| Internet-Draft | Verifiable Random Selection | September 2023 |
| Thomson | Expires 20 March 2024 | [Page] |
A process for performing random selection without bias is described.¶
This note is to be removed before publishing as an RFC.¶
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On occasion, a group of people might agree that it is necessary to select from a set of options, but cannot agree on a selection. In such cases, a random selection might be acceptable, but any potential for bias might not be.¶
A process for selection in way that is verifiable and not subject to bias or influence by any party can be useful in such situations. This document describes one such process.¶
The IETF Nominating Committee [NOMCOM] is an example of where a random selection is necessary. Ten people are drawn from a larger pool of eligible volunteers. As the selected group is entrusted with considerable responsibility, there is a need to avoid any risk of bias in the outcome.¶
This document describes a process that is an alternative to RFC 3797 [RFC3797].¶
A random selection process might be invoked to select a subset of one or more items from a longer list of options. The purpose of this process is to select uniformly at random with minimal risk that the selection is influenced by anyone, including those responsible for executing the process.¶
The process for random selection is as follows:¶
The facilitator performs the following in any order:¶
Options are selected by taking from the sorted list in order, starting from the value with the lowest lexical value.¶
There might be constraints on selection, such as requirements on diversity within the final selection, or disqualifications of individual options (see below). If any option cannot be selected, skip that option and select the next option from the list. Options can only be skipped as a result of known constraints on selection, disqualifications, and any factor that is not potentially subject to external influence.¶
An option might become unavailable after selection for reasons that are unexpected or could be subject to external influence. For instance, when selecting volunteers, a selected person could become unavailable through illness or another change of circumstance. In that case, the complete set of selections is produced, applying any constraints as above. After all selections are made, any options that have become unavailable are publicly noted as disqualified from selection and the process is iterated.¶
Subsequent iterations start at the key generation stage (Step 5 above), using the next one-time code; see Section 2.3. Using a one-time code avoids having to wait for new randomness to become available, but might give the facilitator some influence over the outcome. Alternatively, the entire process can be repeated. Section 3.1 explores the consequences of this choice in more detail.¶
This process does not describe how the list of options is assembled, or how constraints on selection are agreed. This document only describes how a random selection is made.¶
Options require labels. This process requires that each option be given a unique and unambiguous label that is a sequence of bytes.¶
Labels could be anything, but using UTF-8 encoded Unicode strings [UTF8] without leading or trailing whitespace can be most amenable to use in many contexts as they can represent many concepts clearly and in an accessible fashion.¶
It should be clear what option each label corresponds to. Names are often excellent labels. Any options with the same name can have extra text added to disambiguate them.¶
The use of Unicode strings allows the possibility that some strings appear to be equal when rendered, despite having very different character sequences. Such differences are significant; a single choice of encoding needs to be made for each label prior to the release of randomness.¶
The facilitator announces the set of labels that will be used prior to any randomness being available.¶
A source of randomness needs to be chosen. This source needs to produce sufficient entropy both to ensure that all possible selection outcomes are equally likely (see Section 3.3 of [RFC3797]) and to make pre-computation of options infeasible (see Section 3).¶
The randomness source might be assembled from multiple discrete sources. Each source and the date at which the entropy will be sampled needs to be announced.¶
A process for turning the randomness from each source into a single sequence of bytes needs to be specified clearly. This too should be announced. Section 4 of [RFC3797] describes a method for the combination and canonical encoding of multiple sources that each produce multiple integers.¶
Public lotteries are a good source of entropy, often providing in excess of 20 bits of entropy each. Choosing three or four different lotteries likely provides sufficient entropy.¶
The facilitator announces which lotteries are to be used, the date of the lottery, and the encoding process. This announcement needs to occur before any of the lotteries are run.¶
A one-time code provides a facilitator with the ability to generate substitute selections in case of unexpected unavailability of one or more options.¶
The facilitator selects a secret sequence of bytes. This could be a string that is UTF-8 encoded as is done for labels.¶
The facilitator then iteratively applies SHA-256 [SHA2] to this sequence multiple times. This generates a hash commitment. [RFC1760] describes this process for use in generating one-time passwords.¶
Concretely, if H(secret) is the process of hashing once, H^2(secret) =
H(H(secret)) is hashing twice. H^n = H(H^{n-1}(secret)) is hashing n
times.¶
How many times the secret is hashed depends on the facilitator's judgment of the need to find substitutes. Hashing many more times than is expected to be necessary will ensure that substitutes can be produced immediately.¶
