RFC 9523 | NTP Extention with Khronos | February 2024
Rozen-Schiff, et al. | Informational | [Page]

Stream:
  Internet Engineering Task Force (IETF)
RFC:
  9523
Category:
  Informational
Published:
  February 2024
ISSN:
  2070-1721
Authors:
  N. Rozen-Schiff
  Hebrew University of Jerusalem
  D. Dolev
  Hebrew University of Jerusalem
  T. Mizrahi
  Huawei Network.IO Innovation Lab
  M. Schapira
  Hebrew University of Jerusalem

# RFC 9523

# A Secure Selection and Filtering Mechanism for the Network Time Protocol with Khronos

## Abstract

The Network Time Protocol version 4 (NTPv4), as defined in RFC 5905, is the mechanism used by NTP clients to synchronize with NTP servers across the Internet. This document describes a companion application to the NTPv4 client, named "Khronos", that is used as a "watchdog" alongside NTPv4 and that provides improved security against time-shifting attacks. Khronos involves changes to the NTP client's system process only. Since it does not affect the wire protocol, the Khronos mechanism is applicable to current and future time protocols.¶

## Status of This Memo

This document is not an Internet Standards Track specification; it is published for informational purposes.¶

This document is a product of the Internet Engineering Task Force (IETF). It represents the consensus of the IETF community. It has received public review and has been approved for publication by the Internet Engineering Steering Group (IESG). Not all documents approved by the IESG are candidates for any level of Internet Standard; see Section 2 of RFC 7841.¶

Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at https://www.rfc-editor.org/info/rfc9523.¶

## Copyright Notice

Copyright (c) 2024 IETF Trust and the persons identified as the document authors. All rights reserved.¶

This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Revised BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Revised BSD License.¶

## 1. Introduction

NTPv4, as defined in [RFC5905], is vulnerable to time-shifting attacks in which the attacker changes (shifts) the clock of a network device. Time-shifting attacks on NTP clients can be based on interfering with the communication between the NTP clients and servers or compromising the servers themselves. Time-shifting attacks on NTP are possible even if NTP communication is encrypted and authenticated. A weaker machine-in-the-middle (MITM) attacker can shift time simply by dropping or delaying packets, whereas a powerful attacker that has full control over an NTP server can do so by explicitly determining the NTP response content. This document introduces a time-shifting mitigation mechanism called "Khronos". Khronos can be integrated as a background-monitoring application (watchdog) that guards against time-shifting attacks in any NTP client. An NTP client that runs Khronos is interoperable with NTPv4 servers that are compatible with [RFC5905]. The Khronos mechanism does not affect the wire mechanism; therefore, it is applicable to any current or future time protocol.¶

Khronos is a mechanism that runs in the background, continuously monitoring the client clock (which is updated by NTPv4) and calculating an estimated offset (referred to as the "Khronos time offset"). When the offset exceeds a predefined threshold (specified in Section 5.2), this is interpreted as the client experiencing a time-shifting attack. In this case, Khronos updates the client's clock.¶

When the client is not under attack, Khronos is passive. This allows NTPv4 to control the client's clock and provides the ordinary high precision and accuracy of NTPv4. When under attack, Khronos takes control of the client's clock, mitigating the time shift while guaranteeing relatively high accuracy with respect to UTC and precision, as discussed in Section 7.¶

By leveraging techniques from distributed computing theory for time synchronization, Khronos achieves accurate time even in the presence of powerful attackers who are in direct control of a large number of NTP servers. Khronos will prevent shifting the clock when the ratio of compromised time samples is below 2/3. In each polling interval, a Khronos client randomly selects and samples a few NTP servers out of a local pool of hundreds of servers. Khronos is carefully engineered to minimize the load on NTP servers and the communication overhead. In contrast, NTPv4 employs an algorithm that typically relies on a small subset of the NTP server pool (e.g., four servers) for time synchronization and is much more vulnerable to time-shifting attacks. Configuring NTPv4 to use several hundreds of servers will increase its security, but will incur very high network and computational overhead compared to Khronos and will be bounded by a compromised ratio of half of the time samples.¶

