoted in fractions or decimals can change to the other. If you take care of every contingency that has come up in the past, you might be hit with a new one. When this sort of thing happens, it is generally too late to announce new sources, an action which could raise suspicions of its own as well as causing substantial delay. About the only course of action is to make a reasonable choice within the ambiguity and depend on confidence in the good faith of the selection administrator. With care, such cases should be extremely rare.¶

Based on these experiences, it is again recommended that public lottery numbers or the like be used as the random inputs and financial volumes or prices avoided.¶

Table 3
index	Base64 value of SHA-256	div	selected
1	fgSNUcziqvUcd1j46xGZdpLQmgyW+OZzGfJAx2/EyS0=	31	> 4 <
2	kMd2sgTSiCF1o11lM6Rs8yeQeRMLPnZo5k0wSFPMjHw=	30	> 30 <
3	pwrk69jq8cUF5KrD0vg31SQMOvtf5117Y6Ox5cm38f0=	29	> 19 <
4	KRXZEdXGiprKvqQ2aSnzYQpzaE0YwlfyDTBBI+R8kv8=	28	> 13 <
5	K2qq2NImq28ESPaVB9uCVrI0tPT/NOYAtryUcjGpzt8=	27	> 7 <
6	8PQ4tm652Kr8yV2D2OBKAYrKxWtkddxqtiMvIuknhgU=	26	> 22 <
7	fJQRVYErqgAmJAs7a01/SoACdnCBNcqzrGbUsFticjM=	25	> 12 <
8	wlfiQaw6S/bxcbT2u+7oshpAFxrsy6wIZyFD+uWle80=	24	> 28 <
9	ekEoRHYTkT6p5m2fP3mn354kQSI1pz/B1RKC+Fa8YXA=	23	> 15 <
10	ggmvds6SzOGPwr8vUwSPNHtk7WIsQLYiO2tl0V3yzZQ=	22	> 11 <
11	ntjVm6AGBtydG6l9aiTSSojdcp6UcYhk55Rg71y0Z+s=	21	> 5 <
12	CE14MeW+JUzb+D/gQ82dJF62NBapfROt7Ff2ngkT/XE=	20	> 27 <
13	ZRYzTo0OZ0ASx5keWlh3YH1Di4o9p5jefz+MCWmWjFk=	19	> 23 <
14	lvA2rjCw7sT0+SVNOZB29HZOVvIAiS3yA85wqE9ugPk=	18	> 6 <
15	aQy+Eof9q4MbDZam/D+Sxc5yLixLYdArJ6kr1KmrbKA=	17	> 14 <

Table 4
1. G. Huston (4)	6. M. Richardson (22)
2. R. Salz (30)	7. D. McPherson (12)
3. S. Krishnan (19)	8. B. Stark (28)
4. R. Droms (13)	9. L. Dondet (15)
5. A. Doria (7)	10. R. Draves (11)

10. Source Code

The C source code below makes use of the SHA-256 reference code from [RFC6234]. The original code in [RFC2777] was written by Donald Eastlake except for the code dealing with multiple floating point number input which was written by Matt Crawford. The [RFC2777] code could only handle pools of up to 255 members and was extended to 2**16-1 by Erik Nordmark for the code in [RFC3797]. Both of these earlier versions used MD-5 [RFC1321] rather than SHA-256.¶

Python code by Rich Salz to implement the method in [RFC3797] is available at https://github.com/richsalz/ietf-rfc3797¶

The code below has been extracted from this document, compiled, and tested. While no flaws were found, it is possible that when used with some compiler on some system under some circumstances some flaw will manifest itself.¶

<CODE BEGINS>

<< CODE HAS NOT YET BEEN UPDATED TO COVER EXTENDED SELECTION. >>

//*****************************************************************
/*  Example code for
 *      "Publicly Verifiable Random Selection"
 *          Donald E. Eastlake 3rd
 *              Original February 2004
 *              Updated August 2022 - June 2023
 *
 * Redistribution and use in source and binary forms, with or
 * without modification, is permitted pursuant to, and subject
 * to the license terms contained in, the Revised BSD License
 * set forth in Section 4.c of the IETF Trust's Legal Provisions
 * Relating to IETF Documents
 * (http://trustee.ietf.org/license-info).                       */
//*****************************************************************

