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Security Limited Additional Mechanisms for PKIX and SMIME Internet-Draft This document updates RFC 5280 to replace the algorithm for X.509 policy validation with an equivalent, more efficient algorithm. The original algorithm built a structure which scaled exponentially in the worst case, leaving implementations vulnerable to denial-of-service attacks. Discussion Venues Discussion of this document takes place on the Limited Additional Mechanisms for PKIX and SMIME Working Group mailing list (spasm@ietf.org), which is archived at . Source for this draft and an issue tracker can be found at .

Introduction defines a suite of extensions for specifying certificate policies, along with a mechanism for mapping policies between subject and issuer policy domains in cross-certificates. This mechanism, when evaluated according to the algorithm in produces a policy tree, describing policies asserted by each certificate, and mappings between them. This tree can grow exponentially in the depth of the certification path. This cost asymmetry can lead to a denial-of-service vulnerability in X.509-based applications, such as and . describes this vulnerability. describes the primary mitigation for this vulnerability, a replacement for the policy tree structure. provides updates to which implement this change. Finally, discusses alternative mitigation strategies for X.509 applications.

Summary of Changes from RFC 5280 The algorithm for processing certificate policies and policy mappings is replaced with one which builds an equivalent, but much more efficient structure. This new algorithm does not change the validity status of any certification path, nor which certificate policies are valid for it.

Conventions and Definitions The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 when, and only when, they appear in all capitals, as shown here.

Denial of Service Vulnerability This section discusses how the path validation algorithm defined in can lead to a denial-of-service vulnerability in X.509-based applications.

Policy Trees constructs the valid_policy_tree, a tree of certificate policies, during certification path validation. The nodes at any given depth in the tree correspond to policies asserted by a certificate in the certification path. A node's parent policy is the policy in the issuer certificate which was mapped to this policy, and a node's children are the policies it was mapped to in the subject certificate. For example, suppose a certification path contains:

• An intermediate certificate which asserts policy object identifiers (OIDs) OID1, OID2, and OID5. It contains mappings OID1 to OID3, and OID1 to OID4.
• An end-entity certificate which asserts policy OIDs OID2, OID3, and OID6.

This would result in the tree shown in . Note that OID5 and OID6 are not included or mapped across the whole path, so they do not appear in the final structure.

An Example X.509 Policy Tree

The complete algorithm for building this structure is described in steps (d), (e), and (f) of , steps (h), (i), (j) of , and steps (a), (b), and (g) of .

Exponential Growth The valid_policy_tree grows exponentially in the worst case. In step (d.1) of , a single policy P can produce multiple child nodes if multiple issuer policies map to P. This can cause the tree size to increase in size multiplicatively at each level. In particular, consider a certificate chain where every intermediate certificate asserts policies OID1 and OID2, and then contains the full Cartesian product of mappings:

• OID1 maps to OID1
• OID1 maps to OID2
• OID2 maps to OID1
• OID2 maps to OID2

At each depth, the tree would double in size. For example, if there are two intermediate certificates and one end-entity certificate, the resulting tree would be as depicted in .

An Example X.509 Policy Tree with Exponential Growth

Attack Vector An attacker can use the exponential growth to mount a denial-of-service attack against an X.509-based application. The attacker sends certificate chain as in and triggers the target application's certificate validation process. For example, the target application may be a TLS server that performs client certificate validation. The target application will consume far more resources processing the input than the attacker consumed to send it, preventing it from servicing other clients.

Avoiding Exponential Growth This document mitigates the denial-of-service vulnerability described in by replacing the policy tree with a policy graph structure, described in this section. The policy graph grows linearly instead of exponentially. This removes the asymmetric cost in policy validation. X.509 implementations SHOULD perform policy validation by building a policy graph, following the procedure described in . This replacement procedure computes the same policies as in , however one of the outputs is in a different form. See for details. describes alternative mitigations for implementations that depend on the original, exponential-sized output.