A Khronos client iteratively "crowdsources" time queries across NTP servers and applies a provably secure algorithm for eliminating "suspicious" responses and for averaging over the remaining responses. In each Khronos poll interval, the Khronos client selects, uniformly at random, a small subset (e.g., 10-15 servers) of a large server pool (containing hundreds of servers). While Khronos queries around three times more servers per polling interval than NTP, Khronos's polling interval can be longer (e.g., 10 times longer) than NTPv4, thereby minimizing the load on NTP servers and the communication overhead. Moreover, Khronos's random server selection may even help to distribute queries across the whole pool.¶

Khronos's security was evaluated both theoretically and experimentally with a prototype implementation. According to this security analysis, if a local Khronos pool consists of, for example, 500 servers, one-seventh of whom are controlled by an attacker and Khronos queries 15 servers in each Khronos poll interval (around 10 times the NTPv4 poll interval), then over 20 years of effort are required (in expectation) to successfully shift time at a Khronos client by over 100 ms from UTC. The full exposition of the formal analysis of this guarantee is available at [Khronos].¶

Khronos maintains a time offset value (the Khronos time offset) and uses it as a reference for detecting attacks. This time offset value computation differs from the current NTPv4 in two key aspects:¶

- First, in each Khronos poll interval, Khronos periodically communicates with only a few (tens) randomly selected servers out of a pool consisting of a large number (e.g., hundreds) of NTP servers.¶
- Second, Khronos computes the Khronos time offset based on an approximate agreement technique to remove outliers, thus limiting the attacker's ability to contaminate the time samples (offsets) derived from the queried NTP servers.¶

These two aspects allow Khronos to minimize the load on the NTP servers and to provide provable security guarantees against both MITM attackers and attackers capable of compromising a large number of NTP servers.¶

We note that, to some extent, Network Time Security (NTS) [RFC8915] could make it more challenging for attackers to perform MITM attacks, but is of little impact if the servers themselves are compromised.¶

## 2. Conventions Used in This Document

### 2.1. Terms and Abbreviations

NTPv4:
  Network Time Protocol version 4. See [RFC5905].¶
System process:
  See the "Selection Algorithm" and the "Cluster Algorithm" sections of [RFC5905].¶
Security Requirements:
  See "Security Requirements of Time Protocols in Packet Switched Networks" [RFC7384].¶
NTS:
  Network Time Security. See "Network Time Security for the Network Time Protocol" [RFC8915].¶

### 2.2. Notations

When describing the Khronos algorithm, the following notation is used:¶

Table 1: Khronos Notation
Notation | Meaning
--- | ---
n | The number of candidate servers in a Khronos pool (potentially hundreds).
m | The number of servers that Khronos queries in each poll interval (up to tens).
w | An upper bound on the distance between any "truechimer" NTP server (as in [RFC5905]) and UTC.
B | An upper bound on the client's clock error rate (ms/sec).
ERR | An upper bound on the client's clock error between Khronos polls (ms).
K | The number of Khronos pool resamplings until reaching "panic mode".
H | Predefined threshold for a Khronos time offset triggering clock update by Khronos.

The recommended values are discussed in Section 3.3.¶

## 3. Khronos Design

Khronos periodically queries a set of m (tens) servers from a large (hundreds) server pool in each Khronos poll interval, where the m servers are selected from the server pool at random. Based on empirical analyses, to minimize the load on NTP servers while providing high security, the Khronos poll interval should be around 10 times the NTPv4 poll interval (i.e., a Khronos clock update occurs once every 10 NTPv4 clock updates). In each Khronos poll interval, if the Khronos time offset exceeds a predetermined threshold (denoted as H), an attack is indicated.¶

Unless an attack is indicated, Khronos uses only one sample from each server (avoiding the "Clock Filter Algorithm" as defined in Section 10 of [RFC5905]). When under attack, Khronos uses several samples from each server and executes the "Clock Filter Algorithm" for choosing the best sample from each server with low jitter. Then, given a sample from each server, Khronos discards outliers by executing the procedure described in Section 3.2.¶

Between consecutive Khronos polls, Khronos keeps track of clock offsets, e.g., by catching clock discipline (as in [RFC5905]) calls. The sum of offsets is referred to as the "Khronos inter-poll offset" (denoted as tk), which is set to zero after each Khronos poll.¶