The facilitator publishes H^n(secret) and n prior to any randomness being
available.¶
Once randomness is available, the first iteration of the selection process uses
H^{n-1}(secret), or the preimage of the original published value. In the
i-th iteration of the selection process, they use H^{n-i}(secret), or the
preimage of the last published value. At each iteration of the process, the
facilitator publishes the one-time code they use.¶
The chosen secret cannot be used. If the process iterates enough times to reach that point, new randomness and a new one-time code will need to be generated.¶
After the selection process is complete, the facilitator publishes their chosen secret.¶
Once randomness is available, the facilitator constructs a byte sequence from the randomness as described in Section 2.2. They also obtain the one-time code as described in Section 2.3.¶
The HKDF-Extract function (Section 2.2 of [HKDF]) with a hash function of
SHA-256 is used to extract entropy and produce a pseudorandom key (or PRK). The
salt input is set to the bytes of the one-time code, and the input keying material
or IKM is set to the bytes from the randomness sources.¶
PRK = HKDF-Extract(salt=one-time-code, IKM=randomness)¶
This produces a PRK value.¶
The HKDF-Extract function (Section 2.3 of [HKDF]) with a hash function of
SHA-256 is used as a pseudorandom function. The pseudorandom key input, PRF,
is taken from the previous step (Section 2.4); the label for each option is used
as the info input; and the output length, L, is 32 (measured in bytes).¶
position = HKDF-Expand(PRK, info=label, L=32)¶
This produces a value, position, that can be sorted to produce a final
ordering.¶
A facilitator needs to communicate clearly throughout the process.¶
Announcements regarding labels, randomness, and one-time codes -- including the encoding of each -- need to be made prior to any randomness becoming available. A single announcement for all of this information might be sufficient.¶
Once randomness is available, a single announcement can include the revealed one-time code and the result of that iteration of selection.¶
For all announcements, allowing some time for validation and questions is advisable. If it takes time to confirm that an option is available for selection, the next iteration of the process cannot be started until that time passes.¶
When publishing values, the facilitator can use hexadecimal encoding to produce text strings that might be easier to use.¶
For the sorting and selection process, using hexadecimal strings might also help simplify handling. Hexadecimal strings sort identically to the underlying byte sequence. If the hexadecimal strings are printed one to a line, with the input label (or name) after it on the same line, that can make it easier to identify options in the sorted output.¶
The sample code in Appendix A uses this method. It does not sort its output, as
that can be performed by a standard sort tool.¶
This process uses SHA-256 as its hash function for both one-time codes (Section 2.3) and the KDF (Sections 2.4 and 2.5). A different hash function could be used, but then it would not be this process.¶
Low entropy randomness in a selection process could allow an attacker to compute all possible outcomes. Then, the attacker might be able to select options (or labels for options) that improve the odds of an outcome favorable to them. Given the use of one-time codes in this process, the only attacker who is in any position to take advantage of this is the facilitator.¶
An appeals process or similar can help safeguard against a facilitator that might be untrustworthy.¶
A facilitator has a limited ability to influence the selection process. This influence depends on the facilitator being able to cause a selected option to become disqualified somehow.¶
For example, if the process selects from volunteers for a task, the facilitator might need to check that selected volunteers are available to perform that task. A facilitator will know who will be selected as a substitute, if that becomes necessary. If the facilitator prefers that a substitute is selected, they could attempt to force the use of a substitute, such as by not investing enough effort in confirming availability.¶
This process is not robust against this attack; it depends on some amount of trust in the facilitator. If concerns exist about the impartiality of the facilitator, the entire process can be re-run if an option becomes unavailable. However, this adds another period of waiting for fresh randomness, which could be too slow. This is therefore a question of balancing a small dependency on the facilitator against expedience.¶
The facilitator needs to keep the value they choose for generating one-time codes a secret until the process completes and all selections are made.¶
An attacker that obtains this secret -- or any unused one-time code -- gains the foreknowledge available to the facilitator described in Section 3.1.¶
This document has no IANA actions.¶
This section includes simple python code for running this process. Separate scripts exist for running selection (Figure 1) and managing one-time codes (Figure 2).¶
Values for the randomness and one-time code are provided as the first and second arguments to the python script in Figure 1, which implements steps 6 and 7 of the process in Section 2.¶
#!/usr/bin/env python3
import sys
def hmacsha256(k, v):
from cryptography.hazmat.backends import default_backend
from cryptography.hazmat.primitives import hashes, hmac
ctx = hmac.HMAC(k, hashes.SHA256(), backend=default_backend())
ctx.update(v)
return ctx.finalize()
def extract(salt, ikm):
return hmacsha256(salt, ikm)
def expand(prk, info):
return hmacsha256(prk, info + bytes([1]))
# The canonical encoding of the randomness.
ikm = sys.argv[1].encode('utf8')
