verify.go

// Copyright 2011 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package x509

import (
	"bytes"
	"errors"
	"fmt"
	"net"
	"net/url"
	"reflect"
	"runtime"
	"strconv"
	"strings"
	"time"
	"unicode/utf8"

	"github.com/google/certificate-transparency-go/asn1"
)

type InvalidReason int

const (
	// NotAuthorizedToSign results when a certificate is signed by another
	// which isn't marked as a CA certificate.
	NotAuthorizedToSign InvalidReason = iota
	// Expired results when a certificate has expired, based on the time
	// given in the VerifyOptions.
	Expired
	// CANotAuthorizedForThisName results when an intermediate or root
	// certificate has a name constraint which doesn't permit a DNS or
	// other name (including IP address) in the leaf certificate.
	CANotAuthorizedForThisName
	// TooManyIntermediates results when a path length constraint is
	// violated.
	TooManyIntermediates
	// IncompatibleUsage results when the certificate's key usage indicates
	// that it may only be used for a different purpose.
	IncompatibleUsage
	// NameMismatch results when the subject name of a parent certificate
	// does not match the issuer name in the child.
	NameMismatch
	// NameConstraintsWithoutSANs results when a leaf certificate doesn't
	// contain a Subject Alternative Name extension, but a CA certificate
	// contains name constraints.
	NameConstraintsWithoutSANs
	// UnconstrainedName results when a CA certificate contains permitted
	// name constraints, but leaf certificate contains a name of an
	// unsupported or unconstrained type.
	UnconstrainedName
	// TooManyConstraints results when the number of comparision operations
	// needed to check a certificate exceeds the limit set by
	// VerifyOptions.MaxConstraintComparisions. This limit exists to
	// prevent pathological certificates can consuming excessive amounts of
	// CPU time to verify.
	TooManyConstraints
	// CANotAuthorizedForExtKeyUsage results when an intermediate or root
	// certificate does not permit an extended key usage that is claimed by
	// the leaf certificate.
	CANotAuthorizedForExtKeyUsage
)

// CertificateInvalidError results when an odd error occurs. Users of this
// library probably want to handle all these errors uniformly.
type CertificateInvalidError struct {
	Cert   *Certificate
	Reason InvalidReason
	Detail string
}

func (e CertificateInvalidError) Error() string {
	switch e.Reason {
	case NotAuthorizedToSign:
		return "x509: certificate is not authorized to sign other certificates"
	case Expired:
		return "x509: certificate has expired or is not yet valid"
	case CANotAuthorizedForThisName:
		return "x509: a root or intermediate certificate is not authorized to sign for this name: " + e.Detail
	case CANotAuthorizedForExtKeyUsage:
		return "x509: a root or intermediate certificate is not authorized for an extended key usage: " + e.Detail
	case TooManyIntermediates:
		return "x509: too many intermediates for path length constraint"
	case IncompatibleUsage:
		return "x509: certificate specifies an incompatible key usage: " + e.Detail
	case NameMismatch:
		return "x509: issuer name does not match subject from issuing certificate"
	case NameConstraintsWithoutSANs:
		return "x509: issuer has name constraints but leaf doesn't have a SAN extension"
	case UnconstrainedName:
		return "x509: issuer has name constraints but leaf contains unknown or unconstrained name: " + e.Detail
	}
	return "x509: unknown error"
}

// HostnameError results when the set of authorized names doesn't match the
// requested name.
type HostnameError struct {
	Certificate *Certificate
	Host        string
}

func (h HostnameError) Error() string {
	c := h.Certificate

	var valid string
	if ip := net.ParseIP(h.Host); ip != nil {
		// Trying to validate an IP
		if len(c.IPAddresses) == 0 {
			return "x509: cannot validate certificate for " + h.Host + " because it doesn't contain any IP SANs"
		}
		for _, san := range c.IPAddresses {
			if len(valid) > 0 {
				valid += ", "
			}
			valid += san.String()
		}
	} else {
		if c.hasSANExtension() {
			valid = strings.Join(c.DNSNames, ", ")
		} else {
			valid = c.Subject.CommonName
		}
	}

	if len(valid) == 0 {
		return "x509: certificate is not valid for any names, but wanted to match " + h.Host
	}
	return "x509: certificate is valid for " + valid + ", not " + h.Host
}

