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Network Working Group                                    P. Hallam-Baker
Internet-Draft                                             April 4, 2019
Intended status: Informational
Expires: October 6, 2019


               Mathematical Mesh Part VI: The Trust Mesh
                    draft-hallambaker-mesh-trust-01

Abstract

   This paper extends Shannon's concept of a 'work factor' as applied to
   evaluation of cryptographic algorithms to provide an objective
   measure of the practical security offered by a protocol or
   infrastructure design.  Considering the hypothetical work factor
   based on an informed estimate of the probable capabilities of an
   attacker with unknown resources provides a better indication of the
   relative strength of protocol designs than the computational work
   factor of the best-known attack.

   The social work factor is a measure of the trustworthiness of a
   credential issued in a PKI based on the cost of having obtained the
   credential through fraud at a certain point in time.  Use of the
   social work factor allows evaluation of Certificate Authority based
   trust models and peer to peer (Web of Trust) models to be evaluated
   in the same framework.  The analysis demonstrates that both
   approaches have limitations and that in certain applications, a
   blended model is superior to either by itself.

   The final section of the paper describes a proposal to realize this
   blended model using the Mathematical Mesh.

   This document is also available online at
   http://mathmesh.com/Documents/draft-hallambaker-mesh-trust.html [1] .

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any




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

   This Internet-Draft will expire on October 6, 2019.

Copyright Notice

   Copyright (c) 2019 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
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Table of Contents

   1.  Work Factor . . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Computational Work Factor . . . . . . . . . . . . . . . .   3
     1.2.  Hypothetical Work Factor  . . . . . . . . . . . . . . . .   4
     1.3.  Known Unknowns  . . . . . . . . . . . . . . . . . . . . .   5
     1.4.  Defense in Depth  . . . . . . . . . . . . . . . . . . . .   6
     1.5.  Mutual Reinforcement  . . . . . . . . . . . . . . . . . .   7
     1.6.  Safety in Numbers . . . . . . . . . . . . . . . . . . . .   8
     1.7.  Cost Factor . . . . . . . . . . . . . . . . . . . . . . .  10
     1.8.  Social Work Factor  . . . . . . . . . . . . . . . . . . .  12
       1.8.1.  Related work  . . . . . . . . . . . . . . . . . . . .  14
   2.  The problem of trust  . . . . . . . . . . . . . . . . . . . .  14
     2.1.  Existing approaches . . . . . . . . . . . . . . . . . . .  15
       2.1.1.  Trust After First Use (TAFU)  . . . . . . . . . . . .  15
       2.1.2.  Direct Trust  . . . . . . . . . . . . . . . . . . . .  16
       2.1.3.  Certificate Authority . . . . . . . . . . . . . . . .  16
       2.1.4.  Web of Trust  . . . . . . . . . . . . . . . . . . . .  17
       2.1.5.  Chained notary  . . . . . . . . . . . . . . . . . . .  18
       2.1.6.  A blended approach  . . . . . . . . . . . . . . . . .  19
   3.  The Mesh of Trust . . . . . . . . . . . . . . . . . . . . . .  21
     3.1.  Master Profile  . . . . . . . . . . . . . . . . . . . . .  21
     3.2.  Uniform Data Fingerprints . . . . . . . . . . . . . . . .  21
     3.3.  Strong Internet Names . . . . . . . . . . . . . . . . . .  22
     3.4.  Trust notary  . . . . . . . . . . . . . . . . . . . . . .  23
     3.5.  Endorsement . . . . . . . . . . . . . . . . . . . . . . .  23
     3.6.  Evaluating trust  . . . . . . . . . . . . . . . . . . . .  23
   4.  Conclusions . . . . . . . . . . . . . . . . . . . . . . . . .  24



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   5.  Security Considerations . . . . . . . . . . . . . . . . . . .  24
   6.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  24
     6.1.  Normative References  . . . . . . . . . . . . . . . . . .  24
     6.2.  Informative References  . . . . . . . . . . . . . . . . .  24
     6.3.  URIs  . . . . . . . . . . . . . . . . . . . . . . . . . .  25
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  26

1.  Work Factor

   Recent events have highlighted both the need for open standards-based
   security protocols and the possibility that the design of such
   protocols may have been sabotaged [Schneier2013] . We thus face two
   important and difficult challenges, first to design an Internet
   security infrastructure that offers practical security against the
   class of attacks revealed, and secondly, to convince potential users
   that the proposed new infrastructure has not been similarly
   sabotaged.

   The measure of a security of a system is the cost and difficulty of
   making a successful attack.  The security of a safe is measured by
   the length time it is expected to resist attack using a specified set
   of techniques.  The security of a cryptographic algorithm against a
   known attack is measured by the computational cost of the attack.

   This paper extends Shannon's concept of a 'work factor' [Shannon1949]
   to provide an objective measure of the security a protocol or
   infrastructure offers against other forms of attack.

1.1.  Computational Work Factor

   The term 'Computational Work Factor' is used to refer to Shannon's
   original concept.

   One of Shannon's key insights was that the work factor of a
   cryptographic algorithm could be exponential.  Adding a single bit to
   the key size of an ideal symmetric algorithm presents only a modest
   increase in computational effort for the defender but doubles the
   work factor for the attacker.

   More precisely, the difficulty of breaking a cryptographic algorithm
   is generally measured by the work-factor ratio.  If the cost of
   encrypting a block with 56-bit DES is x, the worst case cost of
   recovering the key through a brute force attack is 2^56x.  The
   security of DES has changed over time because x has fallen
   exponentially.

   While the work factor is traditionally measured in terms of the
   number of operations, many cryptanalytic techniques permit memory



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   used to be traded for computational complexity.  An attack requiring
   2^64 bytes of memory that reduces the number of operations required
   to break a 128 bit cipher to 2^64 is a rather lower concern than one
   which reduces the number of operations to 2^80.  The term 'cost' is
   used to gloss over such distinctions.

