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Internet Engineering Task Force (IETF)              Phillip Hallam-Baker
Internet-Draft                                         Comodo Group Inc.
Intended Status: Standards Track                        October 27, 2014
Expires: April 30, 2015


                        PRISM Proof Trust Model
                 draft-hallambaker-prismproof-trust-01

Abstract

   This paper extends Shanon's concept of a 'work factor' 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, peer to peer (Web of Trust) models to be evaluated in
   the same framework. The analysis shows that each model has clear
   benefits over the other for some classes of user but most classes of
   user are served better by a combination of both.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
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   Internet-Drafts are working documents of the Internet Engineering
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Copyright Notice

   Copyright (c) 2014 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
   (http://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



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   to this document. Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.


















































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Table of Contents

   1.  Work Factor  . . . . . . . . . . . . . . . . . . . . . . . . .  4
      1.1.  Computational Work Factor . . . . . . . . . . . . . . . .  4
      1.2.  Hypothetical Work Factor  . . . . . . . . . . . . . . . .  5
         1.2.1.  Known Unknowns . . . . . . . . . . . . . . . . . . .  6
         1.2.2.  Defense in Depth . . . . . . . . . . . . . . . . . .  7
         1.2.3.  Mutual Reinforcement . . . . . . . . . . . . . . . .  8
         1.2.4.  Safety in Numbers  . . . . . . . . . . . . . . . . .  8
      1.3.  Cost Factor . . . . . . . . . . . . . . . . . . . . . . .  9
      1.4.  Social Work Factor  . . . . . . . . . . . . . . . . . . . 11
   2.  The Problem of Evaluating Trust  . . . . . . . . . . . . . . . 13
      2.1.  Probability and Risk  . . . . . . . . . . . . . . . . . . 13
      2.2.  Reputation  . . . . . . . . . . . . . . . . . . . . . . . 14
      2.3.  Curated Spaces  . . . . . . . . . . . . . . . . . . . . . 15
      2.4.  Trustworthy Time  . . . . . . . . . . . . . . . . . . . . 15
   3.  Maximizing Social Work Factor to Maximize Trust  . . . . . . . 15
      3.1.  Trust Specifiers  . . . . . . . . . . . . . . . . . . . . 16
         3.1.1.  Key Identifiers  . . . . . . . . . . . . . . . . . . 16
         3.1.2.  Self Signed Certificates . . . . . . . . . . . . . . 17
      3.2.  Trust Assertions  . . . . . . . . . . . . . . . . . . . . 17
         3.2.1.  Certificate Authority Issued Certificates  . . . . . 17
         3.2.2.  Key Signingey Signing  . . . . . . . . . . . . . . . 19
         3.2.3.  Adding Key Endorsement to PKIX . . . . . . . . . . . 19
      3.3.  Trust Meta Assertions . . . . . . . . . . . . . . . . . . 22
         3.3.1.  Revocation and Status Checkings Checking . . . . . . 22
         3.3.2.  Notarization . . . . . . . . . . . . . . . . . . . . 22
         3.3.3.  Transparency . . . . . . . . . . . . . . . . . . . . 22
      3.4.  Other Approaches  . . . . . . . . . . . . . . . . . . . . 22
         3.4.1.  DNSSEC . . . . . . . . . . . . . . . . . . . . . . . 23
         3.4.2.  SPKI / SDSI  . . . . . . . . . . . . . . . . . . . . 23
         3.4.3.  Identity Based Cryptography  . . . . . . . . . . . . 23
   4.  Maximizing Social Work Factor in a Notary Infrastructure . . . 24
   5.  Conclusions and Related Work . . . . . . . . . . . . . . . . . 25
   Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . 25



















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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. The community thus faces 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 security of a system should measured by the difficulty of
   attacking it. 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 Shanon's concept of a 'work factor' 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 Shanon's
   original concept.

   One of Shanon'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 x * 2^56. The
   security of DES has changed over time because the cost x has fallen
   exponentially.