// UnknownAuthorityError results when the certificate issuer is unknown
type UnknownAuthorityError struct {
	Cert *Certificate
	// hintErr contains an error that may be helpful in determining why an
	// authority wasn't found.
	hintErr error
	// hintCert contains a possible authority certificate that was rejected
	// because of the error in hintErr.
	hintCert *Certificate
}

func (e UnknownAuthorityError) Error() string {
	s := "x509: certificate signed by unknown authority"
	if e.hintErr != nil {
		certName := e.hintCert.Subject.CommonName
		if len(certName) == 0 {
			if len(e.hintCert.Subject.Organization) > 0 {
				certName = e.hintCert.Subject.Organization[0]
			} else {
				certName = "serial:" + e.hintCert.SerialNumber.String()
			}
		}
		s += fmt.Sprintf(" (possibly because of %q while trying to verify candidate authority certificate %q)", e.hintErr, certName)
	}
	return s
}

// SystemRootsError results when we fail to load the system root certificates.
type SystemRootsError struct {
	Err error
}

func (se SystemRootsError) Error() string {
	msg := "x509: failed to load system roots and no roots provided"
	if se.Err != nil {
		return msg + "; " + se.Err.Error()
	}
	return msg
}

// errNotParsed is returned when a certificate without ASN.1 contents is
// verified. Platform-specific verification needs the ASN.1 contents.
var errNotParsed = errors.New("x509: missing ASN.1 contents; use ParseCertificate")

// VerifyOptions contains parameters for Certificate.Verify. It's a structure
// because other PKIX verification APIs have ended up needing many options.
type VerifyOptions struct {
	DNSName       string
	Intermediates *CertPool
	Roots         *CertPool // if nil, the system roots are used
	CurrentTime   time.Time // if zero, the current time is used
	// Options to disable various verification checks.
	DisableTimeChecks              bool
	DisableCriticalExtensionChecks bool
	DisableNameChecks              bool
	DisableEKUChecks               bool
	DisablePathLenChecks           bool
	DisableNameConstraintChecks    bool
	// KeyUsage specifies which Extended Key Usage values are acceptable. A leaf
	// certificate is accepted if it contains any of the listed values. An empty
	// list means ExtKeyUsageServerAuth. To accept any key usage, include
	// ExtKeyUsageAny.
	//
	// Certificate chains are required to nest extended key usage values,
	// irrespective of this value. This matches the Windows CryptoAPI behavior,
	// but not the spec.
	KeyUsages []ExtKeyUsage
	// MaxConstraintComparisions is the maximum number of comparisons to
	// perform when checking a given certificate's name constraints. If
	// zero, a sensible default is used. This limit prevents pathological
	// certificates from consuming excessive amounts of CPU time when
	// validating.
	MaxConstraintComparisions int
}

const (
	leafCertificate = iota
	intermediateCertificate
	rootCertificate
)

// rfc2821Mailbox represents a “mailbox” (which is an email address to most
// people) by breaking it into the “local” (i.e. before the '@') and “domain”
// parts.
type rfc2821Mailbox struct {
	local, domain string
}

// parseRFC2821Mailbox parses an email address into local and domain parts,
// based on the ABNF for a “Mailbox” from RFC 2821. According to
// https://tools.ietf.org/html/rfc5280#section-4.2.1.6 that's correct for an
// rfc822Name from a certificate: “The format of an rfc822Name is a "Mailbox"
// as defined in https://tools.ietf.org/html/rfc2821#section-4.1.2”.
func parseRFC2821Mailbox(in string) (mailbox rfc2821Mailbox, ok bool) {
	if len(in) == 0 {
		return mailbox, false
	}

	localPartBytes := make([]byte, 0, len(in)/2)