   The Computational Work Factor ratio WF-C (A) of a cryptographic
   algorithm A, is the cost of the best-known attack divided by the cost
   of the algorithm itself.

1.2.  Hypothetical Work Factor

   Modern cryptographic algorithms use keys of 128 bits or more and
   present a work factor ratio of 2^128 against brute force attack.
   This work factor is at least 2^72 times higher than DES and
   comfortably higher than the work factor of 2^80 operations that is
   generally believed to be the practical limit to current attacks.

   Though Moore's law has delivered exponential improvements in
   computing performance over the past four decades, this has been
   achieved through continual reductions in the minimum feature size of
   VLSI circuits.  As the minimum feature size rapidly approaches the
   size of individual atoms, this mechanism has already begun to stall
   [Intel2018] .

   While an exceptionally well-resourced attacker may gain performance
   advances through use of massive parallelism, faster clock rates made
   possible by operating at super-low temperatures and custom designed
   circuits, the return on such approaches is incremental rather than
   exponential.

   Performance improvements may allow an attacker to break systems with
   a work factor several orders of magnitude greater than the public
   state of the art.  But an advance in cryptanalysis might permit a
   potentially more significant reduction in the work factor.

   The primary consideration in the choice of a cryptographic algorithm
   therefore is not the known computational work factor as measured
   according to the best publicly known attack but the confidence that
   the computational work factor of the best attack that might be known
   to the attacker.

   While the exact capabilities of the adversary are unknown, a group of
   informed experts may arrive at a conservative estimate of their
   likely capabilities.  In particular, it is the capabilities of
   nation-state actors that generally give rise to greatest concern in
   security protocol design.  In this paper we refer to this set of
   actors as nation-state class adversaries in recognition of the fact



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   that certain technology companies posses computing capabilities that
   rival if not exceed those of the largest state actors and those
   capabilities could at least in theory be co-opted for other purposes
   in certain circumstances.

   The probability that a nation-state class has discovered an attack
   against AES-128 with a work factor ratio of 2^120 might be considered
   relatively high while the probability that an attack with a work
   factor ratio of less than 2^64 is very low.

   We define the hypothetical work factor function WF-H (A, p) as
   follows: If WF is a work factor ratio and p is an informed estimate
   of the probability that an adversary has developed an attack with a
   work factor ratio against algorithm A of WF or less then WF-H (A, p)
   = WF.

   Since the best-known public attack is known to the attacker, WF-H (A,
   1) = _CWF (A)

   The inverse function WF-H' (A, WF) returns the estimated probability
   that the work factor of algorithm A is at least WF.

   The hypothetical work factor and its inverse may be used to compare
   the relative strengths of protocol designs.  Given designs A and B,
   we can state that B is an improvement on A if WF-H (A,p) > WF-H (B,p)
   for all p.

   When considering a protocol or infrastructure design we can thus
   improve a protocol by either:

   o  Increasing WF-H (A,p) for some p, or

   o  Decreasing WF-H '(A,WF)

1.3.  Known Unknowns

   Unlike the computational work factor, the hypothetical work factor
   does not provide an objective measure of the security offered by a
   design.  The purpose of the hypothetical work factor is to allow the
   protocol designer to compare the security offered by different design
   choices.

   The task that the security engineer faces is to secure the system
   from all attacks whether the attacks themselves are known or unknown.
   In the current case it is known that an attacker is capable of
   breaking at least some of the cryptographic algorithms in use.  But
   not which algorithms are affected or the nature of the attack(s).




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   Unlike the computational work factor, the hypothetical work factor
   does not deliver an academically rigorous, publication and citation
   worthy measure of the strength of a design.  That is not its purpose.
   the purpose of the hypothetical work factor is to assist the protocol
   designer in designing protocols.

   Design of security protocols has always required the designer to
   consider attackers whose capabilities are not currently known and
   thus involved a considerable degree of informed opinion and
   guesswork.  Whether correctly or not, the decision to reject changes
   to the DNSSEC protocol to enable deployment in 2002 rested in part on
   a statement by a Security Area Director that a proposed change gave
   him 'a bad feeling in his gut'.  The hypothetical work factor permits
   the security designer to model to quantify such intestinally based
   assumptions and model the effect on the security of the resulting
   design.

   Security is a property of systems rather than individual components.
   While it is quite possible that there are no royal roads to
   cryptanalysis and cryptanalysis of algorithms such as AES 128 is
   infeasible even for the nation state class adversaries, such
   adversaries are not limited to use of cryptanalytic attacks.

   Despite the rise of organized cyber-crime, many financial systems
   still employ weak cryptographic systems that are known to be
   vulnerable to cryptanalytic attacks that are well within the
   capabilities of the attackers.  But fraud based on such techniques
   remains vanishingly rare as it is much easier for the attackers to
   persuade bank customers to simply give their access credentials to
   the attacker.

   Even if a nation-state class attacker has a factoring attack which
   renders an attack on RSA-2048 feasible, it is almost certainly easier
   for a nation-state class attacker to compromise a system using
   RSA-2048 in other ways.  For example, persuading the target of the
   surveillance to use cryptographic devices with a random number
   generator that leaks a crib for the attacker.  Analyzing the second
   form of attack requires a different type of analysis which is
   addressed in the following section on social work factor.

1.4.  Defense in Depth

   The motivation behind introducing the concept of the hypothetical
   work factor is a long experience of seeing attempts to make security
   protocols more robust being deflected by recourse to specious
   arguments based on the computational work factor.





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   For example, consider the case in which a choice between a single
   security control and a defense in depth strategy is being considered:

   o  Option A: Uses algorithm X for protection.

   o  Option B: Uses a combination of algorithm X and algorithm Y for
      protection such that the attacker must defeat both to break the
      system and algorithms based on different cryptographic principles
      are chosen so as to minimize the risk of a common failure mode.

   If the computational work factor for both algorithms X and Y is
   2^128, both options present the same work factor ratio.  Although
   Option B offers twice the security, it also requires twice the work.