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

   [Note that in the following analysis, the constraints of the IETF
   document format make use of the established notation impractical and
   a confusing mess, hence the departure from Shannon's notation.]




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   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 about the limit to current attacks.

   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 magnitue 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. The probability that a government attacker 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) <= WF_C (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



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   all p.

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

      *  Increasing WF_H(A,p) for some p, or

      *  Decreasing WF_H'(A,WF)

1.2.1. 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).

   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 PRISM-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



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   persuade bank customers to simply give their access credentials to
   the attacker.

   Even if a PRISM-class attacker has a factoring attack which renders
   an attack on RSA-2048 feasible, it is almost certainly easier for a
   PRISM-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.

1.2.2. 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.

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

      *  Option A: Uses algorithm X for protection.

      *  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.





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1.2.3. 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) 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.

   Both concerns are mitigated if instead of using the output of one
   generator directly, the value R1(s1) XOR R2(s2) is used where R1 and
   R2 are independent random number generators 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.

1.2.4. 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 PRISM-class attack, the
   concern is not just whether an individual communication might be
   compromised but the number of communications that may be compromised



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   for a given amount of effort.

   'Perfect' Forward Secrecy is an optional feature supported in IPSec
   and TLS. Current implementations of TLS offer a choice between:

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

      *  Direct key exchange followed by a perfect forward secrecy
         exchange with a work factor dependent on the difficulty of
         breaking 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.

   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 Comodo OCSP server
   receives over 2 billion hits a day and this represents only a
   fraction of the number of uses of SSL 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.

   There is security in numbers: If every communication is protected by
   perfect forward secrecy the hypothetical work factor for decrypting
   every communication is the hypothetical work factor of decrypting one
   communication times the number of communications.

1.3. 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 PRISM-class
   attacker may use any and every tool at their disposal including tools
   that are unique to government backed adversaries such as the threat



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   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.
   Subversion of cryptographic apparatus such as Hardware Security
   Modules (HSMs) and SSL accelerators faces similar constraints. A HSM
   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.

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

   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



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   have the incentive and when governments do engage in activities such
   as counterfeiting banknotes this has been done for motives beyond
   mere peculation.

   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

      *  Increasing the cost

      *  Reducing the incentive

      *  Reducing the expected gain

      *  Reducing the probability that the incentive will be realized

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

1.4. 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.

   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,



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   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 is only
   possible because each and every citizen is in effect a party to the
   conspiracy. The erasure and replacement of the past is possible
   because the risk of exposure is 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 cryptographic information
   security is small in size but encompases 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 WF_S(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
   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.






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   The Social Work Factor of perpetrating such a fraud today is
   prohibitive, the cost 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 there is a strong
   consensus among Egyptian archeologists that something of the sort
   happened to Tutankhamun before the discovery of his tomb by Howard
   Carter.

2. The Problem of Evaluating Trust

   The Prism-Proof Email testbed attempts to facilitate the development
   and deployment of a new email privacy protection infrastructure by
   dividing the problem into the parts for which there are known, well
   established (if not necessarily perfect) solutions and the parts for
   which there are not with clearly defined interfaces between the two
   parts.

   The Trust Publication Web Service is a JSON/REST Web service that
   supports the publication of all existing forms of trust assertion
   (PKIX, OpenPGP, SAML). For the sake of future simplicity, a new ASN.1
   message format for OpenPGP-style key endorsement is proposed so that
   all the forms of trust assertion that might be used in a PKI may be
   expressed without recourse to multiple data encoding formats. The
   Trust Publication Web Service need not be a trusted service since its
   role is essentially that of a proxy, routing messages such as
   certificate requests to the appropriate destination(s).

   The Omnibroker Web Service is a trusted service that a mail user
   agent or proxy can query to determine which security enhancements
   (encryption, signature, etc.) should be added to an outbound message
   (among other functions).