### 3.1. Khronos Calibration - Gathering the Khronos Pool

Calibration is performed the first time Khronos is executed and periodically thereafter (once every two weeks). The calibration process generates a local Khronos pool of n (up to hundreds) NTP servers that the client can synchronize with. To this end, Khronos makes multiple DNS queries to the NTP pools. Each query returns a few NTP server IPs that Khronos combines into one set of IPs considered as the Khronos pool. The servers in the Khronos pool should be scattered across different regions to make it harder for an attacker to compromise or gain MITM capabilities with respect to a large fraction of the Khronos pool. Therefore, Khronos calibration queries general NTP server pools (e.g., pool.ntp.org) and not just the pool in the client's state or region. In addition, servers can be selected to be part of the Khronos pool manually or by using other NTP pools (such as NIST Internet time servers).¶

The first Khronos update requires m servers, which can be found in several minutes. Moreover, it is possible to query several DNS pool names to vastly accelerate the calibration and the first update.¶

The calibration is the only Khronos part where DNS traffic is generated. Around 125 DNS queries are required by Khronos to obtain addresses of 500 NTP servers, which is higher than Khronos pool size (n). Assuming the calibration period is two weeks, the expected DNS traffic generated by the Khronos client is less than 10 DNS queries per day, which is usually several orders of magnitude lower than the total daily number of DNS queries per machine.¶

### 3.2. Khronos's Poll and System Processes

In each Khronos poll interval, the Khronos system process randomly chooses a set of m (tens) servers out of the Khronos pool of n (hundreds) servers and samples them. Note that the randomness of the server selection is crucial for the security of the scheme; therefore, any Khronos implementation must use a secure randomness implementation such as what is used for encryption key generation.¶

Khronos's polling times of different servers may spread uniformly within its poll interval, which is similar to NTPv4. Servers that do not respond during the Khronos poll interval are filtered out. If less than one-third of the m servers are left, a new subset of servers is immediately sampled in the exact same manner (which is called the "resampling" process).¶

Next, out of the time samples received from this chosen subset of servers, the lowest third of the samples' offset values and the highest third of the samples' offset values are discarded.¶

Khronos checks that the following two conditions hold for the remaining sampled offsets (considering w and ERR defined in Table 1):¶

- The maximal distance between every two offsets does not exceed 2w (can be verified by considering just the minimum and the maximum offsets).¶
- The distance between the offset's average and the Khronos inter-poll offset is ERR+2w at most.¶

In the event that both of these conditions are satisfied, the average of the offsets is set to be the Khronos time offset. Otherwise, resampling is performed. This process spreads the Khronos client's queries across servers, thereby improving security against powerful attackers (as discussed in Section 5.3) and mitigating the effect of a DoS attack on NTP servers that renders them non-responsive. This resampling process continues in subsequent Khronos poll intervals until the two conditions are both satisfied or the number of times the servers are resampled exceeds a "panic trigger" (K in Table 1). In this case, Khronos enters panic mode.¶

In panic mode, Khronos queries all the servers in its local Khronos pool, orders the collected time samples from lowest to highest, and eliminates the lowest third and the highest third of the samples. The client then calculates the average of the remaining samples and sets this average to be the new Khronos time offset.¶

If the Khronos time offset exceeds a predetermined threshold (H), it is passed on to the clock discipline algorithm in order to steer the system time (as in [RFC5905]). In this case, the user and/or admin of the client machine should be notified about the detected time-shifting attack, e.g., by a message written to a relevant event log or displayed on screen.¶

Note that resampling immediately follows the previous sampling since waiting until the next polling interval may increase the time shift in face of an attack. This shouldn't generate high overhead since the number of resamples is bounded by K (after K resamplings, panic mode is in place) and the chances of ending up with repeated resampling are low (see Section 5 for more details). Moreover, in an interval following a panic mode, Khronos executes the same system process that starts by querying only m servers (regardless of previous panic).¶

### 3.3. Khronos's Recommended Parameters

According to empirical observations (presented in [Khronos]), querying 15 servers at each poll interval (i.e., m=15) out of 500 servers (i.e., n=500) and setting w to be around 25 ms provides both high time accuracy and good security. Specifically, when selecting w=25 ms, approximately 83% of the servers' clocks are, at most, w away from UTC and within 2w from each other, satisfying the first condition of Khronos's system process. For a similar reason, the threshold for a Khronos time offset triggering a clock update by Khronos (H) should be between w and 2w; the default is 30 ms. Note that in order to support scenarios with congested links, using a higher w value, such as 1 second, is recommended.¶