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <ctype.h>

//  SHA-256, RFC 6234
#include "sha.h"


// CONSTANTS
#define MAXLINE 256

//  Local prototypes in alphabetic order
//*****************************************************************
void     b64print ( uint8_t *p, int length );
void     b64toHex ( void );
int      b64v ( char );
long int getinteger ( char *prompt );
int      getNP ( void );
int      getSeed ( char *key );
void     hashChain ( void );
void     hexprint ( uint8_t *p, int length );
void     hexToB64 ( void );
int      longremainder ( unsigned int divisor,
                         uint8_t hash[SHA256HashSize] );
double   NPentropy ( void );
void     probe ( void );    // RFC3797 but with SHA-256
void     testSHA256 ( void );
void     xprintf ( char *message, int x );


//  Global Variables
//*****************************************************************
char    tin[MAXLINE+2];  // type in buffer
int     debug = 0; // debug level
int     keysize;
char    key[800];  // where key string is accumulated
unsigned int    N; // Number of items to be selected
unsigned int    P; // Size of pool
char    b64[] = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
      "abcdefghijklmnopqrstuvwxyz0123456789+/";


//  Main driver/dispatch routine
//*****************************************************************
int main ( int argc, const char * argv[] ) {
char       *cherr;
int         i, ioerr;
char        ch;

nextcommand:
xprintf ( "How may I serve you? ", 101 );
cherr = fgets( tin, MAXLINE, stdin );   // get commeand
if ( cherr == NULL )
    exit ( 102 );
for ( i=0; i < MAXLINE; ++i ){
    ch = tin[i];
    if ( debug > 0 ) {
        ioerr = printf ( "%s%X%s",
            "Processing character 0X", ch, "\n");
        if ( ioerr <= 0 )
            exit ( 103 );
        }
    switch ( ch ) {
        case '?': // help
            xprintf ( " ? -> Help\n"
            " d -> set debug level\n"
            " e -> entropy needed\n"
            " h -> hash chain\n"
            " p -> select from pool\n"
                      " q -> quit\n", 104 );
            if ( debug )
                xprintf ( " t -> test SHA-256\n"
                " 8 -> hex to base64\n"
                        " 9 -> base64 to hex\n", 105
                    );  // falls through
        case 0: // "gets" string is zero terminated
            goto nextcommand;
        case ' ': case '\n': case '\t': // skip white space
        case'\v': case '\r': case '\f': case '\b': case 127:
            continue;  // try next character
        case 'd': case 'D': // set debug level
            debug = (int)getinteger ( "Set debug level" );
            goto nextcommand;
        case 'e': case 'E':  // calculate entropy needed
            if ( !getNP ( ) )
                NPentropy ( );
            goto nextcommand;
        case 'h': case 'H': // calculate hash chain
            if ( !getSeed ( key ) )
                hashChain ( );
            goto nextcommand;
        case 'p': case 'P':  // select from pool
            if ( !getNP ( ) && !getSeed ( key ) )
                probe ( );
            goto nextcommand;
        case 'q': case 'Q': case '\a':  // quit
            exit ( 0 );
        case 't': case 'T':
            testSHA256 ( );
            goto nextcommand;
        case '8':
            hexToB64 ( );
            goto nextcommand;
        case '9':
            b64toHex ( );
            goto nextcommand;
        default:
            ioerr = printf ( "%s%s%s",
                             "Undefined command: ",
                             tin, "\n");
            if ( ioerr <= 0 )
                exit ( 106 );
            goto nextcommand;
        }  // end switch
    }  // end for
}  // end main