   Between the Trust Publication Web Service and the Omnibroker service
   sits the hard research problem of how to make sense of and what value
   to place on the CA issued certificates, peer to peer key
   endorsements, revocation information and other signed assertions that
   might exist.

   Robust implementation of public key cryptography allows the signature
   on a signed assertion to be verified as belonging to a holder of the
   corresponding signature key with near certainty. But such an
   assertion can only be considered trustworthy if the purported signer
   is trustworthy and is the actual holder of the corresponding signing
   key, claims that are in turn established by more signed assertions.
   Expanding the scope of our search increases the number of documents
   on which we are relying for trust rather than answering the question
   we wish to answer.







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2.1. Probability and Risk

   Attempting to analyze the trustworthiness of a signed assertion in a
   heterarchical topology such as Phil Zimmerman's Web of Trust leads to
   an infinite regression. Alice may see that Bob's key has been signed
   by Carol, Doug and Edward but this should only give Alice more
   confidence in the validity of Bon's key if she knows that Carol Doug
   and Edward are distinct individuals.

   Probability is a model of events that are random. An attack is a
   conscious act on the part of an attacker and is only random insofar
   as the attacker's motive may not require a particular choice of
   victim or method. In such cases the particular attack is 'random'
   from the point of view of the victim but that an attack would take
   place is due to the fact that the attacker had motive, means and
   opportunity.

   The motive for an attacker depends on the perceived rather than the
   actual difficulty of breaking a system. It might be some time before
   a competent attacker attempts to break an insecure system that is for
   some reason generally believed to be secure. But the rate of attack
   is likely to increase rapidly once the vulnerability is widely known.
   The system has not become less trustworthy over time, rather the
   system was always untrustworthy and it is only the consequences of
   that fact that have changed.

   Analyzing the trustworthiness of a Web of Trust using an estimate of
   the probability that an assertion might be fraudulent is
   unsatisfactory because it requires us to provide as an input to our
   calculations the very quantity we are trying to arrive at as an
   output.

   Attempting to estimate the probability of default for each assertion
   in a Web of trust leads us to an infinite recursion as Alice trusts
   Bob trusts Carol trusts Alice. We can define the inductive step but
   have no base case to ground it with.

2.2. Reputation

   Another frequently proposed metric for analyzing the trustworthiness
   of assertions is 'reputation'. Reputation is a measure of risk based
   on reports of past behavior.

   Reputation has proved somewhat effective in online restaurant
   reviews. A restaurant that receives a high number of good reviews is
   likely to be worth visiting but ratings based on a small number of
   reviews can be wildly inaccurate. A glowing review may have been
   written by a satisfied customer or by an unscrupulous proprietor. A
   series of negative reviews may be written by unsatisfied customers or
   a jealous competitor.




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   Restaurant reviews work because there is a widely shared
   understanding of what makes a good or a bad restaurant. There is no
   similar shared understanding of the quality of a public key
   validation process except among specialists in the field.

2.3. Curated Spaces

   'Reputation based' systems have proved highly effective at
   controlling email abuse but these systems use a large quantity of
   empirical data including from honeypot email servers, expert analysis
   of abuse traffic and content analysis to arrive at reputation scores.
   It is the action of the curator that turns the raw data into a useful
   measure of risk rather than the mechanical application of a clever
   algorithm.

   There is a good argument to be made for introducing a curator into a
   PKI trust model but that is an argument about who should perform the
   analysis rather than how the analysis is to be performed.

2.4. Trustworthy Time

   The problem of grounding the Web of Trust is solved if there is
   available a notary authority whose trustworthiness is beyond
   reasonable dispute. Once a trust assertion has been notarized by such
   a notary authority, the cost of forgery becomes the cost of suborning
   the notary authority.

   As is demonstrated later, use of linked timestamps and cross-
   notarization amongst notaries makes it possible to establish a
   timestamp notary infrastructure such that perpetrating a forgery
   requires each and every notary in the infrastructure is compromised.