Policy Graphs The tree structure from is an unnecessarily inefficient representation of a certification path's policy mappings. A single certificate policy may correspond to multiple nodes, but each node is identical, with identical children. This redundancy is the source of the exponential growth described in . A policy graph is a directed acyclic graph of policy nodes. Where adds multiple duplicate nodes, a policy graph adds a single node with multiple parents. See for the procedure for building this structure. shows the updated representation of the example in .

A More Efficient Representation of an X.509 Policy Tree

This graph's size is bounded linearly by the total number of certificate policies () and policy mappings (). The policy tree from is the tree of all paths from the root to a leaf in the policy graph, so no information is lost in the graph representation.

Verification Outputs describes the entire valid_policy_tree structure as an output of the verification process. Section 12.2 of instead only outputs the authorities-constrained policies, the user-constrained policies, and their associated qualifiers. As the valid_policy_tree is the exponential structure, computing it reintroduces the denial-of-service vulnerability. X.509 implementations SHOULD NOT output the entire valid_policy_tree structure and instead SHOULD limit output to just the set of authorities-constrained and/or user-constrained policies, as described in . and discuss other mitigations for applications where this option is not available. X.509 implementations MAY omit policy qualifiers from the output to simplify processing. Note already recommends that certification authorities omit policy qualifiers from policy information terms.

Updates to RFC 5280 This section provides updates to . This implements the changes described in .

Updates to Section 6.1 This update replaces a paragraph of as follows: OLD:

• A particular certification path may not, however, be appropriate for all applications. Therefore, an application MAY augment this algorithm to further limit the set of valid paths. The path validation process also determines the set of certificate policies that are valid for this path, based on the certificate policies extension, policy mappings extension, policy constraints extension, and inhibit anyPolicy extension. To achieve this, the path validation algorithm constructs a valid policy tree. If the set of certificate policies that are valid for this path is not empty, then the result will be a valid policy tree of depth n, otherwise the result will be a null valid policy tree.

NEW:

• A particular certification path may not, however, be appropriate for all applications. Therefore, an application MAY augment this algorithm to further limit the set of valid paths. The path validation process also determines the set of certificate policies that are valid for this path, based on the certificate policies extension, policy mappings extension, policy constraints extension, and inhibit anyPolicy extension. To achieve this, the path validation algorithm constructs a valid policy set, which may be empty if no certificate policies are valid for this path.

Updates to Section 6.1.2 This update replaces entry (a) of with the following text:

1. valid_policy_graph: A directed acyclic graph of certificate policies with their optional qualifiers; each of the leaves of the graph represents a valid policy at this stage in the certification path validation. If valid policies exist at this stage in the certification path validation, the depth of the graph is equal to the number of certificates in the chain that have been processed. If valid policies do not exist at this stage in the certification path validation, the graph is set to NULL. Once the graph is set to NULL, policy processing ceases. Implementations MAY omit qualifiers if not returned in the output. Each node in the valid_policy_graph includes three data objects: the valid policy, a set of associated policy qualifiers, and a set of one or more expected policy values. Nodes in the graph can be divided into depths, numbered starting from zero. A node at depth x can have zero or more children at depth x+1, with the exception of depth zero, one or more parents at depth x-1. No other edges between nodes may exist. If the node is at depth x, the components of the node have the following semantics:
   1. The valid_policy is a single policy OID representing a valid policy for the path of length x.
   2. The qualifier_set is a set of policy qualifiers associated with the valid policy in certificate x. It is only necessary to maintain this field if policy qualifiers are returned to the application. See Section 6.1.5, step (g).
   3. The expected_policy_set contains one or more policy OIDs that would satisfy this policy in the certificate x+1.
   The initial value of the valid_policy_graph is a single node with valid_policy anyPolicy, an empty qualifier_set, and an expected_policy_set with the single value anyPolicy. This node is considered to be at depth zero. The graph additionally satisfies the following invariants:
   • For any depth x and policy OID P-OID, there is at most one node at depth x whose valid_policy is P-OID.
   • The expected_policy_set of a node whose valid_policy is anyPolicy is always {anyPolicy}.
   • A node at depth x whose valid_policy is anyPolicy, except for the one at depth zero, always has exactly one parent: a node at depth x-1 whose valid_policy is also anyPolicy.
   • Each node at depth greater than 0 has either one or more parent nodes whose valid_policy is not anyPolicy, or a single parent node whose valid_policy is anyPolicy. That is, a node cannot simultaneously be a child of both anyPolicy and some non-anyPolicy OID.
   is a graphic representation of the initial state of the valid_policy_graph. Additional figures will use this format to describe changes in the valid_policy_graph during path processing.