//  print as base64
//*****************************************************************
void b64print ( uint8_t *p, int length ) {
uint8_t   nib;
int      ioerr;

while ( length > 0 ) {
    nib = p[0] >> 2;
    ioerr = printf ( "%c", b64[nib] ); // print 1st 6 bits
    if ( ioerr <= 0 )
      exit ( 1000 );
    nib = ( p[0] & 0x3 ) << 4; // get bottom 2 bits of 1st byte
    if ( --length ) {
      nib += ( p[1] >> 4 ); // get top 4 bits of 2nd byte
      ioerr = printf ( "%c", b64[nib] ); //print 2nd 6 bits
      if ( ioerr <= 0 )
        exit ( 1001 );
      nib = ( p[1] & 0xF ) << 2; // get bottom 4 bits of 2nd byte
      if ( --length ) {
        nib += ( p[2] >> 6 ); // get top 2 bits of 3rd byte
        ioerr = printf ( "%c%c", b64[nib], b64[ p[2] & 0x3F ] );
        if ( ioerr <= 0 )
          exit ( 1002 );
      }
      else { // length was 2, print rest of 2nd byte
        ioerr = printf ( "%c=", b64[nib] );
        if ( ioerr <= 0 )
          exit ( 1003 );
      }
    }
    else { // length was 1, print rest of 1st byte
      ioerr = printf ( "%c==", b64[nib] );
      if ( ioerr <= 0 )
        exit ( 1004 );
    }
    p += 3;
    --length;
} // while
} // end b64print


//  read base64, print as hex
//*****************************************************************
void b64toHex ( void ) {
char       clean[MAXLINE];
uint8_t    val64[((MAXLINE*3)/4)+2];
int        i, j, k, v;
int        equalsigns = 0;
char      *cherr;

xprintf ( "Type some Base64: ", 901 );
cherr = fgets ( tin, MAXLINE, stdin );
if ( cherr == NULL )
    exit ( 902 );
for ( i = 0, j = 0; i < MAXLINE; ++i ) {
    if ( ( tin[i] == '\n' ) || ( tin[i] == 0 ) )
        break;  // end of the line
    if ( isspace ( tin[i] ) )
        continue;  // skip white space
    if ( isalnum ( tin[i] ) ||
         ( tin[i] == '+' ) || ( tin[i] == '/') ) {
        if ( equalsigns ) {
            xprintf ( "Stuff after an equal sign.\n", 803 );
            return;
            }
        clean[j] = tin[i];
        ++j;
        continue;
        }
    if ( tin[i] == '=' ) {
        switch ( equalsigns ) {
            case 0:
                    v = j % 4;
                if ( ( v != 2 ) && ( v != 3 ) )
                    xprintf ( "Wrong length before '='.\n",
                                  904 );
                // fall through
            case 1:
                    ++equalsigns;
                    break; // out of switch equalsigns
            case 2:
                    xprintf ( "Too many equal signs.\n", 905 );
                return;
            } // switch equalsigns
        } // if equal sign
    } // for i
clean[j] = 0;
if ( debug ) {
    hexprint ( (uint8_t *)clean, j+1 );
    xprintf ( " ", 907 );
    }
v = j % 4;
if ( v == 1 )
    xprintf ( "Wrong length.\n", 906 );
for ( i = 0, k = 0; i < j; i += 4, k += 3 ) {
val64[k] = ( b64v ( clean[i] ) << 2 ) |
           ( ( b64v ( clean[i+1] ) >> 4 ) & 0xF );
if ( ( i + 2 ) < j ) {
    val64[k+1] = ( b64v ( clean[i+1] ) << 4 ) |
                 ( ( b64v ( clean[i+2] ) >> 2 ) &0xF );
    if ( ( i + 3 ) < j ) {
        val64[k+2] = ( b64v ( clean[i+2] ) << 6 ) |
                         b64v ( clean[i+3] );
        }
    }
} // for i
hexprint ( val64, ( (j*3)/4 ) );
xprintf ( "\n", 908 );
} // end b64toHex


//  convert a base64 char to int
//*****************************************************************
int b64v ( char ch ) {
int     i;

for ( i = 0; i < 64; ++i )
    if ( ch == b64[i] )
        return i;
exit ( 999 );
}


//  prompt for and get an integer input
//*****************************************************************
long int getinteger ( char *prompt ) {
long int    i;
char        *cherr;
int         j, ioerr;

nexttry:
ioerr = printf ( "%s", prompt );
if ( ioerr < 0 )
    exit ( 201 );
xprintf ( " (or 'quit' to exit) ", 202 );
cherr = fgets ( tin, MAXLINE, stdin  );
if ( cherr == NULL )
    exit ( 203 );
j = sscanf ( tin, "%ld", &i );
if ( ( j == EOF ) ||
     ( !j && ( ( tin[0] == 'q' ) ||
             ( tin[0] == 'Q' ) ) ) )
    exit ( j );
if ( j == 1 )
    return i;
goto nexttry;
} // end getinteger