   The argument that normally wins is that both options present the same
   computational work factor ratio of 2^128, Option A is simpler and
   therefore Option A should be chosen.  This despite the obvious fact
   that only Option B offers defense in depth.

   If we consider the adversary of being capable of performing a work
   factor ratio of 2^80 and the probability the attacker has discovered
   an attack capable of breaking algorithms X and Y to be 10% in each
   case, the probability that the attacker can break Option A is 10%
   while the probability that an attack on Option B is only 1%, a
   significant improvement.

   While Option B clearly offers a significant potential improvement in
   security, this improvement is only fully realized if the
   probabilities of a feasible attack are independent.

1.5.  Mutual Reinforcement

   The defense in depth approach affords a significant improvement in
   security but an improvement that is incremental rather than
   exponential in character.  With mutual reinforcement we design the
   mechanism such that in addition to requiring the attacker to break
   each of the component algorithms, the difficulty of the attacks is
   increased.

   For example, consider the use of a Deterministic Random Number
   Generator R(s,n) which returns a sequence of values R(s,1), R(s,2)...
   from an initial seed s.

   Two major concerns in the design of such generators are the
   possibility of bias and that the seed value be somehow leaked through
   a side channel.





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   Both concerns are mitigated if instead of using the output of one
   generator directly, two independent random number generators with
   distinct seeds are used.

   For example, consider the use of the value R1(s1,n) XOR R2(s2,n)
   where R1(s,n) and R2(s,n) are different random number generation
   functions and s1, s2 are distinct seeds.

   The XOR function has the property of preserving randomness so that
   the output is guaranteed to be at least as random as either of the
   generators from which it is built (provided that there is not a
   common failure mode).  Further, recovery of either random seed is at
   least as hard as using the corresponding generator on its own.  Thus,
   the Hypothetical work factor for the combined system is improved to
   at least the same extent as in the defense in depth case.

   But any attempt to break either generator must now face the
   additional complexity introduced by the output being masked with the
   unknown output of the other.  An attacker cannot cryptanalyze the two
   generator functions independently.  If the two generators and the
   seeds are genuinely independent, the combined hypothetical work
   factor is the product of the hypothetical work factors from which it
   is built.

   While implementing two independent generators and seeds represents a
   significant increase in cost for the implementer, a similar
   exponential leverage might be realized with negligible additional
   complexity through use of a cryptographic digest of the generator
   output to produce the masking value.

1.6.  Safety in Numbers

   In a traditional security analysis, the question of concern is
   whether a cryptanalytic attack is feasible or not.  When considering
   an indiscriminate intercept capability as in a nation-state class
   attack, the concern is not just whether an individual communication
   might be compromised but the number of communications that may be
   compromised for a given amount of effort.

   'Perfect' Forward Secrecy is an optional feature supported in IPSec
   and TLS.  In 2008, implementations of TLS/1.2 [RFC6246] purported to
   offer a choice between:

   Direct key exchange with a work factor dependent on the difficulty of
   breaking RSA 2048






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   Direct key exchange followed by a perfect forward secrecy exchange
   with a work factor dependent on the difficulty of breaking both RSA
   2048 and DH 1024.

   Using the computational work factor alone suggests that the second
   scheme has little advantage over the first since the computational
   work factor of Diffie Hellman using the best-known techniques 2^80
   while the computational work factor for RSA 2048 is 2^112.  Use of
   the perfect forward secrecy exchange has a significant impact on
   server performance but does not increase the difficulty of
   cryptanalysis.

   Use of perfect forward secrecy with a combination of RSA and Diffie
   Hellman does not provide a significant improvement in the
   hypothetical work factor either if individual messages are
   considered.  The RSA and Diffie Hellman systems are closely related
   and so an attacker that can break RSA 2048 can almost certainly break
   RSA 1024.  Moreover, computational work factor for DH 1024 is only
   2^80 and thus feasibly within the reach of a well-funded and
   determined attacker.

   According to the analysis informally applied during design, use of
   perfect forward secrecy does provide an important security benefit
   when multiple messages are considered.  While a sufficiently funded
   and determined attacker could conceivably break tens, hundreds or
   even thousands of DH 1024 keys a year, it is rather less likely that
   an attacker could break millions a year.  The OCSP servers operated
   by Comodo CA receive over 2 billion hits a day and this represents
   only a fraction of the number of uses of TLS on the Internet.  Use of
   perfect forward secrecy does not prevent an attacker from decrypting
   any particular message but raises the cost of indiscriminate
   intercept and decryption.

   Unfortunately, this analysis is wrong because the TLS key exchange
   does not achieve a work factor dependent on the difficulty of
   breaking both RSA 2048 and DH 1024.  The pre-master secret
   established in the initial RSA 2048 exchange is only used to
   authenticate the key exchange process itself.  The session keys used
   to encrypt content are derived from the weaker ephemeral key
   exchange, the parameters of which are exchanged in plaintext.  Due to
   this defect in the design of the protocol, the Work Factor of the
   protocol is the work factor of DH1024 alone.

   Nor does the use of Diffie Hellman in this fashion provide security
   when multiple messages are exchanged.  The Logjam attack [Adrian2015]
   exploits the fact that the difficulty of breaking the discrete
   logarithm involves four major steps, the first three of which are the
   most computationally intensive and only depend on the shared group



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   parameters.  The cost of breaking a hundred Diffie Hellman public
   keys is not a hundred times the cost of breaking a single key, there
   is almost no difference.

   Work factor analysis exposes these flaws in the design of the
   TLS/1.2.  Since the session keys used to encrypt traffic do not
   depend on knowing the secret established in the RSA2048 exchange, the
   work factor of the protocol is the lesser of 2^80 and 2^112.

   A simple means of ensuring that the work factor of a protocol is not
   reduced by a fresh key exchange is to use a one-way function such as
   a cryptographic digest or a key exchange to combine the output of the
   prior exchange with its successor.  This principle is employed in the
   double ratchet algorithm [Ratchet] used in the Signal protocol.  In
   the Mesh, the HKDF Key Derivation function [RFC5869] is frequently
   used for the same purpose.