   Initial value of the valid_policy_graph State Variable

Updates to Section 6.1.3 This update replaces steps (d), (e), and (f) of with the following text:

4. If the certificate policies extension is present in the certificate and the valid_policy_graph is not NULL, process the policy information by performing the following steps in order:
   1. For each policy P not equal to anyPolicy in the certificate policies extension, let P-OID denote the OID for policy P and P-Q denote the qualifier set for policy P. Perform the following steps in order:
      1. Let parent_nodes be the nodes at depth i-1 in the valid_policy_graph where P-OID is in the expected_policy_set. If parent_nodes is not empty, create a child node as follows: set the valid_policy to P-OID, set the qualifier_set to P-Q, set the expected_policy_set to {P-OID}, and set the parent nodes to parent_nodes. For example, consider a valid_policy_graph with a node of depth i-1 where the expected_policy_set is {Gold, White}, and a second node where the expected_policy_set is {Gold, Yellow}. Assume the certificate policies Gold and Silver appear in the certificate policies extension of certificate i. The Gold policy is matched, but the Silver policy is not. This rule will generate a child node of depth i for the Gold policy. The result is shown as .

         Processing an Exact Match

      2. If there was no match in step (i) and the valid_policy_graph includes a node of depth i-1 with the valid_policy anyPolicy, generate a child node with the following values: set the valid_policy to P-OID, set the qualifier_set to P-Q, set the expected_policy_set to {P-OID}, and set the parent node to the anyPolicy node at depth i-1. For example, consider a valid_policy_graph with a node of depth i-1 where the valid_policy is anyPolicy. Assume the certificate policies Gold and Silver appear in the certificate policies extension of certificate i. The Gold policy does not have a qualifier, but the Silver policy has the qualifier Q-Silver. If Gold and Silver were not matched in (i) above, this rule will generate two child nodes of depth i, one for each policy. The result is shown as .

         Processing Unmatched Policies when a Leaf Node Specifies anyPolicy

   2. If the certificate policies extension includes the policy anyPolicy with the qualifier set AP-Q and either (a) inhibit_anyPolicy is greater than 0 or (b) i<n and the certificate is self-issued, then: For each policy OID P-OID (including anyPolicy) which appears in the expected_policy_set of some node in the valid_policy_graph for depth i-1, if P-OID does not appear as the valid_policy of some node at depth i, create a single child node with the following values: set the valid_policy to P-OID, set the qualifier_set to AP-Q, set the expected_policy_set to {P-OID}, and set the parents to the nodes at depth i-1 where P-OID appears in expected_policy_set. This is equivalent to running step (1) above, as if the certificate policies extension contained a policy with OID P-OID and qualifier set AP-Q. For example, consider a valid_policy_graph with a node of depth i-1 where the expected_policy_set is {Gold, Silver}, and a second node of depth i-1 where the expected_policy_set is {Gold, Bronze}. Assume anyPolicy appears in the certificate policies extension of certificate i with policy qualifiers AP-Q, but Gold and Silver do not appear. This rule will generate two child nodes of depth i, one for each policy. The result is shown below as .

      Processing Unmatched Policies When the Certificate Policies Extension Specifies anyPolicy

   3. If there is a node in the valid_policy_graph of depth i-1 or less without any child nodes, delete that node. Repeat this step until there are no nodes of depth i-1 or less without children. For example, consider the valid_policy_graph shown in below. The two nodes at depth i-1 that are marked with an 'X' have no children, and they are deleted. Applying this rule to the resulting graph will cause the nodes at depth i-2 that is marked with a 'Y' to be deleted. In the resulting graph, there are no nodes of depth i-1 or less without children, and this step is complete.