	if in[0] == '"' {
		// Quoted-string = DQUOTE *qcontent DQUOTE
		// non-whitespace-control = %d1-8 / %d11 / %d12 / %d14-31 / %d127
		// qcontent = qtext / quoted-pair
		// qtext = non-whitespace-control /
		//         %d33 / %d35-91 / %d93-126
		// quoted-pair = ("\" text) / obs-qp
		// text = %d1-9 / %d11 / %d12 / %d14-127 / obs-text
		//
		// (Names beginning with “obs-” are the obsolete syntax from
		// https://tools.ietf.org/html/rfc2822#section-4. Since it has
		// been 16 years, we no longer accept that.)
		in = in[1:]
	QuotedString:
		for {
			if len(in) == 0 {
				return mailbox, false
			}
			c := in[0]
			in = in[1:]

			switch {
			case c == '"':
				break QuotedString

			case c == '\\':
				// quoted-pair
				if len(in) == 0 {
					return mailbox, false
				}
				if in[0] == 11 ||
					in[0] == 12 ||
					(1 <= in[0] && in[0] <= 9) ||
					(14 <= in[0] && in[0] <= 127) {
					localPartBytes = append(localPartBytes, in[0])
					in = in[1:]
				} else {
					return mailbox, false
				}

			case c == 11 ||
				c == 12 ||
				// Space (char 32) is not allowed based on the
				// BNF, but RFC 3696 gives an example that
				// assumes that it is. Several “verified”
				// errata continue to argue about this point.
				// We choose to accept it.
				c == 32 ||
				c == 33 ||
				c == 127 ||
				(1 <= c && c <= 8) ||
				(14 <= c && c <= 31) ||
				(35 <= c && c <= 91) ||
				(93 <= c && c <= 126):
				// qtext
				localPartBytes = append(localPartBytes, c)

			default:
				return mailbox, false
			}
		}
	} else {
		// Atom ("." Atom)*
	NextChar:
		for len(in) > 0 {
			// atext from https://tools.ietf.org/html/rfc2822#section-3.2.4
			c := in[0]

			switch {
			case c == '\\':
				// Examples given in RFC 3696 suggest that
				// escaped characters can appear outside of a
				// quoted string. Several “verified” errata
				// continue to argue the point. We choose to
				// accept it.
				in = in[1:]
				if len(in) == 0 {
					return mailbox, false
				}
				fallthrough

			case ('0' <= c && c <= '9') ||
				('a' <= c && c <= 'z') ||
				('A' <= c && c <= 'Z') ||
				c == '!' || c == '#' || c == '$' || c == '%' ||
				c == '&' || c == '\'' || c == '*' || c == '+' ||
				c == '-' || c == '/' || c == '=' || c == '?' ||
				c == '^' || c == '_' || c == '`' || c == '{' ||
				c == '|' || c == '}' || c == '~' || c == '.':
				localPartBytes = append(localPartBytes, in[0])
				in = in[1:]

			default:
				break NextChar
			}
		}

		if len(localPartBytes) == 0 {
			return mailbox, false
		}

		// https://tools.ietf.org/html/rfc3696#section-3
		// “period (".") may also appear, but may not be used to start
		// or end the local part, nor may two or more consecutive
		// periods appear.”
		twoDots := []byte{'.', '.'}
		if localPartBytes[0] == '.' ||
			localPartBytes[len(localPartBytes)-1] == '.' ||
			bytes.Contains(localPartBytes, twoDots) {
			return mailbox, false
		}
	}

	if len(in) == 0 || in[0] != '@' {
		return mailbox, false
	}
	in = in[1:]

	// The RFC species a format for domains, but that's known to be
	// violated in practice so we accept that anything after an '@' is the
	// domain part.
	if _, ok := domainToReverseLabels(in); !ok {
		return mailbox, false
	}

	mailbox.local = string(localPartBytes)
	mailbox.domain = in
	return mailbox, true
}