//  get pool size and number of items to pick
//  returns zero for success, non-zero for failure
//****************************************************************
int getNP ( void ) {

P = (unsigned int)getinteger ( "Type size of pool:" );
if ( ( P > 65535 ) ||
     ( P <= 0 ) ) {
    xprintf ( "Pool zero, negative, or too big.\n", 301 );
    return ( 1 );
}
N = (unsigned int)getinteger (
        "Type number of items to be selected:" );
if ( N > P ){
    xprintf ( "Pool too small.\n", 302 );
    return ( 1 );
}
return ( 0 );  // got possibly reasonable values
} // end getNP


//  get the "random" inputs. echo back to user so the user may
//  be able to tell if truncation or other glitches occur.
//
//  Up to 16 inputs each of which can be either up to 16 integers
//      or up to 16 floating point numbers
//
//  output 1 for failure, 0 for success
//****************************************************************
int getSeed ( char *key ) {
long int    temp, array[16];
int         i, ioerr, j, k, k2;
char        sarray[16][256];
char        *cherr;

for ( i = 0, keysize = 0; i < 16; ++i ) {
    if ( keysize > 511 ) {
        xprintf ( "Too much input.\n", 400 );
        return ( 1 );
    }
    ioerr = printf (
        "Type #%d randomness or 'end' followed by new line.\n"
        "Up to 16 integers or the word 'float' followed by up\n"
        "to 16 x.y format reals.\n", i+1 );
    if ( ioerr <= 0 )
        exit ( 401 );
    cherr = fgets ( tin, MAXLINE, stdin );
    if ( cherr == NULL )
        exit ( 402 );
    j = sscanf ( tin,  // try to parse as "long int"s
                "%ld%ld%ld%ld%ld%ld%ld%ld%ld%ld%ld%ld%ld%ld%ld%ld",
                &array[0], &array[1], &array[2], &array[3],
                &array[4], &array[5], &array[6], &array[7],
                &array[8], &array[9], &array[10], &array[11],
                &array[12], &array[13], &array[14], &array[15] );
    if ( j == EOF )
        exit ( 403 );
    if ( !j ) {
        if ( ( tin[0] == 'e' ) || ( tin[0] == 'E' ) ) // "e"nd
            break; // break out of "for i"
        else {   // floating point code by Matt Crawford
            j = sscanf ( tin,
                    "float %ld.%[0-9]%ld.%[0-9]%ld.%[0-9]%ld.%[0-9]"
                    "%ld.%[0-9]%ld.%[0-9]%ld.%[0-9]%ld.%[0-9]"
                    "%ld.%[0-9]%ld.%[0-9]%ld.%[0-9]%ld.%[0-9]"
                    "%ld.%[0-9]%ld.%[0-9]%ld.%[0-9]%ld.%[0-9]",
                    &array[0], sarray[0], &array[1], sarray[1],
                    &array[2], sarray[2], &array[3], sarray[3],
                    &array[4], sarray[4], &array[5], sarray[5],
                    &array[6], sarray[6], &array[7], sarray[7],
                    &array[8], sarray[8], &array[9], sarray[9],
                    &array[10], sarray[10], &array[11], sarray[11],
                    &array[12], sarray[12], &array[13], sarray[13],
                    &array[14], sarray[14], &array[15], sarray[15] );
            if ( j == 0 || j & 1 ) {
                    xprintf ( "Bad format.", 404 );
                return ( 1 );
            }
            else {
                for ( k = 0, j /= 2; k < j; k++ )
                /* strip trailing zeros */
                    for ( k2 = (int)strlen(sarray[k]);
                        sarray[k][--k2]=='0'; )
                            sarray[k][k2] = '\0';
                    ioerr = printf ( "%ld.%s\n", array[k],
                                     sarray[k] );
                    if ( ioerr <= 0 )
                        exit ( 405 );
                    keysize += sprintf ( &key[keysize], "%ld.%s",
                                        array[k], sarray[k] );
                }
                keysize += sprintf ( &key[keysize], "/" );
            }
        }
        else
        { // sort integer values, not a very efficient algorithm
            for ( k2 = 0; k2 < j - 1; ++k2 )
                for ( k = 0; k < j - 1; ++k )
                    if ( array[k] > array[k+1] ) {
                        temp = array[k];
                        array[k] = array[k+1];
                        array[k+1] = temp;
                        }
            for ( k = 0; k < j; ++k ) {  // print for user check
                ioerr = printf ( "%ld ", array[k] );
                if ( ioerr <= 0 )
                    exit ( 406 );
                keysize += sprintf ( &key[keysize], "%ld.",
                                     array[k] );
            }
            keysize += sprintf ( &key[keysize], "/" );
        }
}    // end "for i"
if ( i == 0 ) {
    xprintf ( "No key input.\n", 407 );
    return ( 1 );
}
ioerr = printf ( "Key is:\n %s\n", key );
if ( ioerr <= 0 )
    exit ( 408 );
return ( 0 );
}  // end getSeed