      Pruning the valid_policy_graph

5. If the certificate policies extension is not present, set the valid_policy_graph to NULL.
6. Verify that either explicit_policy is greater than 0 or the valid_policy_graph is not equal to NULL;

Updates to Section 6.1.4 This update replaces step (b) of with the following text:

2. If a policy mappings extension is present, then for each issuerDomainPolicy ID-P in the policy mappings extension:
   1. If the policy_mapping variable is greater than 0 and there is a node in the valid_policy_graph of depth i where ID-P is the valid_policy, set expected_policy_set to the set of subjectDomainPolicy values that are specified as equivalent to ID-P by the policy mappings extension.
   2. If the policy_mapping variable is greater than 0, no node of depth i in the valid_policy_graph has a valid_policy of ID-P, but there is a node of depth i with a valid_policy of anyPolicy, then generate a child node of the node of depth i-1 that has a valid_policy of anyPolicy as follows:
      1. set the valid_policy to ID-P;
      2. set the qualifier_set to the qualifier set of the policy anyPolicy in the certificate policies extension of certificate i; and
      3. set the expected_policy_set to the set of subjectDomainPolicy values that are specified as equivalent to ID-P by the policy mappings extension.
   3. If the policy_mapping variable is equal to 0:
      1. delete the node, if any, of depth i in the valid_policy_graph where ID-P is the valid_policy.
      2. If there is a node in the valid_policy_graph of depth i-1 or less without any child nodes, delete that node. Repeat this step until there are no nodes of depth i-1 or less without children.

Updates to Section 6.1.5 This update replaces step (g) of with the following text:

7. Calculate the user_constrained_policy_set as follows. The user_constrained_policy_set is a set of policy OIDs, along with associated policy qualifiers.
   1. If the valid_policy_graph is NULL, set valid_policy_node_set to the empty set.
   2. If the valid_policy_graph is not NULL, set valid_policy_node_set to the set of policy nodes whose valid_policy is not anyPolicy and whose parent list is a single node with valid_policy of anyPolicy.
   3. If the valid_policy_graph is not NULL and contains a node of depth n with the valid_policy anyPolicy, add it to valid_policy_node_set.
   4. Compute authority_constrained_policy_set, a set of policy OIDs and associated qualifiers as follows. For each node in valid_policy_node_set:
      1. Add the node's valid_policy to authority_constrained_policy_set.
      2. Collect all qualifiers in the node, its ancestors, and descendants and associate them with valid_policy. Applications that do not use policy qualifiers MAY skip this step to simplify processing.
   5. Set user_constrained_policy_set to authority_constrained_policy_set.
   6. If the user-initial-policy-set is not anyPolicy:
      1. Remove any elements of user_constrained_policy_set which do not appear in user-initial-policy-set.
      2. If anyPolicy appears in authority_constrained_policy_set with qualifiers AP-Q, for each OID P-OID in user-initial-policy-set which does not appear in user_constrained_policy_set, add P-OID with qualifiers AP-Q to user_constrained_policy_set.

Additionally, this update replaces the final paragraph as follows: OLD:

• If either (1) the value of explicit_policy variable is greater than zero or (2) the valid_policy_tree is not NULL, then path processing has succeeded.

NEW:

• If either (1) the value of explicit_policy variable is greater than zero or (2) the user_constrained_policy_set is not empty, then path processing has succeeded.

Updates to Section 6.1.6 This update replaces with the following text:

• If path processing succeeds, the procedure terminates, returning a success indication together with final value of the user_constrained_policy_set, the working_public_key, the working_public_key_algorithm, and the working_public_key_parameters. Note the original procedure described in included a valid_policy_tree structure as part of the output. This structure grows exponentially in the size of the input, so computing it risks denial-of-service vulnerabilities in X.509-based applications, such as and . Accordingly, this output is deprecated. Computing this structure is NOT RECOMMENDED. An implementation which requires valid_policy_tree for compatibility with legacy systems may compute it from valid_policy_graph by recursively duplicating every multi-parent node. This may be done on-demand when the calling application first requests this output. However, this computation may consume exponential time and memory, so such implementations SHOULD mitigate denial-of-service in other ways, such as limiting the depth or size of the tree.