   The work factor downgrade issue was addressed in TLS/1.3 [RFC8446]
   albeit in a less direct fashion by encrypting the ephemeral key
   exchange.

1.7.  Cost Factor

   As previously discussed, cryptanalysis is not the only tool available
   to an attacker.  Faced with a robust cryptographic defense, Internet
   criminals have employed 'social engineering' instead.  A nation-state
   class attacker may use any and every tool at their disposal including
   tools that are unique to government backed adversaries such as the
   threat of legal sanctions against trusted intermediaries.

   Although attackers can and will use every tool at their disposal,
   each tool carries a cost and some tools require considerable advance
   planning to use.  It is conceivable that the AES standard published
   by NIST contains a backdoor that somehow escaped the extensive peer
   review.  But any such effort would have had to have begun well in
   advance of 1998 when the Rijndael cipher was first published.

   Nation-state class actors frequently rely for security on the same
   infrastructures that they are attempting to attack.  Thus, the
   introduction of vulnerabilities that might also be exploited by the
   opposition incurs a cost to both.  This concern is recognized in the
   NSA 'NOBUS' doctrine: Nobody but us.  To introduce a vulnerability in
   a random number generator that can only be exploited by a party that
   knows the necessary private key is acceptable.  But introducing a
   vulnerability that depends on the use of an unpublished cryptanalytic
   technique is not because that same technique might be discovered by
   the opposition.




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   Subversion of cryptographic apparatus such as Hardware Security
   Modules (HSMs) and SSL accelerators faces similar constraints.  HSMs
   may be compromised by an adversary but the compromise must have taken
   place before the device was manufactured or serviced.

   Just as computational attacks are limited by the cryptanalytic
   techniques known to and the computational resources available to the
   attacker, social attacks are limited by the cost of the attack and
   the capacity of the attacker.

   The Cost Factor C(t) is an estimate of the cost of performing an
   attack on or before a particular date in time (t).

   For the sake of simplicity, currency units are used under the
   assumption that all the resources required are fungible and that all
   attackers face the same costs.  But such assumptions may need to be
   reconsidered when there is a range of attackers with very different
   costs and capabilities.  A hacktivist group could not conceivably
   amass the computational and covert technical resources available to
   the NSA but such a group could in certain circumstances conceivably
   organize a protest with a million or more participants while the
   number of NSA employees is believed to still be somewhat fewer.

   The computational and hypothetical work factors are compared against
   estimates of the computational resources of the attacker.  An attack
   is considered to be infeasible if that available computational
   resources do not allow the attack to be performed within a useful
   period of time.

   The cost factor is likewise compared against an incentive estimate,
   I(t) which is also time based.

   o  An attack is considered to be productive for an attacker if there
      was a time t for which I(t) > C(t).

   o  An attack is considered to be unproductive if there is no time at
      which it was productive for that attacker.

   Unlike Cost Factor for which a lower bound based on the lowest cost
   and highest capacity may be usefully applied to all attackers,
   differences in the incentive estimate between attackers are likely to
   be very significant.  Almost every government has the means to
   perform financial fraud on a vast scale but only rarely does a
   government have the incentive.  When governments do engage in
   activities such as counterfeiting banknotes this has been done for
   motives beyond mere peculation.





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   While government actors do not respond to the same incentives as
   Internet criminals, governments fund espionage activities in the
   expectation of a return on their investment.  A government agency
   director who does not produce the desired returns is likely to be
   replaced.

   For example, when the viability of SSL and the Web PKI for protecting
   Internet payments was considered in the mid-1990s, the key question
   was whether the full cost of obtaining a fraudulently issued
   certificate would exceed the expected financial return where the full
   cost is understood to include the cost of registering a bogus
   corporation, submitting the documents and all the other activities
   that would be required if a sustainable model for payments fraud was
   to be established.

   For an attack to be attractive to an attacker it is not just
   necessary for it to be productive, the time between the initial
   investment and the reward and the likelihood of success are also
   important factors.  An attack that requires several years of advance
   planning is much less attractive than an attack which returns an
   immediate profit.

   An attack may be made less attractive by

   o  Increasing the cost

   o  Reducing the incentive

   o  Reducing the expected gain

   o  Reducing the probability that the incentive will be realized

   o  Increasing the time between the initial investment and the return.

   Most real-world security infrastructures are based on more than one
   of these approaches.  The WebPKI is designed to increase the cost of
   attack by introducing validation requirements and reduce the expected
   gain through its revocation infrastructure.

1.8.  Social Work Factor

   In the cost factor analysis, it is assumed that all costs are
   fungible, and the attack capacity of the attacker is only limited by
   their financial resources.  Some costs are not fungible however, in
   particular inducing a large number of people to accept a forgery
   without the effort being noticed requires much more than a limitless
   supply of funds.




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   In a computational attack an operation will at worst fail to deliver
   success.  There is no penalty for failure beyond having failed to
   succeed.  When attempting to perpetuate a fraud on the general
   public, every attempt carries a risk of exposure of the entire
   scheme.  When attempting to perform any covert activity, every
   additional person who is indoctrinated into the conspiracy increases
   the chance of exposure.

   The totalitarian state envisioned by George Orwell in 1984 was only
   plausible because each and every citizen is coerced to act as a party
   to the conspiracy.  The erasure and replacement of the past was
   possible because the risk of exposure was nil.

   In 2011, I expressed concern to a retired senior member of the NSA
   staff that the number of contractors being hired to perform cyber-
   sabotage operations represented a security risk and might be creating
   a powerful constituency with an interest in the aggressive
   militarization of cyberspace rather than preparing for its defense.
   Subsequent disclosures by Robert Snowden have validated the
   disclosure risk aspect of these concerns.  Empirically, the NSA, an
   organization charged with protecting the secrecy of government
   documents, was unable to maintain the secrecy of their most important
   secrets when the size of the conspiracy reached a few ten thousand
   people.