   The analysis of the set of trust assertions begins by asserting a
   Social Work Factor to the earliest assertion prior to the time at
   which it was notarized. This provides the base case of the induction
   from which the rest of the analysis proceeds.

3. Maximizing Social Work Factor to Maximize Trust

   As previously described, the purpose of the Social Work Factor is to
   support the design process by allowing the consequences of different
   design approaches to be considered.

   When designing a trust infrastructure, there are two different
   attacks that need to be considered. First there is the attack where a
   credential is issued for an entirely fictitious persona, secondly
   there is the attack where a credential is issued to an impostor
   impersonating a real persona.






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   The consequences of the two attacks are very different, particularly
   where a confidentiality infrastructure is concerned. Indeed it might
   be considered desirable to encourage participants to create and use
   fictitious personas to provide anonymity for their actions in certain
   circumstances. An impostor who gains a credential for a real person
   can use it to persuade relying parties that their communications are
   confidential when they are in fact compromised and can steal the use
   of the target's reputation.

   The context of an attack is also important. The confidentiality of
   the private communications of an individual is an issue for that
   individual and their correspondents alone. The confidentiality of the
   communications of an individual acting for their employer is much
   more complex. In addition to the employer having an interest in
   protecting the confidentiality of the communication, there may be a
   legitimate employer interest in being able to view the contents. For
   example, it is now generally accepted in many countries that most
   government employees do not have a right of privacy from the people
   who they ultimately work for unless their job function falls into a
   narrowly scoped exception.

3.1. Trust Specifiers

   A trust specifier is a mechanism that identifies a public key either
   directly (e.g. a self-signed certificate) or indirectly (e.g. a Key
   identifier).

   Trust specifiers are not trust assertions but may be used to create
   trust assertions. For example, an OpenPGP fingerprint does not make
   any statement about the owner of a public key but an OpenPGP
   fingerprint printed on a business card is an explicit claim that the
   specified public key may be used to send encrypted email to the
   individual named on the card.

3.1.1. Key Identifiers

   PGP introduced the use of key fingerprints as the basis for key
   exchange. A cryptographic digest value is computed from the user's
   public key and used as the basis for key endorsement (called key
   signing in the PGP terminology).

   The term 'fingerprint' has no formal definition in the PKIX
   specifications but the term is widely used to refer to a message
   digest of the entire contents of a certificate. Since this use is
   incompatible with the PGP usage, the term Key Identifier is prefered
   as this is unambiguous in both contexts.

   In PKIX, the key identifier value is a value chosen by the issuer to
   uniquely identify a public key. The Key Identifier value of the
   issuing public key is specified using the authorityKeyInfo extension
   and the Key Identifier value of the subject is specified in the



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   subjectKeyIdentifier extension.

   While a PKIX Key Identifier is not required to have the strong
   binding to the corresponding public key that an OpenPGP identifier
   does, a profile could require that certificates specify 'strong' Key
   Identifiers formed using a cryptographic message digest of the public
   key parameters.

   Strong Key Identifiers are not trust assertions but they may be used
   to facilitate the creation of trust assertions through key signing, a
   form of the endorsement mechanism discussed below.

   Strong Key Identifiers may also be used to publish informal key
   assertions by adding them to a business card or a Web Page. Such uses
   might be facilitated through definition of appropriate URI and QR
   code formats.

3.1.2. Self Signed Certificates

   In the context of PKI, the term 'certificate' is generally understood
   to refer to an X.509 public key certificate that binds a name and/or
   an Internet address to a public key.ublic key.

   A certificate may be either a self signed certificate or a CA issued
   certificate. Since the work factor of creating a self-signed
   certificate is negligible, such certificates demonstrate little in
   themselves but present the subject's public key data in a format that
   is compatible with many existing applications.