Other Mitigations X.509 implementations that are unable switch to the policy graph structure SHOULD mitigate the denial-of-service attack in other ways. This section describes alternate mitigation and partial mitigation strategies.

Limit Certificate Depth The policy tree grows exponentially in the depth of a certification path, so limiting the depth and certificate size can mitigate the attack. However, this option may not be viable for all applications. Too low of a limit may reject existing paths which the application wishes to accept. Too high of a limit may still admit a DoS attack for the application. By modifying the example in to increase the number of policies asserted in each ertificate, an attacker could still achieve O(N^(depth/2)) scaling.

Limit Policy Tree Size The attack can be mitigated by limiting the number of nodes in the policy tree, and rejecting the certification path if this limit is reached. This limit should be set high enough to still admit existing valid certification paths for the application, but low enough to no longer admit a DoS attack.

Inhibit Policy Mapping If policy mapping is disabled via the initial-policy-mapping-inhibit setting (see ), the attack is mitigated. This also significantly simplifies the X.509 implementation, which reduces the risk of other security bugs. However, this will break compatibility with any existing certification paths which rely on policy mapping. To facilitate this mitigation, certificate authorities SHOULD NOT issue certificates with the policy mappings extension (). Applications maintaining policies for accepted trust anchors are RECOMMENDED to forbid this extension in participating certificate authorities.

Disable Policy Checking An X.509 validator can mitigate this attack by disabling policy validation entirely. This may be viable for applications which do not require policy validation. In this case, critical policy-related extensions, notably the policy constraints (), MUST be treated as unrecognized extensions as in and be rejected.

Verify Signatures First X.509 validators SHOULD verify signatures in certification paths before or in conjunction with policy verification. This limits the attack to entities in control of CA certificates. For some applications, this may be sufficient to mitigate the attack. However, other applications may still be impacted. For example:

• Any application that evaluates an untrusted PKI, such as a hosting provider that evaluates a customer-supplied PKI
• Any application that evaluates an otherwise trusted PKI, but where untrusted entities have technically-constrained intermediate certificates where policy mapping and path length are unconstrained.

Security Considerations discusses how 's policy tree algorithm can lead to denial-of-service vulnerabilities in X.509-based applications, such as and . replaces this algorithm to avoid this issue. As discussed in , the new structure scales linearly with the input. This means input limits in X.509 validators will more naturally bound processing time, thus avoiding these vulnerabilities.

IANA Considerations This document has no IANA actions.

References Normative References This memo profiles the X.509 v3 certificate and X.509 v2 certificate revocation list (CRL) for use in the Internet. An overview of this approach and model is provided as an introduction. The X.509 v3 certificate format is described in detail, with additional information regarding the format and semantics of Internet name forms. Standard certificate extensions are described and two Internet-specific extensions are defined. A set of required certificate extensions is specified. The X.509 v2 CRL format is described in detail along with standard and Internet-specific extensions. An algorithm for X.509 certification path validation is described. An ASN.1 module and examples are provided in the appendices. [STANDARDS-TRACK] In many standards track documents several words are used to signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. RFC 2119 specifies common key words that may be used in protocol specifications. This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the defined special meanings. Informative References International Telecommunications Union This document specifies version 1.3 of the Transport Layer Security (TLS) protocol. TLS allows client/server applications to communicate over the Internet in a way that is designed to prevent eavesdropping, tampering, and message forgery. This document updates RFCs 5705 and 6066, and obsoletes RFCs 5077, 5246, and 6961. This document also specifies new requirements for TLS 1.2 implementations.

Acknowledgements The author thanks Bob Beck, Adam Langley, Matt Mueller, and Ryan Sleevi for many valuable discussions that led to discovering this issue, understanding it, and developing the mitigation.