Furthermore, according to Khronos security analysis, setting K to be 3 (i.e., if the two conditions are not satisfied after three resamplings, then Khronos enters panic mode) is safe when facing time-shifting attacks. In addition, the probability of an attacker forcing a panic mode on a client when K=3 is negligible (less than 0.000002 for each polling interval).¶

Khronos's effect on precision and accuracy are discussed in Sections 5 and 7.¶

## 4. Operational Considerations

Khronos is designed to defend NTP clients from time-shifting attacks while using public NTP servers. As such, Khronos is not applicable for data centers and enterprises that synchronize with local atomic clocks, GPS devices, or a dedicated NTP server (e.g., due to regulations).¶

Khronos can be used for devices that require and depend upon timekeeping within a configurable constant distance from UTC.¶

### 4.1. Load Considerations

One requirement from Khronos is not to induce excessive load on NTP servers beyond that of NTPv4, even if it is widely integrated into NTP clients. We discuss below the possible causes for a Khronos-induced load on servers and how this can be mitigated.¶

Servers in pool.ntp.org are weighted differently by the NTP server pool when assigned to NTP clients. Specifically, server owners define a "server weight" (the "netspeed" parameter) and servers are assigned to clients probabilistically according to their proportional weight. Khronos's queries are equally distributed across a pool of servers. To avoid overloading servers, Khronos queries servers less frequently than NTPv4, with the Khronos query interval set to 10 times the default NTPv4 maxpoll (interval) parameter. Hence, if Khronos queries are targeted at servers in pool.ntp.org, any target increase in server load (in terms of multiplicative increase in queries or number of bytes per second) is controlled by the poll interval configuration, which was analyzed in [Ananke].¶

Consider the scenario where an attacker attempts to generate significant load on NTP servers by triggering multiple consecutive panic modes at multiple NTP clients. We note that to accomplish this, the attacker must have MITM capabilities with respect to the communication between each and every client in a large group of clients and a large fraction of all NTP servers in the queried pool. This implies that the attacker must either be physically located at a central location (e.g., at the egress of a large ISP) or launch a wide-scale attack (e.g., on BGP or DNS); thereby, it is capable of carrying similar and even higher impact attacks regardless of Khronos clients.¶

## 5. Security Considerations

### 5.1. Threat Model

The threat model encompasses a broad spectrum of attackers impacting a subset (e.g., one-third) of the servers in NTP pools. These attackers can range from a fairly weak (yet dangerous) MITM attacker that is only capable of delaying and dropping packets (e.g., using the Bufferbloat attack [RFC8033]) to an extremely powerful attacker who is in control of (even authenticated) NTP servers and is capable of fully determining the values of the time samples returned by these NTP servers (see detailed attacker discussion in [RFC7384]).¶

For example, the attackers covered by this model might be:¶

1. in direct control of a fraction of the NTP servers (e.g., by exploiting a software vulnerability),¶
2. an ISP (or other attacker at the Autonomous System level) on the default BGP paths from the NTP client to a fraction of the available servers,¶
3. a nation state with authority over the owners of NTP servers in its jurisdiction, or¶
4. an attacker capable of hijacking (e.g., through DNS cache poisoning or BGP prefix hijacking) traffic to some of the available NTP servers.¶

The details of the specific attack scenario are abstracted by reasoning about attackers in terms of the fraction of servers with respect to which the attacker has adversarial capabilities. Attackers that can impact communications with (or control) a higher fraction of the servers (e.g., all servers) are out of scope. Considering the pool size across the world to be in the thousands, such attackers will most likely be capable of creating far worse damage than time-shifting attacks.¶

Notably, Khronos provides protection from MITM and powerful attacks that cannot be achieved by cryptographic authentication protocols since, even with such measures in place, an attacker can still influence time by dropping/delaying packets. However, adding an authentication layer (e.g., NTS [RFC8915]) to Khronos will enhance its security guarantees and enable the detection of various spoofing and modification attacks.¶

Moreover, Khronos uses randomness to independently select the queried servers in each poll interval, preventing attackers from exploiting observations of past server selections.¶