   As with Key Identifiers, a self signed certificate is not a useful
   trust assertion in its own right but may be used to facilitate the
   creation of trust assertions through notarization or endorsement. A
   public key certificate may also be used as the basis for making a
   Certificate Signing Request to a Certificate Authority.

3.2. Trust Assertions

   In a PKI, a trust assertion makes a statement about the holder of a
   public key. In the PKIX model as currently deployed and used, the
   only forms of trust assertion are Key Signing Certificates and End
   Entity Certificates. In the OpenPGP model every user is also a trust
   provider and trust assertions are created in peer-to-peer fashion to
   create a Web of Trust.

3.2.1. Certificate Authority Issued Certificates

   A Certificate Authority (CA) is a trusted third party that issues
   digital certificates. A private CA issues certificates for a closed
   community of relying parties, a public CA issues certificates without
   restriction on the relying parties.




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   In the Web PKI, providers of Web browsers and platform providers
   embed the trust anchors of selected public Certificate Authorities
   into the application as default trust providers.

   Operation of a Certificate Authority involves two types of
   certificate. A certificate is either a certificate signing
   certificate or an end entity certificate. While it is possible for a
   Certificate Authority to lose control of a signing key used to issue
   certificates, the Social Work Factor for such attacks can be made
   prohibitively high.

   A CA Certificate Policy defines (among other things) the validation
   criteria that the CA applies before deciding to issue a certificate.
   A certificate policy is designed to provide a balance between the
   social work factor presented to an attacker and the cost to the CA
   and the subject. The CA-Browser forum Extended Validation practices
   are designed to present a very high social work factor to attackers
   while Domain Validation presents a significantly lower cost to both
   subjects and attackers.

   The EV guidelines in particular are designed to present a social work
   factor that increases each time an attacker attempts an attack.
   Registering one corporation is relatively straightforward.
   Registering a corporation in a way that prevents ownership being
   traced back to the owners is rather more difficult. Registering
   hundreds of false front corporations is considerably harder as any
   common link between the corporations means that if one corporation is
   discovered to be a front for fraudulent purposes, the rest will come
   under close scrutiny. scrutiny.

   A major advantage of the CA certificate issue approach is that they
   allow a high degree of trust to be established very quickly while it
   takes a considerable time to establish trust in a pure Web of Trust
   approach.

   The main drawback to the CA issue approach is in providing trust to
   individuals for personal use rather than corporate or government
   entities or to employees working for such entities. Corporations and
   Government entities invest in obtaining EV validated certificates as
   a cost of doing business that has an established return. There is no
   obvious return on obtaining a similar high assurance credential for
   personal use but validating an individual's credentials is just as
   complicated as validating the credentials of a corporation. The
   history of the UK National Identity card suggests that there is no
   reason to expect that the cost of provisioning credentials would be
   significantly reduced at scale.

   The CA issue model has been successfully applied to issue of
   credentials to employees for use within an organization and such
   credentials are occasionally used for external purposes such as
   S/MIME email. But such certificates are not intended for personal use



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   and are typically revoked when employment ends.

3.2.2. Key Signingey Signing

   In the OpenPGP model every key holder is a trust provider and every
   key may be used to provide trust through 'key signing'. The trust
   value of key signing depends on how close the relying party is to the
   signer. A key that I have signed myself is far more trustworthy than
   a key signed by a friend of a friend of a friend.

   The Social Work Factor of forging an individual key signing is low
   but could be fixed in time through use of a notary. A recent key
   signing purporting to be for the public key of Barack Obama would
   have negligible evidentiary value unless produced by someone very
   close to me or endorsed through other means. A key signing that had
   been notarized during his time as a Harvard student would be
   considerably more trustworthy.

   As the separation between the relying party and the signer becomes
   larger it becomes increasingly desirable to require multiple
   independent key signing paths. The Social Work Factor combined with
   an absolutely reliable notary service provide a firm basis for
   evaluating the trust value of such Webs of trust: The trustworthiness
   of a key is dependent on whether the incentive to create a forgery
   ever exceeded the Social Work Factor of performing a forgery.