// domainToReverseLabels converts a textual domain name like foo.example.com to
// the list of labels in reverse order, e.g. ["com", "example", "foo"].
func domainToReverseLabels(domain string) (reverseLabels []string, ok bool) {
	for len(domain) > 0 {
		if i := strings.LastIndexByte(domain, '.'); i == -1 {
			reverseLabels = append(reverseLabels, domain)
			domain = ""
		} else {
			reverseLabels = append(reverseLabels, domain[i+1:len(domain)])
			domain = domain[:i]
		}
	}

	if len(reverseLabels) > 0 && len(reverseLabels[0]) == 0 {
		// An empty label at the end indicates an absolute value.
		return nil, false
	}

	for _, label := range reverseLabels {
		if len(label) == 0 {
			// Empty labels are otherwise invalid.
			return nil, false
		}

		for _, c := range label {
			if c < 33 || c > 126 {
				// Invalid character.
				return nil, false
			}
		}
	}

	return reverseLabels, true
}

func matchEmailConstraint(mailbox rfc2821Mailbox, constraint string) (bool, error) {
	// If the constraint contains an @, then it specifies an exact mailbox
	// name.
	if strings.Contains(constraint, "@") {
		constraintMailbox, ok := parseRFC2821Mailbox(constraint)
		if !ok {
			return false, fmt.Errorf("x509: internal error: cannot parse constraint %q", constraint)
		}
		return mailbox.local == constraintMailbox.local && strings.EqualFold(mailbox.domain, constraintMailbox.domain), nil
	}

	// Otherwise the constraint is like a DNS constraint of the domain part
	// of the mailbox.
	return matchDomainConstraint(mailbox.domain, constraint)
}

func matchURIConstraint(uri *url.URL, constraint string) (bool, error) {
	// https://tools.ietf.org/html/rfc5280#section-4.2.1.10
	// “a uniformResourceIdentifier that does not include an authority
	// component with a host name specified as a fully qualified domain
	// name (e.g., if the URI either does not include an authority
	// component or includes an authority component in which the host name
	// is specified as an IP address), then the application MUST reject the
	// certificate.”

	host := uri.Host
	if len(host) == 0 {
		return false, fmt.Errorf("URI with empty host (%q) cannot be matched against constraints", uri.String())
	}

	if strings.Contains(host, ":") && !strings.HasSuffix(host, "]") {
		var err error
		host, _, err = net.SplitHostPort(uri.Host)
		if err != nil {
			return false, err
		}
	}

	if strings.HasPrefix(host, "[") && strings.HasSuffix(host, "]") ||
		net.ParseIP(host) != nil {
		return false, fmt.Errorf("URI with IP (%q) cannot be matched against constraints", uri.String())
	}

	return matchDomainConstraint(host, constraint)
}

func matchIPConstraint(ip net.IP, constraint *net.IPNet) (bool, error) {
	if len(ip) != len(constraint.IP) {
		return false, nil
	}

	for i := range ip {
		if mask := constraint.Mask[i]; ip[i]&mask != constraint.IP[i]&mask {
			return false, nil
		}
	}

	return true, nil
}

func matchDomainConstraint(domain, constraint string) (bool, error) {
	// The meaning of zero length constraints is not specified, but this
	// code follows NSS and accepts them as matching everything.
	if len(constraint) == 0 {
		return true, nil
	}

	domainLabels, ok := domainToReverseLabels(domain)
	if !ok {
		return false, fmt.Errorf("x509: internal error: cannot parse domain %q", domain)
	}

	// RFC 5280 says that a leading period in a domain name means that at
	// least one label must be prepended, but only for URI and email
	// constraints, not DNS constraints. The code also supports that
	// behaviour for DNS constraints.