   The community of commercial practitioners of cryptographic
   information security is small in size but encompasses many
   nationalities.  Many members of the community are bound by
   ideological commitments to protecting personal privacy as an
   unqualified moral objective.

   Introducing a backdoor into a HSM, application or operating system
   platform requires that every person with access to the platform
   source or who might be called in to audit the code be a party to the
   conspiracy.  Tapping the fiber optic cables that support the Internet
   backbone requires only a small work crew and digging equipment.
   Maintaining a covert backdoor in a major operating system platform
   would require hundreds if not thousands of engineers to participate
   in the conspiracy.

   The Social Work Factor _SWF(t) is a measure of the cost of
   establishing a fraud in a conspiracy starting at date t.  The cost is
   measured in the number of actions that the party perpetrating the
   fraud must perform that carry a risk of exposure.

   In general, the Social Work Factor will increase over time.
   Perpetrating a fraud claiming that the Roman emperor Nero never
   existed today would require that millions of printed histories be



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   erased and rewritten, every person who has ever taught or taken a
   lesson in Roman history would have to participate in the fraud.  The
   Social Work Factor would be clearly prohibitive.

   The Social Work Factor in the immediate aftermath of Nero's
   assassination in 68 would have been considerably lower.  While the
   emperor Nero was obviously not erased from history, this did happen
   to Akhenaten, an Egyptian pharaoh of the 18^th dynasty whose
   monuments were dismantled, statues destroyed, and his name erased
   from the lists of kings.

1.8.1.  Related work

   It has not escaped the notice of the author that the social work
   factor might be applied as a general metric for assessing the
   viability of a conspiracy hypothesis.

   Applying social work factor analysis to the moon landing conspiracy
   theory we note that almost all of the tens of thousands of NASA
   employees who worked on the Apollo project would have had to be a
   part of the conspiracy and so would an even larger number of people
   who worked for NASA contractors.  The cost of perpetrating the hoax
   would have clearly exceeded any imaginable benefit while the risk of
   the hoax being exposed would have been catastrophic.

2.  The problem of trust

   Traditional (symmetric key) cryptography allows two parties to
   communicate securely provided they both know a particular piece of
   information known as a key that must be known to encrypt or decrypt
   the content.  Public Key cryptography proposed by Diffie and Hellman
   [Diffie76] provides much greater flexibility by using separate keys
   for separate roles such that it is possible to do one without being
   able to do the other.  In a public key system, an encryption key
   allows information to be encrypted but not to be decrypted.  That
   role can only be performed using the corresponding decryption key.

   The Mathematical Mesh recryption services further extend the
   capabilities of traditional public key infrastructures by further
   partitioning of the roles associated with the private key.  In the
   Mesh, this capability is referred to as 'recryption' as it was
   originally conceived of as being a form of Proxy Re-encryption as
   described by Blaze et. al. but it might equally well be considered as
   realizing distributed key generation as described by Pedersen.  A
   decryption key is split into two or more parts such that both parts
   must be involved to complete a private key operation.  These parts
   are then distributed to separate parties, thus achieving
   cryptographic enforcement of a separation of duties.



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   Public key cryptography allows many (but certainly not all)
   information security concerns to be reduced to management of
   cryptographic keys.  If Alice knows the Bob's encryption key, she can
   send Bob an encrypted message that only he can read.  If Bob knows
   Alice's signature key, Bob can verify that a digital signature on the
   message really was created by Alice.

   A Public Key Infrastructure (PKI) is a combination of technologies,
   practices and services that support the management of public key
   pairs.  In particular, if Alice does not know Bob's public key, any
   infrastructure that is designed to provide her with this information
   may be regarded as a form of PKI.

   The big challenge faced in the design, deployment of operation of a
   PKI is that while Alice and Bob can communicate with perfect secrecy
   if they use each other's actual public keys, they will have worse
   than no security if an attacker can persuade them to use keys they
   control instead.  One of the chief concerns in PKI therefore is to
   allow users to assess the level of risk they face, a quality known as
   trust.

2.1.  Existing approaches

   Few areas of information security have engaged so much passionate
   debate or diverse proposals as PKI architecture.  Yet despite the
   intensity of this argument the state of deployment of PKI in the
   Internet has remained almost unchanged.

   TLS and SSH, the only Internet security protocols that have
   approached ubiquity both operate at the transport layer.  The use of
   IPSEC is largely limited to providing VPN access.  DNSSEC remains a
   work in progress.  Use of end-to-end secure email messaging is
   negligible and shows no sign of improvement as long as competition
   between S/MIME and OpenPGP remains at a stalemate in which one has a
   monopoly on mindshare and the other a monopoly on deployment.

2.1.1.  Trust After First Use (TAFU)

   Trust After First Use is a simple but often effective form of PKI.
   Instead of trying to verify each other's public key the first time
   they attempt to communicate, the parties record the public key
   credentials presented in their first interaction and check that the
   same credentials are presented in subsequent transactions.  While
   this approach does not absolutely guarantee that 'Alice' is really
   talking to 'Bob', as the conversation continues over hours, months or
   even years, they are both assured that they are talking to the same
   person.




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2.1.2.  Direct Trust

   In the direct trust model, credentials are exchanged in person.  The
   exchange may be of the actual public key itself or by means of a
   'fingerprint' which is simply a means of formatting a cryptographic
   digest of the key to the user.

   Use of direct trust is robust and avoids the need to introduce any
   form of trusted third party.  It is also limited for the obvious
   reason that it is not always possible for users to meet in person.
   For this reason, protocols that attempt to offer a direct trust model
   often turn out to be being used in trust-after-first-use mode in
   practice when the behavior of users is examined.

2.1.3.  Certificate Authority

   The archetype of what is generally considered to be 'PKI' was
   introduced in Kohnfelder's 1978 Msc. Thesis [Kohnfelder78] . A
   Certificate Authority (CA)whose signature key is known to all the
   participants issues certificates binding the user's public key to
   their name and/or contact address(es).