### 5.2. Attack Detection

Khronos detects time-shifting attacks by constantly monitoring NTPv4's (or potentially any other current or future time protocol) clock and the offset computed by Khronos and checking whether the offset exceeds a predetermined threshold (H). NTPv4 controls the client's clock unless an attack was detected. Under attack, Khronos takes control over the client's clock in order to prevent its shift.¶

Analytical results (in [Khronos]) indicate that if a local Khronos pool consists of 500 servers, one-seventh of whom are controlled by a MITM attacker, and 15 of those servers are queried in each Khronos poll interval, then success in shifting time of a Khronos client by even a small degree (100 ms) takes many years of effort (over 20 years in expectation). See a brief overview of Khronos's security analysis below.¶

### 5.3. Security Analysis Overview

Time samples that are at most w away from UTC are considered "good", whereas other samples are considered "malicious". Two scenarios are considered:¶

- Scenario A: Less than two-thirds of the queried servers are under the attacker's control.¶
- Scenario B: The attacker controls more than two-thirds of the queried servers.¶

Scenario A consists of two sub-cases:¶

1. There is at least one good sample in the set of samples not eliminated by Khronos (in the middle third of samples), and¶
2. there are no good samples in the remaining set of samples.¶

In sub-case 1, the other remaining samples, including those provided by the attacker, must be close to a good sample (otherwise, the first condition of Khronos's system process in Section 3.2 is violated and a new set of servers is chosen). This implies that the average of the remaining samples must be close to UTC.¶

In sub-case 2, since more than a third of the initial samples were good, both the (discarded) third-lowest-value samples and the (discarded) third-highest-value samples must each contain a good sample. Hence, all the remaining samples are bounded from both above and below by good samples, and so is their average value, implying that this value is close to UTC [RFC5905].¶

In Scenario B, the worst possibility for the client is that all remaining samples are malicious (i.e., more than w away from UTC). However, as proved in [Khronos], the probability of this scenario is extremely low, even if the attacker controls a large fraction (e.g., one-fourth) of the n servers in the local Khronos pool. Therefore, the probability that the attacker repeatedly reaches this scenario decreases exponentially, rendering the probability of a significant time shift negligible. We can express the improvement ratio of Khronos over NTPv4 by the ratios of their single-shift probabilities. Such ratios are provided in Table 2, where higher values indicate higher improvement of Khronos over NTPv4 and are also proportional to the expected time until a time-shift attack succeeds once.¶

Table 2: Khronos Improvement
Attack Ratio | 6 Samples | 12 Samples | 18 Samples | 24 Samples | 30 Samples
--- | --- | --- | --- | --- | ---
1/3 | 1.93e+01 | 3.85e+02 | 7.66e+03 | 1.52e+05 | 3.03e+06
1/5 | 1.25e+01 | 1.59e+02 | 2.01e+03 | 2.54e+04 | 3.22e+05
1/7 | 1.13e+01 | 1.29e+02 | 1.47e+03 | 1.67e+04 | 1.90e+05
1/9 | 8.54e+00 | 7.32e+01 | 6.25e+02 | 5.32e+03 | 4.52e+04
1/10 | 5.83e+00 | 3.34e+01 | 1.89e+02 | 1.07e+03 | 6.04e+03
1/15 | 3.21e+00 | 9.57e+00 | 2.79e+01 | 8.05e+01 | 2.31e+02

In addition to evaluating the probability of an attacker successfully shifting time at the client's clock, we also evaluated the probability that the attacker succeeds in launching a DoS attack on the servers by causing many clients to enter panic mode (and querying all the servers in their local Khronos pools). This probability (with the previous parameters of n=500, m=15, w=25, and K=3) is negligible even for an attacker who controls a large number of servers in clients' local Khronos pools, and it is expected to take decades to force a panic mode.¶

Further details about Khronos's security guarantees can be found in [Khronos].¶

## 6. Khronos Pseudocode

The pseudocode for Khronos Time Sampling Scheme, which is invoked in each Khronos poll interval, is as follows:¶

    counter = 0
    S = []
    T = []
    While counter < K do
       S = sample(m) //get samples from (tens of) randomly chosen servers
       T = bi_side_trim(S,1/3) //trim lowest and highest thirds
       if (max(T) - min(T) <= 2w) and (|avg(T) - tk| < ERR + 2w), then
           return avg(T) // Normal case
       end
       counter ++
    end
    // panic mode
    S = sample(n)
    T = bi-sided-trim(S,1/3) //trim lowest and highest thirds
    return avg(T)