//  print out a hash Chain based on key
//*****************************************************************
void hashChain ( void )
{
int            i, ioerr;
long int       j;
SHA256Context  context;
uint8_t        hash[SHA256HashSize];

j = getinteger ( "Length of chain to print:" );
if ( j > 99 ) {
    j = 99;
    xprintf ( "Chain length clipped at 99.\n", 500 );
    }
testSHA256 ( );
SHA256Reset ( &context );
SHA256Input ( &context, (uint8_t *)key, (int)strlen ( key ) );
SHA256Result ( &context, hash );
if ( debug ) {
    xprintf ( "Hex of SHA-256 of Key:\n", 501 );
    hexprint ( hash, SHA256HashSize );
    xprintf ( "\n", 502 );
    }
xprintf ( "00-", 505 );
b64print ( hash, SHA256HashSize );
    xprintf ( "\n", 506 );
for ( i = 1; i <= j; ++i ) {
    SHA256Reset ( &context );
    SHA256Input ( &context, hash, SHA256HashSize );
    SHA256Result ( &context, hash );
    ioerr = printf ( "%02d-", i );
    if ( ioerr <= 0 )
        exit ( 503 );
    b64print ( hash, SHA256HashSize );
    xprintf ( "\n", 504 );
} // for i
} // end hashChain


// print out a SHA-256 hash in hex
//****************************************************************
void hexprint ( uint8_t *p, int length ) {
int    i, ioerr;

for ( i = 0; i < length; ++i ) {
ioerr = printf ( "%02X", p[i] );
if ( ioerr <= 0 )
    exit ( 601 );
 } // for i
} // end hexprint


//  read hex, print as base64
//*****************************************************************
void hexToB64 ( void ) {
uint8_t   hexval[(MAXLINE/2)+2];
char      clean[MAXLINE];
char     *cherr;
int       i, j, v, ioerr;

xprintf ( "Type some bytes in hex: ", 1101 );
cherr = fgets ( tin, MAXLINE, stdin );
if ( cherr == NULL )
    exit ( 1102 );
for ( i = 0, j = 0; i < MAXLINE; ++i ) {
    if ( ( tin[i] == '\n' ) || ( tin[i] == 0 ) )
      break;  // end of the line
    if ( isspace ( tin[i] ) )
      continue;  // skip white space
    if ( isxdigit ( tin[i] ) ) {
      clean[j] = tolower ( tin[i] );
      ++j;
      continue;
    }
    ioerr = printf ( "Non-hex digit encountered: %02X\n", tin[i] );
    if ( ioerr <= 0 )
        exit ( 1103 );
    return;
} // for i
clean[j] = 0;
if ( j & 1 ) {
    ioerr = printf ( "Odd number of hex digits? %i\n", j );
    if ( ioerr <= 0 )
        exit ( 1104 );
    return;
}
for ( i = 0; i < j; ++i ) { // from clean to hexval
    if ( clean[i] >= 'a' && clean[i] <= 'f' )
        v = clean[i] - 'a' + 10;
    else
        v = clean[i] - '0';
    if ( i & 1 )
        hexval[i/2] += v;
    else
        hexval[i/2] = v << 4;
}
if ( debug ) {
    hexprint ( hexval, j/2 );
    xprintf ( "\n", 1105 );
}
b64print ( hexval, j/2 );
xprintf ( "\n", 1106 );
} // end hexToB64