   This approach forms the basis of almost every widely deployed PKI
   including the EMV PKI that support smart card payments, the CableLabs
   PKI that supports the use of set top boxes to access copyright
   protected content and the WebPKI mentioned earlier that supports the
   use of TLS in online commerce.

   One area in which the CA model has not met with widespread success is
   the provision of end-to-end secure email described in the original
   paper.  Despite the fact that S/MIME secure email has been supported
   by practically every major email client for over 20 years, only a
   small number of users are aware that email encryption is supported
   and even fewer user it on a regular basis.

   One of the reasons for this lack of uptake is the lack of uptake
   itself.  Until a critical mass of users is established, the network
   effect presents as the chicken and egg problem.  Another reason for
   the failure is the sheer inconvenience use of S/MIME presents to the
   user.  Obtaining, installing and maintaining certificates requires
   significant user effort and knowledge.  But even if these obstacles
   are addressed (as the Mesh attempts to do), as far as the open
   Internet is concerned, S/MIME provides little or no benefit over a
   direct trust model because there is no equivalent of the WebPKI for
   email.






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   Most CAs that operate WebPKI services also offer S/MIME PKI services,
   but these are seldom used except by enterprises and government
   agencies where certificates are usually issued for internal use only.

   One of the chief difficulties in establishing a MailPKI analogous to
   the WebPKI is the difficulty of establishing a set of validation
   requirements that are cost effective to users and present a
   meaningful social work factor to attackers.

   When VeriSign began operating the first Internet CA, two classes of
   email certificate were offered that have since become a de facto
   industry standard:

   Class 1:  The CA verified that the subject applying for the
      certificate could read email sent to the address specified in the
      certificate.

   Class 2:  The requirements of class 1 plus the requirement that the
      certificate be issued through a Registration Authority that had
      been separately determined to meet the considerably more stringent
      validation requirements for organizations specified in class 3 and
      in particular, demonstrated ownership of the corresponding domain
      name.

   Class 2 certificates were designed to be issued by organizations to
   their employees and arguably present a more than adequate social work
   factor to prevent most forms of attack.  S/MIME certificates are in
   daily use to secure very sensitive communications relating to very
   high value transactions.  But this represents a niche application of
   what was intended to be a ubiquitous infrastructure that would
   eventually secure every email communication.

   The only type of certificate that the typical Internet user can
   obtain is class 1 which at best offers a small improvement on social
   work factor over Trust After First Use.

2.1.4.  Web of Trust

   The concept of the Web of Trust was introduced by Zimmerman with the
   launch of PGP.  It represents the antithesis of the hierarchical CA
   model then being proposed for the Privacy Enhance Mail scheme being
   considered by the IETF at the time.  A core objection to this model
   was the fact that users could only communicate securely by obtaining
   a certificate from a CA.  The goal of PGP was to democratize the
   process by making every user a trust provider.






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   Like S/MIME, OpenPGP protocol has achieved some measure of success
   but has fallen far short of its original goal of becoming ubiquitous
   and almost none of the users have participated in the Web of Trust.

   One of the chief technical limitations of the Web of Trust is that
   trust degrades over distance.  An introduction from a friend of a
   friend has less value than one from a friend.  As the number of users
   gets larger, the chains of trust get longer, and the trustworthiness
   of the link becomes smaller.

   Another limitation is that as is fitting for a concept launched at
   the high tide of postmodernism, the trust provided is inherently
   relative.  Every user has a different view of the Web of Trust and
   thus a different degree of trust in the other users.  This makes it
   impossible for a commercial service to offer to navigate the Web of
   Trust on a user's behalf.

2.1.5.  Chained notary

   The rise of BitCoin [Bitcoin] and the blockchain technology on which
   it is based have given rise to numerous proposals that make use of a
   tamper-evident notary as either the basis for a new PKI (e.g.
   NameCoin [Namecoin] ) or to provide additional audit controls for an
   existing PKI (e.g.  Certificate Transparency [RFC6962] ).

   The principle of making a digital notary service tamper-evident by
   means of combining each output of the notary with the input of its
   successor using a cryptographic digest was proposed in 1991 by Haber
   and Stornetta [Haber91] . Every output of the notary depends on every
   one of the previous inputs.  Thus, any attempt to modify an input
   will cause every subsequent output to be invalidated.

   Notaries operating according to these principles can quickly achieve
   prohibitively high social work factors by simply signing their output
   values at regular intervals and publishing a record of the signed
   values.  Any attempt by the notary to tamper with the log will
   produce a non-repudiable proof of the defection.  Thus once an input
   value is enrolled in a chained notary, the social work factor for
   modifying that input subsequent to that becomes the same as the
   social work factor for subverting the notary and every party that has
   a record of the signed outputs of that notary.

   Enrolling the signed outputs of one notary as an input to another
   independently operated notary establishes a circumstance in which it
   is not possible for one notary to defect unless the other does as
   well.  Applying the same principle to a collection of notaries
   establishes a circumstance in which it is not possible for any notary
   to defect without that defection becoming evident unless every other



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   notary also defects.  If such infrastructures are operated in
   different countries by a variety of reputable notaries, the social
   work factor of modifying an input after it is enrolled may be
   considered as to rapidly approach infinity.

   One corollary of this effect is that just as there is only one global
   postal system, one telephone system and one Internet, convergence of
   the chained notary infrastructure is also inevitable.  Users seeking
   the highest possible degree of tamper evidence will seek out notaries
   that cross notarize with the widest and most diverse range of other
   notaries.  I propose a name for this emergent infrastructure, the
   Internotary.

   According to the image presented in the popular press, it is the
   minting of new cryptocurrency that provides stability to the
   distributed leger at the heart of BitCoin, Etherium and their many
   imitators.  The fact that notaries that do not require proof of work,
   proof of stake or any other form of seigniorage offer the same social
   work factor (effectively infinite) as those that do demonstrates that
   it is not necessary to consume nation-state level quantities of
   electricity to operate such infrastructures.