   Use of peer-to-peer key signing does provide a viable model for
   establishing high assurance credentials for personal use but
   establishing a high degree of assurance is like making the best
   quality Scotch whisky: the product takes an inordinately long time to
   reach maturity. It is hard to see how key-signing could be made a
   viable model for commercial use. It is an especially poor fit for
   issue of credentials to employees as the employer has no control over
   the issue or use of the credential and no ability to revoke the
   credential when an employee is terminated.

   One advantage frequently cited for OpenPGP over PKIX is that there is
   no CA role and the infrastructure is therefore 'free'. Neither the
   premise, nor the conclusion holds, Many profitable businesses have
   been built on the basis of open source software and a Web of Trust
   that reached critical mass would offer abundant opportunities to
   companies with PKI expertise.

   Nor is the lack of business stakeholders in an infrastructure
   necessarily an advantage. One of the reasons that the Web PKI has
   been successful is that there are many businesses that promote the
   use of SSL certificates.







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3.2.3. Adding Key Endorsement to PKIX

   Considering the Social Work Factor presented by trust assertions in
   the PKIX and OpenPGP model establishes clear benefits to both
   approaches. Each model best suits a different community.

   One approach to a next generation PKI therefore would be to simply
   enable the use of either scheme in any application. This is not the
   best approach however as it leaves the email security market in a
   BetaMax/VHS standards war that has been stalemated for almost two
   decades. Further, attempting to maintain the use of two different
   PKIs leads to an unnecessary increase in complexity.

   A PKI that combines the PKIX and OpenPGP approaches offers clear
   advantages over both. For many practical reasons that will only be
   summarised here, it is better to extend the existing PKIX
   infrastructure to support Key Signing rather than start from the
   OpenPGP message formats or attempt to design a system based on a new
   encoding format. These include the deployed base of S/MIME email
   clients, the use of PKIX to support SSL and the widespread support
   for PKIX in common code platforms.

   Rather than attempting to force peer-to-peer Key Signing model into
   the existing PKIX model, a new structure, the Key Endorsement is
   proposed instead. While it is technically possible to use PKIX cross
   certificates as a substitute for PGP Key Signing, the legacy PKIX
   infrastructure is designed on the assumption that a cross certificate
   is either completely trustworthy or completely untrustworthy. It is
   better to introduce a new data format to represent new semantics than
   to attempt to retrofit new semantics into a legacy format with a
   deployed infrastructure.

   I propose the introduction of a Key Endorsement, similar to a PKIX
   certificate except that:

      *  A Key Endorsement is signed by a PKIX end entity certificate,
         not a Key Signing Certificate.

      *  Instead of a validity interval, there is an issue time.

      *  The signer and subject key identifiers are required elements of
         the structure rather than optional extensions.

      *  Key endorsements are not intended for direct use by relying
         applications.

   Adding Key Endorsements to the PKIX model allows the use of both
   trust models in combination.






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3.2.3.1. Peer Endorsement

   Key endorsement may also be used to endorse keys of peers. While the
   ability of the 16 year old Alice to accurately validate the public
   keys of her peers is questionable, the value of a notarized
   endorsement increases over time.

   Relying on peer endorsement alone requires that the relying party be
   'close' to the signer. Using a combination of CA issued certificates
   and Key Endorsements allows a high social work factor to be
   established even for a remote population. It is quite feasible for an
   attacker to generate a network of one, a hundred or even a million
   key signing events but generating a fraudulent network that contains
   a mixture of CA validated certificates and key endorsements has a
   much higher social work factor.

3.2.3.2. Self Endorsement

   Self endorsement is a special form of endorsement as a person is
   least likely to make false statements that might harm their own
   security. Although this is possible in the case that coercion or
   undue psychological pressure is applied.