// get remainder of dividing a SHA-256 hash
//   by a small positive number
//****************************************************************
int longremainder ( unsigned int divisor,
                    uint8_t hash[SHA256HashSize] ) {
long int     kruft;
int          i;

if ( divisor <= 0 )
    exit ( 1 );
for ( i = 0, kruft = 0; i < SHA256HashSize; ++i )
    {
    kruft = ( kruft << 8 ) + hash[i];
    kruft %= divisor;
    }
return (int)kruft;
}  // end longremainder


//  calculate how many bits of entropy it takes to select N from P
//      withour replacement. Print and return it.
//****************************************************************
/*               P!
    log  ( ----------------- )
       2    N! * ( P - N )!
*/
double NPentropy ( void )
{
long int    i;
double      result = 0.0;
int         ioerr;

if (    ( N < 1 )   // not selecting anything?
   ||   ( N >= P )  // selecting all of pool or more?
   )
   result = 0.0;    // degenerate case
else {
    for ( i = P; i > ( P - N ); --i )
        result += log ( i );
    for ( i = N; i > 1; --i )
        result -= log ( i );
    /* divide by [ log (base e) of 2 ] to convert to bits */
    result /= log ( 2 );
}
ioerr = printf ( "Approximately %.1f bits of entropy needed.\n",
                    result );
if ( ioerr <= 0 )
    exit ( 701 );
return result;
} // end NPentropy


//  Select N items from the pool of P items using the probe method
//****************************************************************
void probe ( void ) {
unsigned short     *selected;
SHA256Context      context;
uint8_t            hash[SHA256HashSize];
unsigned int       i, remaining, divisor;
int                j, k;
unsigned char      unch1, unch2;

selected =
  (unsigned short *)malloc ( P * sizeof ( unsigned short ) );
if ( !selected )
    xprintf ( "Out of memory.\n", 801 );
for ( i = 0; i < P; ++i )
    selected [i] = (unsigned short)(i + 1);
xprintf (
"index          base64 value of SHA-256          div selected\n",
    802 );
remaining = N;
divisor = P;
testSHA256 ( );
for ( i = 0; i < N; ++i, --remaining, --divisor ) {
    SHA256Reset ( &context );
    unch1 = i >> 8;
    unch2 = i & 0xFF;
    SHA256Input ( &context, &unch1, 1 );
    SHA256Input ( &context, &unch2, 1 );
    SHA256Input ( &context, (uint8_t *)key, keysize );
    SHA256Input ( &context, &unch1, 1 );
    SHA256Input ( &context, &unch2, 1 );
    SHA256Result ( &context, hash );
    k = longremainder ( divisor, hash );
    for ( j = 0; j < P; ++j) {
        if ( selected[j] )
            if ( --k < 0 ) {
                printf ( "%3d ", i + 1 );
                b64print ( hash, SHA256HashSize );
                printf ( " %3d  >%3d<\n", divisor, selected[j] );
                selected[j] = 0;
                break;  // for j
            }
    } // for j
} // for i
free ( (void *)selected );
} // end probe


//  Test that SHA-256 code seems to be working
//****************************************************************
void testSHA256 ( void ) {
SHA256Context  context;
char           test1[] = "abc";
uint8_t        correct[] = { 0xBA, 0x78, 0x16, 0xBF, 0x8F, 0x01,
    0xCF, 0xEA, 0x41, 0x41, 0x40, 0xDE, 0x5D, 0xAE, 0x22, 0x23,
    0xB0, 0x03, 0x61, 0xA3, 0x96, 0x17, 0x7A, 0x9C, 0xB4, 0x10,
    0xFF, 0x61, 0xF2, 0x00, 0x15, 0xAD };
uint8_t        hash[SHA256HashSize];
int            i;