   The attraction of employing such notaries in a PKI system is that the
   social work factor to forge a credential prior to a date that has
   already been notarized as past is infinite.  It is obvious that
   almost none of the thousands of OpenPGP keys registered with the key
   server infrastructure for 'Barack Obama' are genuine and so all the
   registered keys are untrustworthy.  But if it was known that one
   particular key had been registered in the 1980s, before Obama had
   become a political leader, that particular key would be considerably
   more trustworthy than the rest.

   The use of chained notaries may be viewed as providing a distributed
   form of Trust After First Use. The first use event in this case is
   the enrollment of the event in the notary.  Instead of Alice having
   to engage in separate first use events with Bob, Carol, Doug and
   every other user she interacts with, a single first use event with
   the internotary supports all her existing and future contacts.

2.1.6.  A blended approach

   As we have seen, different PKI architectures have emerged to serve
   different communities of use by offering different forms of trust.
   The trust provided by the OpenPGP and S/MIME PKIs to the communities
   they serve is distinct.  The S/MIME PKI does not provide a useful
   means of establishing a trusted relationship in a personal capacity.
   The OpenPGP PKI is not appropriate for establishing a trust
   relationship in an enterprise capacity.  Yet despite this obvious



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   difference in capabilities, there has been no convergence between
   these competing approaches in the past two decades.

   The only convergence in approach that has developed over this period
   is within the applications that rely on PKI.  Most SSH clients and
   servers make provision for use of CA issued certificates for
   authentication.  Most email clients may be configured to support
   OpenPGP in addition to S/MIME.

   While offering the choice of CA issued, direct trust or Web of Trust
   credentials is better than insisting on the use of the one, true PKI,
   this approach is less powerful than a blended approach allowing the
   user to make use of all of them.

   In the blended approach, every user is a trust provider and can
   provide endorsements to other user and some (but not necessarily all)
   users have CA issued certificates.

   This approach follows the same patterns that have been applied in the
   issue of government credentials for centuries.  In many countries,
   passport applications must be endorsed by either a member of a
   profession that has frequent interaction with the public (e.g.
   doctors, lawyers and clerics), a licensed and registered set of
   public notaries or both.

   Analysis of the blended approach in terms of work factor reveals the
   surprising result that it can achieve a higher social work factor
   than either the CA model alone or the Web of Trust model alone.

   Consider the case that Alice and Bob have each obtained a certificate
   that presents a Social Work Factor of $10.  Applying the CA model in
   isolation, $10 is the limit to the SFW that can be achieved.  But if
   Alice and Bob were to meet and exchange endorsements, the SFW may be
   increased by up to $10.  If the exchange of endorsements is made in
   person by means of some QR code mediated cryptographic protocol, we
   might reasonably ascribe a SWF of $20 to each credential.

   This higher SWF can now be used to evaluate the value of endorsements
   issued by Alice and Bob to user Carol and of Carol to Doug, neither
   of whom has a CA issued certificates.  While the SWF of Carol is
   certainly less than $20 and the SWF or Doug is even lower, it is
   certainly greater than $0.

   While these particular values are given for the sake of example, it
   is clearly the case that as with the WebPKI, the blended approach
   permits trust to be quantified according to objective criteria even
   if the reliability of the values assigned remains subjective.  The
   Google Page Rank algorithm did not have to be perfect to be useful



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   and just as the deployment of the Web spurred the development of
   engines offering better and more accurate search engines, deployment
   of blended PKI may be reasonably be expected to lead to the
   development of better and more accurate means of evaluating trust.

   The power of the blended approach is that it provides the reach of
   the Web of Trust model with the resilience of the CA model while
   permitting a measurable improvement in work factor over both.

   Combining the blended trust model with the internotary model allows
   these SWF values to be fixed in time.  It is one thing for an
   attacker to spend $100 to impersonate the President of the United
   States.  It is quite another for an attacker to spend $100 per target
   on every person who might become President of the United States in 20
   years' time.

3.  The Mesh of Trust

   The purpose of the Mathematical Mesh is to put the user rather than
   the designer in control of their trust infrastructure.  To this end,
   the Mesh supports use of any credential issued by any form of PKI and
   provides a means of using these credentials in a blended model.

3.1.  Master Profile

   The Mesh provides an infrastructure that enables a user to manage all
   the cryptographic keys and other infrastructure that are necessary to
   provide security.

   A Mesh master profile is the root of trust for each user's personal
   PKI.  By definition, every device, every application key that is a
   part of user's personal Mesh profile is ultimately authenticated
   either directly or indirectly by the signature key published in the
   master profile.

   Unlike user keys in traditional PKIs, a Mesh master profile is
   designed to permit (but not require) life long use.  A Master profile
   can be revoked but does not expire.  It is not possible to change the
   signature key in a master profile.  Should a compromise occur, a new
   master profile must be created.

3.2.  Uniform Data Fingerprints

   Direct trust in the Mesh is realized through use of Uniform Data
   Fingerprints (UDF) [draft-hallambaker-udf] . A UDF consists of a
   cryptographic digest (e.g.  SHA-2-512) over a data sequence and a
   content type identifier.




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   UDFs are presented as a Base32 encoded sequence with separators every
   25 characters.  UDFs may be presented at different precisions
   according to the intended use.  The 25-character presentation
   provides a work factor of 2^117 and is short enough to put on a
   business card or present as a QR code.  The 50-character presentation
   provides a work factor of 2^242 and is compact enough to be used in a
   configuration file.

   For example, the UDF of the text/plain sequence "UDF Data Value" may
   be presented in either of the following forms:

   MDDK7-N6A72-7AJZN-OSTRX-XKS7D
   MDDK7-N6A72-7AJZN-OSTRX-XKS7D-JAFXI-6OZSL-U2VOA-TZQ6J-MHPTS

   The UDF of a user's master profile signature key is used as a
   persistent, permanent identifier of the user that is unique to them
   and will remain constant for their entire life unless they have
   reason to replace their master profile with a new one.  The exchange
   of master profile UDFs is the means by which Mesh users establish
   direct trust.