   A user may be expected to have multiple public keys issued over the
   course of their life, for use at school, university, at different
   employers and for personal use. In the existing PKIX model each of
   these keys are independent. Key endorsement allows a user to
   countersign new keys with older keys, establishing a personal web of
   trust that develops over time so that the social work factor is
   preserved and increased over time rather than starting from scratch
   each time a certificate is issued.

   For example, Alice is issued a certificate at school which she uses
   to sign a key endorsement for a personal key she creates. When Alice
   goes to University, she endorses her university key with her personal
   key and vice versa. On graduating, Alice becomes a journalist.
   Sources can send her encrypted messages containing tips confident in
   the knowledge that Alice is the same Alice who attended the high
   school and university listed in her official biography.

3.2.3.3. Key Endorsement Parties

   A PGP Key Signing party is an event held to facilitate exchange of
   PGP fingerprints. Like the use of hashtags and many other important
   constructs in social media, key signing parties are a practice that
   have arisen out of use rather than being part of the original model.

   Recognizing a Key Endorsement Party as being a special form of peer
   endorsement enables special consideration when making a trust
   evaluation. It is not practical for a thousand attendees at an
   international conference to perform mutual key endorsements with



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   every other participant (a half million pairs!) but it is entirely
   practical to establish a scheme in which anyone who gets their key
   endorsed by some number (e.g. five) of qualified Key Endorsers will
   have their key endorsed by the Key Endorsement Party key at the end.

3.3. Trust Meta Assertions

   Trust Meta Assertions are trust assertions that make statements about
   other trust assertions

3.3.1. Revocation and Status Checkings Checking

   Real users and real administrators make mistakes from time to time.
   Private keys are lost or stolen or misused. Any system that does not
   provide a mechanism for forgiving mistakes is unlikely to be
   practical in the real world.

   Revocation checking limits the incentive for attack by allowing the
   time window of vulnerability to be limited in the case of a
   fraudulent certificate issue or that a private key is discovered to
   be lost or stolen. This does not increase the social work factor but
   decreases the value of an attack.

3.3.2. Notarization

   Notarization or a Trust Assertion of Key Identifier by a trustworthy
   notary allows the social work factor of forging the trust assertion
   or key identifier to be raised to an infeasible level for dates after
   the notarization took place.

   While a traditional notary might be suborned relatively easily, a
   digital notary can be constructed in such a fashion that post dating
   a notary assertion by more than a few hours or days is infeasible.

3.3.3. Transparency

   Certificate Transparency is a proposed infrastructure to (Laurie et.
   al.). [[Describe]

   Publishing issued certificates increases the probability that an
   attempted fraud will be discovered and thus increases the Social Work
   Factor and reduces the incentive.

3.4. Other Approaches

   The X.509/PKIX and OpenPGP infrastructures are not the only
   infrastructures that have been proposed by they are the only large
   scale infrastructures which large numbers of users rely on today. The
   Social Work Factor over time may be used to evaluate alternative PKI
   options that have not (yet) achieved widespread use.




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3.4.1. DNSSEC

   Like PKIX, DNSSEC is based on a hierarchical trust model. Unlike
   PKIX, DNSSEC is only capable of making statements about DNS names.

   The Social Work Factor is not a useful tool to analyze DNSSEC
   assertions because there is no historical dimension to the DNSSEC
   infrastructure. The trustworthiness of a DNSSEC assertion depends on
   the trustworthiness of the root operator, the TLD registry and the
   party that signed the corresponding DNS zone. If these are
   trustworthy then so is the assertion, there is no alternative if not.

   While the root and registry operators have strong commercial
   incentives not to default, a default may be coerced through
   government action and relying parties have no independent means to
   determine if a default has taken place.

3.4.2. SPKI / SDSI

   The chief distinguishing characteristic of SPKI is that SPKI names
   are not universal. While this has the interesting effect of
   simplifying the evaluation of trust within the SPKI naming
   infrastructure, this effect is lost when attempting to send an email
   because the Internet email system is based on the assumption that the
   namespace is universal. It does not make sense to talk about 'Alice's
   bob@example.com' (although UUCP email did use a scheme of that type.