	mustHaveSubdomains := false
	if constraint[0] == '.' {
		mustHaveSubdomains = true
		constraint = constraint[1:]
	}

	constraintLabels, ok := domainToReverseLabels(constraint)
	if !ok {
		return false, fmt.Errorf("x509: internal error: cannot parse domain %q", constraint)
	}

	if len(domainLabels) < len(constraintLabels) ||
		(mustHaveSubdomains && len(domainLabels) == len(constraintLabels)) {
		return false, nil
	}

	for i, constraintLabel := range constraintLabels {
		if !strings.EqualFold(constraintLabel, domainLabels[i]) {
			return false, nil
		}
	}

	return true, nil
}

// checkNameConstraints checks that c permits a child certificate to claim the
// given name, of type nameType. The argument parsedName contains the parsed
// form of name, suitable for passing to the match function. The total number
// of comparisons is tracked in the given count and should not exceed the given
// limit.
func (c *Certificate) checkNameConstraints(count *int,
	maxConstraintComparisons int,
	nameType string,
	name string,
	parsedName interface{},
	match func(parsedName, constraint interface{}) (match bool, err error),
	permitted, excluded interface{}) error {

	excludedValue := reflect.ValueOf(excluded)

	*count += excludedValue.Len()
	if *count > maxConstraintComparisons {
		return CertificateInvalidError{c, TooManyConstraints, ""}
	}

	for i := 0; i < excludedValue.Len(); i++ {
		constraint := excludedValue.Index(i).Interface()
		match, err := match(parsedName, constraint)
		if err != nil {
			return CertificateInvalidError{c, CANotAuthorizedForThisName, err.Error()}
		}

		if match {
			return CertificateInvalidError{c, CANotAuthorizedForThisName, fmt.Sprintf("%s %q is excluded by constraint %q", nameType, name, constraint)}
		}
	}

	permittedValue := reflect.ValueOf(permitted)

	*count += permittedValue.Len()
	if *count > maxConstraintComparisons {
		return CertificateInvalidError{c, TooManyConstraints, ""}
	}

	ok := true
	for i := 0; i < permittedValue.Len(); i++ {
		constraint := permittedValue.Index(i).Interface()

		var err error
		if ok, err = match(parsedName, constraint); err != nil {
			return CertificateInvalidError{c, CANotAuthorizedForThisName, err.Error()}
		}

		if ok {
			break
		}
	}

	if !ok {
		return CertificateInvalidError{c, CANotAuthorizedForThisName, fmt.Sprintf("%s %q is not permitted by any constraint", nameType, name)}
	}

	return nil
}

const (
	checkingAgainstIssuerCert = iota
	checkingAgainstLeafCert
)

// ekuPermittedBy returns true iff the given extended key usage is permitted by
// the given EKU from a certificate. Normally, this would be a simple
// comparison plus a special case for the “any” EKU. But, in order to support
// existing certificates, some exceptions are made.
func ekuPermittedBy(eku, certEKU ExtKeyUsage, context int) bool {
	if certEKU == ExtKeyUsageAny || eku == certEKU {
		return true
	}

	// Some exceptions are made to support existing certificates. Firstly,
	// the ServerAuth and SGC EKUs are treated as a group.
	mapServerAuthEKUs := func(eku ExtKeyUsage) ExtKeyUsage {
		if eku == ExtKeyUsageNetscapeServerGatedCrypto || eku == ExtKeyUsageMicrosoftServerGatedCrypto {
			return ExtKeyUsageServerAuth
		}
		return eku
	}

	eku = mapServerAuthEKUs(eku)
	certEKU = mapServerAuthEKUs(certEKU)

	if eku == certEKU {
		return true
	}

	// If checking a requested EKU against the list in a leaf certificate there
	// are fewer exceptions.
	if context == checkingAgainstLeafCert {
		return false
	}

	// ServerAuth in a CA permits ClientAuth in the leaf.
	return (eku == ExtKeyUsageClientAuth && certEKU == ExtKeyUsageServerAuth) ||
		// Any CA may issue an OCSP responder certificate.
		eku == ExtKeyUsageOCSPSigning ||
		// Code-signing CAs can use Microsoft's commercial and
		// kernel-mode EKUs.
		(eku == ExtKeyUsageMicrosoftCommercialCodeSigning || eku == ExtKeyUsageMicrosoftKernelCodeSigning) && certEKU == ExtKeyUsageCodeSigning
}