SHA256Reset ( &context );
SHA256Input ( &context, (uint8_t *)test1, 3 );
SHA256Result ( &context, hash );
for ( i = 0; i < SHA256HashSize; ++i ) {
if ( hash[i] == correct[i] )
    continue;
else
    xprintf ( "SHA256 not working.\n", 1201 );
}  // for
if ( debug )
    xprintf ( "SHA256 OK.\n", 1202 );
} // end testSHA256


//  printf a string and exit if io error occurs
//****************************************************************
void xprintf ( char *message, int x) {
int    ioerr;

ioerr = printf ( "%s", message );
if ( ioerr <= 0 )
    exit ( x );
}

<< CODE HAS NOT YET BEEN UPDATED TO COVER EXTENDED SELECTION. >>


<CODE ENDS>

Num	YEAR	CHAIR	SELECTION METHOD
1	1993/1994	Jeff Case	Clergy
2	1994/1995	Fred Baker	Clergy
3	1995/1996	Guy Almes	Clergy
4	1996/1997	Geoff Huston	Spouse
5	1997/1998	Mike St.Johns	Algorithm
6	1998/1999	Donald Eastlake 3rd	RFC 2777
7	1999/2000	Avri Doria	RFC 2777
8	2000/2001	Bernard Aboba	RFC 2777
9	2001/2002	Theodore Ts'o	RFC 2777
10	2002/2003	Phil Roberts	RFC 2777
11	2003/2004	Rich Draves	RFC 2777
12	2004/2005	Danny McPherson	RFC 3797
13	2005/2006	Ralph Droms	RFC 3797
14	2006/2007	Andrew Lange	RFC 3797
15	2007/2008	Lakshminath Dondeti	RFC 3797
16	2008/2009	Joel M. Halpern	RFC 3797
17	2009/2010	Mary Barnes	RFC 3797
18	2010/2011	Tom Walsh	RFC 3797
19	2011/2012	Suresh Krishnan	RFC 3797
20	2012/2013	Matt Lepinski	RFC 3797
21	2013/2014	Allison Mankin	RFC 3797
22	2014/2015	Michael Richardson	RFC 3797
23	2015/2016	Harald Alvestrand	RFC 3797
24	2016/2017	Lucy Lynch	RFC 3797
25	2017/2018	Peter Yee	RFC 3797
26	2018/2019	Scott Mansfield	RFC 3797
27	2019/2020	Victor Kuarsingh	RFC 3797
28	2020/2021	Barbara Stark	RFC 3797
29	2021/2022	Gabriel Montenegro	RFC 3797
30	2022/2023	Rich Salz	RFC 3797
31	2023/2024	Martin Thomson	RFC 3797 + hash chain extensions

Times Set of 10 Selected	Base 2 Log(Times)	Expected Times Each Item Selected	Standard Deviation of Times Item Selected	SD as a % of Expected
1,024	10	51.2	22.1	43.2%
1,048,576	20	52,429	706	1.35%
1,073,741,824	30	53,687,091	22,584	0.0421%
1,099,511,627,776	40	54,975,581,389	722,681	0.00131%

Publicly Verifiable Nominations Committee (NomCom) Random Selection

Abstract

Status of This Memo

Copyright Notice

Table of Contents

1. Introduction

1.1. Requirements Language

2. General Flow of a Publicly Verifiable Process

2.1. Determination of the Pool

2.2. Publication of the Algorithm

2.3. The Selection

3. Randomness

3.1. Sources of Randomness

3.2. Skew

3.3. Entropy Needed

4. A Specific Algorithm for Initial Selection

5. Extended NomCom Selection

6. Handling Real World Problems

6.1. Uncertainty as to the Pool

6.2. Randomness Ambiguities

7. Fully Worked Example

8. Security Considerations

9. IANA Considerations

10. Source Code

11. Normative References

12. Informative References

Appendix A. History of NomCom Voting Member Selection

Appendix B. More Equations and Numbers

Appendix C. Changes from RFC 3797

Appendix D. Versions Change History

D.1. -00 to -01

D.2. -01 to -02

D.3. -02 to -03

Acknowledgements

Author's Address