# This is the one-time code.
salt = bytes.fromhex(sys.argv[2])
prk = extract(salt, ikm)
for line in sys.stdin:
label = line.strip()
order = expand(prk, label.encode('utf8'))
print(f"{order.hex()} {label}")
This script is intended to be used with a separate sorting tool as follows:¶
$ ./select.py "$randomness" "$otp" | sort¶
The script in Figure 2 implements the generation of one-time codes from a secret.¶
#!/usr/bin/env python3
import hashlib
import sys
count = 25
input = bytes.fromhex(sys.argv[1])
# Or, for a hard-coded ASCII string: input = b"secret"
print(f" 0: {input.hex()}")
x = hashlib.sha256(input)
for i in range(1,count):
print(f"{i:>2}: {x.hexdigest()}")
x = hashlib.sha256(x.digest())
print(f"{count:>2}: {x.hexdigest()}")
This script can also be used to verify the value revealed by the facilitator. The value revealed by the facilitator at each iteration of the process can be passed to this script, which should produce all previously revealed values.¶
A committee is tasked with painting a building (which may or may not be a bike shed) and have concluded that three different colors are needed for walls, doors, and trim (eaves, gutters, and so forth). They managed to agree that the blue or anything close to blue was undesirable, but could not otherwise agree. Ultimately the group agreed to follow a random selection process.¶
The list of color names from CSS level 3 [CSS3] was agreed as the basis for selection, with "transparent", "grey", "cyan", and "magenta" being disqualifed on the basis of either being not a color or an alias of another name. A list of those colors that were "blue" enough to be disqualified were agreed.¶
The facilitator chose a secret phrase "totally not a bikeshed", encoded it in UTF-8, and published the output of 10 iterations of SHA-256 in hex: 950ea08d8d5fd3ae415b9967aba7a48aba39ca62a4d98f2e7fe25cb1b8f8c488.¶
The facilitator announced the exact process for public randomness, including the use of three different lotteries on a future date and how the results would be encoded, using the method from RFC 3797. After waiting, the lotteries finally ran to produce the unlikely string of "1.2.3.4.5.6./1.2.3.4.5.6./1.2.3.4.5.6./".¶
The facilitator revealed the output of the 9th hash iteration (5346f2efb5397a6788fc1f1d9c05c6d3f2abe9b7d16d8592a3695b6dbe9f2456) and ran the selection process, producing the following (including only the first few lines, with the hashes truncated for formatting reasons):¶
002ed527ae0a44a86c205d1cdba... lavenderblush 03f710be2b61a6f9c3f89aa5ab5... blue 08bab81380d7f0769cecf9969a8... darkgoldenrod 0c26494fa81f3aed8a9f66e77b7... mediumvioletred 0e1af5d1ccfd44de075cc0bb6d5... bisque 13a07cc9abf3b737e49a62b0634... lightpink¶
As blue was disqualified by prior agreement, the allocation was: walls "lavenderblush", doors "darkgoldenrod", and trim "mediumvioletred". However, upon an attempt to acquire the "lavenderblush" paint, the supplier was unable to source enough to cover the needed area; a substitute was needed.¶
The facilitator revealed the output of the 8th hash iteration (2f70f884997ce80771adbefbbbc6c71a1b921da71896c25ca0f64966bfd0c8ce), producing a new list of selections as follows:¶
00d1c59a9f1b581060a9e732e91... aqua 02b514b0b1807bfe086db524f40... darkgray 0337add95eac62a356b020a273a... cornflowerblue¶
The first option of "aqua" was selected for use on the walls. Concerns were raised about "aqua" being basically blue and that it should have been disqualified instead of "cyan", but the outcome of the process was not in dispute as the qualified colors were very clearly specified as part of the agreed process and that process had been strictly adhered to.¶
Only murmurs about the paint supplier's familial relationship with the facilitator would mean that the color scheme did not last long, though maybe that was a consquence of strident complaints from the neighbors.¶
This document describes an alternative process to that described in RFC 3797 [RFC3797]. It makes no effort to replace RFC 3797, however it is worth noting certain key differences.¶
This process allows for more rapid substitution through the use of a one-time code.¶
This process is marginally more robust against the inclusion of disqualified options. The process in RFC 3797 critically depends on the number of options being known. See Section 5.1 of [RFC3797] recommends that any option found to be invalid remains in the list once the list is fixed. This is because RFC 3797 selects from an ordered list by calculating an index from its PRF output, modulo the number of remaining options.¶
In comparison, this process sorts the output of its PRF, with each output being dependent only on the public randomness, the one-time code, and the label for the option. For the process in this document, only labels need to be fixed prior to learning the randomness, not the composition of the entire list of options. This makes it possible to add or remove options without affecting the ordering of other options, if those changes can be justified.¶
This process might be considered simpler than RFC 3797, even with the use of one-time codes for substitution.¶
The basic underlying idea here comes from Paul Hoffman. [RFC3797] and the one-time code idea are both the work of Donald Eastlake.¶