// isValid performs validity checks on c given that it is a candidate to append
// to the chain in currentChain.
func (c *Certificate) isValid(certType int, currentChain []*Certificate, opts *VerifyOptions) error {
	if !opts.DisableCriticalExtensionChecks && len(c.UnhandledCriticalExtensions) > 0 {
		return UnhandledCriticalExtension{ID: c.UnhandledCriticalExtensions[0]}
	}

	if !opts.DisableNameChecks && len(currentChain) > 0 {
		child := currentChain[len(currentChain)-1]
		if !bytes.Equal(child.RawIssuer, c.RawSubject) {
			return CertificateInvalidError{c, NameMismatch, ""}
		}
	}

	if !opts.DisableTimeChecks {
		now := opts.CurrentTime
		if now.IsZero() {
			now = time.Now()
		}
		if now.Before(c.NotBefore) || now.After(c.NotAfter) {
			return CertificateInvalidError{c, Expired, ""}
		}
	}

	maxConstraintComparisons := opts.MaxConstraintComparisions
	if maxConstraintComparisons == 0 {
		maxConstraintComparisons = 250000
	}
	comparisonCount := 0

	var leaf *Certificate
	if certType == intermediateCertificate || certType == rootCertificate {
		if len(currentChain) == 0 {
			return errors.New("x509: internal error: empty chain when appending CA cert")
		}
		leaf = currentChain[0]
	}

	if !opts.DisableNameConstraintChecks && (certType == intermediateCertificate || certType == rootCertificate) && c.hasNameConstraints() {
		sanExtension, ok := leaf.getSANExtension()
		if !ok {
			// This is the deprecated, legacy case of depending on
			// the CN as a hostname. Chains modern enough to be
			// using name constraints should not be depending on
			// CNs.
			return CertificateInvalidError{c, NameConstraintsWithoutSANs, ""}
		}

		err := forEachSAN(sanExtension, func(tag int, data []byte) error {
			switch tag {
			case nameTypeEmail:
				name := string(data)
				mailbox, ok := parseRFC2821Mailbox(name)
				if !ok {
					return fmt.Errorf("x509: cannot parse rfc822Name %q", mailbox)
				}

				if err := c.checkNameConstraints(&comparisonCount, maxConstraintComparisons, "email address", name, mailbox,
					func(parsedName, constraint interface{}) (bool, error) {
						return matchEmailConstraint(parsedName.(rfc2821Mailbox), constraint.(string))
					}, c.PermittedEmailAddresses, c.ExcludedEmailAddresses); err != nil {
					return err
				}

			case nameTypeDNS:
				name := string(data)
				if _, ok := domainToReverseLabels(name); !ok {
					return fmt.Errorf("x509: cannot parse dnsName %q", name)
				}

				if err := c.checkNameConstraints(&comparisonCount, maxConstraintComparisons, "DNS name", name, name,
					func(parsedName, constraint interface{}) (bool, error) {
						return matchDomainConstraint(parsedName.(string), constraint.(string))
					}, c.PermittedDNSDomains, c.ExcludedDNSDomains); err != nil {
					return err
				}

			case nameTypeURI:
				name := string(data)
				uri, err := url.Parse(name)
				if err != nil {
					return fmt.Errorf("x509: internal error: URI SAN %q failed to parse", name)
				}

				if err := c.checkNameConstraints(&comparisonCount, maxConstraintComparisons, "URI", name, uri,
					func(parsedName, constraint interface{}) (bool, error) {
						return matchURIConstraint(parsedName.(*url.URL), constraint.(string))
					}, c.PermittedURIDomains, c.ExcludedURIDomains); err != nil {
					return err
				}

			case nameTypeIP:
				ip := net.IP(data)
				if l := len(ip); l != net.IPv4len && l != net.IPv6len {
					return fmt.Errorf("x509: internal error: IP SAN %x failed to parse", data)
				}

				if err := c.checkNameConstraints(&comparisonCount, maxConstraintComparisons, "IP address", ip.String(), ip,
					func(parsedName, constraint interface{}) (bool, error) {
						return matchIPConstraint(parsedName.(net.IP), constraint.(*net.IPNet))
					}, c.PermittedIPRanges, c.ExcludedIPRanges); err != nil {
					return err
				}

			default:
				// Unknown SAN types are ignored.
			}

			return nil
		})

		if err != nil {
			return err
		}
	}

	checkEKUs := !opts.DisableEKUChecks && certType == intermediateCertificate

	// If no extended key usages are specified, then all are acceptable.
	if checkEKUs && (len(c.ExtKeyUsage) == 0 && len(c.UnknownExtKeyUsage) == 0) {
		checkEKUs = false
	}