3.4.3. Identity Based Cryptography

   Identity based cryptography is a frequently touted 'alternative' to
   conventional public key cryptography in which the public key of each
   subject is a deterministic function of their name and a master public
   key which is known to everyone. Each user obtains their private key
   from the party that created the master public key pair using the
   master private key.

   While many benefits have been claimed for the Identity based
   approach, applying to the holder of the master private key for a
   private key offers no benefits to key holders over applying to a
   certificate from a CA.

   Identity based cryptography does offer relying parties the ability to
   obtain the public key for a counterparty without the need to
   communicate with another party, but this is hardly much of an
   advantage unless there is no means for certificates to be passed in-
   ban and there is no advantage at all if an external source has to be
   queried to obtain the status of a public key to determine that the
   private key has not been reported lost or compromised.






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   The simplicity of certificate chain validation and status checking in
   Identity Based Cryptography is the result of the technology being
   unable to support these features rather than the features being
   unnecessary.

4. Maximizing Social Work Factor in a Notary Infrastructure

   The ability to determine that a trust event occurred before a certain
   point in time increases the social work factor for forging the event
   after that point in time. If suborning the notary is infeasible, the
   Social Work Factor is raised to an infeasible level.

   Harber and Stornetta proposed a notary that produced a 'catenate
   certificate' in which each notary output is fed as an input into the
   next. It is thus impossible to insert notary events between two prior
   notary events without breaking the cryptographic algorithm used for
   authentication.

   A chain of notary events may be fixed in time by notarizing events
   that are unpredictable in advance but known with a high degree of
   certainty afterward. For example the weekly lottery numbers or the
   closing prices on various equity markets.

   The principal drawback to grounding the notary chains using external
   events is that the ability of a party to verify the trustworthiness
   of the notary is bounded by the trustworthiness of the reports of the
   external events used for verification.

   A better approach is to have establish a large number of
   independently operated notaries and a procedure for cross
   notification that ensures that no notary can default unless every
   other notary defaults. The Social Work Factor of suborning any notary
   then becomes the Social Work Factor of suborning every notary and
   erasing all histories for their notary events.

   For ease of explanation, a two tier notary infrastructure is
   envisaged in which a notary is either a local notary or a meta
   notary.

   Local notaries are notaries that produce a catenate log of
   notarization requests submitted by its users. The current value of
   the notary chain is presented to one or more meta-notaries at regular
   time intervals (e.g. an hour) to prevent backdating of notary claims
   and notarizes the output of one or more meta notaries at regular
   intervals to prevent predating.

   Meta notaries are notaries that only notarize the requests submitted
   by local notaries and by other meta notaries. Before accepting a
   notarization request, a meta notary audits the actions of the notary
   making the request to ensure that the time-stamp values etc. are
   consistent and correct.



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   The schedule of peer to peer notification among meta notaries is set
   such that a notary request made to any of the local notaries served
   will affect the output of every meta notary within a predetermined
   period of time.

   To make use of such a notary infrastructure, a relying party chooses
   at least one meta notary and obtains and maintains a record of the
   catenate certificate chain over time. The trust chain of the chosen
   meta notary may then be used to verify any notary assertion presented
   by any other meta notary which may in turn be used to verify any
   notary assertion from a local notary that participates in the scheme.

   A significant benefit of this approach is that the ability to verify
   notary assertions is assured even if the Local Notary that originally
   produced it ceases functioning. All that is necessary for the
   continued operation of the system to be assured is for the pool of
   meta notaries to be sufficiently large to render suborning all of
   them infeasible.

5. Conclusions and 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 political conspiracy hypothesis.

Author's Address

   Phillip Hallam-Baker
   Comodo Group Inc.

   philliph@comodo.com






















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