3.3.  Strong Internet Names

   A Strong Internet name (SIN) [draft-hallambaker-sin] is a valid
   Internet address that contains a UDF fingerprint of a security policy
   describing interpretation of that name.

   While a SIN creates a strong binding between an Internet address and
   a security policy, it does not provide a mechanism for discovery of
   the security policy.  Nor is it necessarily the case that this is
   publicly available.

   For example, Example Inc holds the domain name example.com and has
   deployed a private CA whose root of trust is a PKIX certificate with
   the UDF fingerprint MB2GK-6DUF5-YGYYL-JNY5E-RWSHZ.

   Alice is an employee of Example Inc., she uses three email addresses:

   alice@example.com  A regular email address (not a SIN).

   alice@mm--mb2gk-6duf5-ygyyl-jny5e-rwshz.example.com  A strong email
      address that is backwards compatible.

   alice@example.com.mm--mb2gk-6duf5-ygyyl-jny5e-rwshz  A strong email
      address that is backwards incompatible.






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   Use of SINs allows the use of a direct trust model to provide end-to-
   end security using existing, unmodified email clients and other
   Internet applications.

   For example, Bob might use Microsoft Outlook 2019, an email
   application that has no support for SINs as his email client.  He
   configures Outlook to direct outbound mail through a SIN-aware proxy
   service.  When Bob attempts to send mail to a strong email address
   for Alice, the proxy recognizes that the email address is a SIN and
   ensures that the necessary security enhancements are applied to meet
   the implicit security policy.

3.4.  Trust notary

   A Mesh trust notary is a chained notary service that accepts
   notarization requests from users and enrolls them in a publicly
   visible, tamper-evident, append-only log.

   The practices for operation of the trust notary are currently
   undefined but should be expected to follow the approach described
   above.

   The trust notary protocol provides support for establishing an
   internotary through cross certification.  The append only log format
   is a DARE Container [draft-hallambaker-dare-container] , the service
   protocol is currently in development.

3.5.  Endorsement

   An endorsement is a document submitted to a trust notary that
   includes a claim of the form 'public key X is held by user Y'.  Mesh
   endorsements may be issued by CAs or by ordinary users.

3.6.  Evaluating trust

   One of the chief advantages of the World Wide Web over previous
   networked hypertext proposals was that it provided no means of
   searching for content.  While the lack of a search capability was an
   obstacle to content discovery in the early Web, competing solutions
   to meeting this need were deployed, revised and replaced.

   The Mesh takes the same approach to evaluation of trust.  The Mesh
   provides an infrastructure for expression of trust claims but is
   silent on their interpretation.  As with the development of search
   for the Web, the evaluation of trust in the Mesh is left to the
   application of venture capital to deep AI.





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4.  Conclusions

   This paper describes the principal approaches used to establish
   Internet trust, a means of evaluating them and a proposed successor.
   It now remains to determine the effectiveness of the proposed
   approach by attempting deployment.

5.  Security Considerations

   This document describes the means by which interparty identification
   risk is managed and controlled in the Mathematical Mesh.

   The security considerations for use and implementation of Mesh
   services and applications are described in the Mesh Security
   Considerations guide [draft-hallambaker-mesh-security] .

6.  References

6.1.  Normative References

   [draft-hallambaker-mesh-security]
              "[Reference Not Found!]".

6.2.  Informative References

   [Adrian2015]
              Adrian, D., "Weak Diffie-Hellman and the Logjam Attack",
              October 2015.

   [Bitcoin]  Finley, K., "After 10 Years, Bitcoin Has Changed
              Everything?And Nothing", November 2018.

   [Diffie76]
              Diffie, W. and M. Hellman, "New Directions in
              Cryptography", November 1976.

   [draft-hallambaker-dare-container]
              Hallam-Baker, P., "Data At Rest Encryption Part 2: DARE
              Container", draft-hallambaker-dare-container-02 (work in
              progress), August 2018.

   [draft-hallambaker-sin]
              Hallam-Baker, P., "Strong Internet Names (SIN)", draft-
              hallambaker-sin-03 (work in progress), April 2018.

   [draft-hallambaker-udf]
              Hallam-Baker, P., "Uniform Data Fingerprint (UDF)", draft-
              hallambaker-udf-12 (work in progress), January 2019.



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   [Haber91]  Haber, S. and W. Stornetta, "How to Time-Stamp a Digital
              Document", 1991.

   [Intel2018]
              Bell, L., "Intel delays 10nm Cannon Lake processors,
              again, until late 2019", July 2018.

   [Kohnfelder78]
              Kohnfelder, L., "Towards a Practical Public-Key
              Cryptosystem", May 1978.

   [Namecoin]
              Inc., N., "Namecoin Web Site", 2019.

   [Ratchet]  Marlinspike, M. and T. Perrin, "The Double Ratchet
              Algorithm", November 2016.

   [RFC5869]  Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
              Key Derivation Function (HKDF)", RFC 5869,
              DOI 10.17487/RFC5869, May 2010.

   [RFC6246]  Sajassi, A., Brockners, F., Mohan, D., and Y. Serbest,
              "Virtual Private LAN Service (VPLS) Interoperability with
              Customer Edge (CE) Bridges", RFC 6246,
              DOI 10.17487/RFC6246, June 2011.

   [RFC6962]  Laurie, B., Langley, A., and E. Kasper, "Certificate
              Transparency", RFC 6962, DOI 10.17487/RFC6962, June 2013.

   [RFC8446]  Rescorla, E., "The Transport Layer Security (TLS) Protocol
              Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018.

   [Schneier2013]
              Schneier, B., "Defending Against Crypto Backdoors",
              October 2013.

   [Shannon1949]
              Shannon, C., "Communication Theory of Secrecy Systems",
              1949.

6.3.  URIs

   [1] http://mathmesh.com/Documents/draft-hallambaker-mesh-trust.html








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Author's Address

   Phillip Hallam-Baker

   Email: phill@hallambaker.com














































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