¶

Note that if clock disciplines can be called during this pseudocode's execution, then each time offset sample, as well as the final output (Khronos time offset), should be normalized with the sum of the clock disciplines offsets (tk) at the time of computing it.¶

## 7. Precision vs. Security

Since NTPv4 updates the clock at times when no time-shifting attacks are detected, the precision and accuracy of a Khronos client are the same as NTPv4 at these times. Khronos is proved to maintain an accurate estimation of the UTC with high probability. Therefore, when Khronos detects that client's clock error exceeds a threshold (H), it considers it to be an attack and takes control over the client's clock. As a result, the time shift is mitigated and high accuracy is guaranteed (the error is bounded by H).¶

Khronos is based on crowdsourcing across servers and regions, changes the set of queried servers more frequently than NTPv4 [Khronos], and avoids some of the filters in NTPv4's system process. These factors can potentially harm its precision. Therefore, a smoothing mechanism can be used where instead of a simple average of the remaining samples, the smallest (in absolute value) offset is used unless its distance from the average is higher than a predefined value. Preliminary experiments demonstrated promising results with precision similar to NTPv4.¶

In applications such as multi-source media streaming, which are highly sensitive to time differences among hosts, note that it is advisable to use Khronos at all hosts in order to obtain high precision, even in the presence of attackers that try to shift each host in a different magnitude and/or direction. Another approach that is more efficient for these cases may be to allow direct time synchronization between one host who runs Khronos to others.¶

## 8. IANA Considerations

This document has no IANA actions.¶

## 9. References

### 9.1. Normative References

[RFC5905]
  Mills, D., Martin, J., Ed., Burbank, J., and W. Kasch, "Network Time Protocol Version 4: Protocol and Algorithms Specification", RFC 5905, DOI 10.17487/RFC5905, June 2010, <https://www.rfc-editor.org/info/rfc5905>.
[RFC7384]
  Mizrahi, T., "Security Requirements of Time Protocols in Packet Switched Networks", RFC 7384, DOI 10.17487/RFC7384, October 2014, <https://www.rfc-editor.org/info/rfc7384>.
[RFC8033]
  Pan, R., Natarajan, P., Baker, F., and G. White, "Proportional Integral Controller Enhanced (PIE): A Lightweight Control Scheme to Address the Bufferbloat Problem", RFC 8033, DOI 10.17487/RFC8033, February 2017, <https://www.rfc-editor.org/info/rfc8033>.
[RFC8915]
  Franke, D., Sibold, D., Teichel, K., Dansarie, M., and R. Sundblad, "Network Time Security for the Network Time Protocol", RFC 8915, DOI 10.17487/RFC8915, September 2020, <https://www.rfc-editor.org/info/rfc8915>.

### 9.2. Informative References

[Ananke]
  Perry, Y., Rozen-Schiff, N., and M. Schapira, "A Devil of a Time: How Vulnerable is NTP to Malicious Timeservers?", Network and Distributed Systems Security (NDSS) Symposium, Virtual, DOI 10.14722/ndss.2021.24302, February 2021, <https://www.ndss-symposium.org/wp-content/uploads/ndss2021_1A-2_24302_paper.pdf>.
[Khronos]
  Deutsch, O., Rozen-Schiff, N., Dolev, D., and M. Schapira, "Preventing (Network) Time Travel with Chronos", Network and Distributed Systems Security (NDSS) Symposium, San Diego, CA, USA, DOI 10.14722/ndss.2018.23231, February 2018, <https://www.ndss-symposium.org/wp-content/uploads/2018/02/ndss2018_02A-2_Deutsch_paper.pdf>.

## Acknowledgements

The authors would like to thank Erik Kline, Miroslav Lichvar, Danny Mayer, Karen O'Donoghue, Dieter Sibold, Yaakov (J) Stein, Harlan Stenn, Hal Murray, Marcus Dansarie, Geoff Huston, Roni Even, Benjamin Schwartz, Tommy Pauly, Rob Sayre, Dave Hart, and Ask Bjorn Hansen for valuable contributions to this document and helpful discussions and comments.¶

## Authors' Addresses