	// If the “any” key usage is permitted, then no more checks are needed.
	if checkEKUs {
		for _, caEKU := range c.ExtKeyUsage {
			comparisonCount++
			if caEKU == ExtKeyUsageAny {
				checkEKUs = false
				break
			}
		}
	}

	if checkEKUs {
	NextEKU:
		for _, eku := range leaf.ExtKeyUsage {
			if comparisonCount > maxConstraintComparisons {
				return CertificateInvalidError{c, TooManyConstraints, ""}
			}

			for _, caEKU := range c.ExtKeyUsage {
				comparisonCount++
				if ekuPermittedBy(eku, caEKU, checkingAgainstIssuerCert) {
					continue NextEKU
				}
			}

			oid, _ := oidFromExtKeyUsage(eku)
			return CertificateInvalidError{c, CANotAuthorizedForExtKeyUsage, fmt.Sprintf("EKU not permitted: %#v", oid)}
		}

	NextUnknownEKU:
		for _, eku := range leaf.UnknownExtKeyUsage {
			if comparisonCount > maxConstraintComparisons {
				return CertificateInvalidError{c, TooManyConstraints, ""}
			}

			for _, caEKU := range c.UnknownExtKeyUsage {
				comparisonCount++
				if caEKU.Equal(eku) {
					continue NextUnknownEKU
				}
			}

			return CertificateInvalidError{c, CANotAuthorizedForExtKeyUsage, fmt.Sprintf("EKU not permitted: %#v", eku)}
		}
	}

	// KeyUsage status flags are ignored. From Engineering Security, Peter
	// Gutmann: A European government CA marked its signing certificates as
	// being valid for encryption only, but no-one noticed. Another
	// European CA marked its signature keys as not being valid for
	// signatures. A different CA marked its own trusted root certificate
	// as being invalid for certificate signing. Another national CA
	// distributed a certificate to be used to encrypt data for the
	// country’s tax authority that was marked as only being usable for
	// digital signatures but not for encryption. Yet another CA reversed
	// the order of the bit flags in the keyUsage due to confusion over
	// encoding endianness, essentially setting a random keyUsage in
	// certificates that it issued. Another CA created a self-invalidating
	// certificate by adding a certificate policy statement stipulating
	// that the certificate had to be used strictly as specified in the
	// keyUsage, and a keyUsage containing a flag indicating that the RSA
	// encryption key could only be used for Diffie-Hellman key agreement.

	if certType == intermediateCertificate && (!c.BasicConstraintsValid || !c.IsCA) {
		return CertificateInvalidError{c, NotAuthorizedToSign, ""}
	}

	if !opts.DisablePathLenChecks && c.BasicConstraintsValid && c.MaxPathLen >= 0 {
		numIntermediates := len(currentChain) - 1
		if numIntermediates > c.MaxPathLen {
			return CertificateInvalidError{c, TooManyIntermediates, ""}
		}
	}

	return nil
}

// formatOID formats an ASN.1 OBJECT IDENTIFER in the common, dotted style.
func formatOID(oid asn1.ObjectIdentifier) string {
	ret := ""
	for i, v := range oid {
		if i > 0 {
			ret += "."
		}
		ret += strconv.Itoa(v)
	}
	return ret
}

// Verify attempts to verify c by building one or more chains from c to a
// certificate in opts.Roots, using certificates in opts.Intermediates if
// needed. If successful, it returns one or more chains where the first
// element of the chain is c and the last element is from opts.Roots.
//
// If opts.Roots is nil and system roots are unavailable the returned error
// will be of type SystemRootsError.
//
// Name constraints in the intermediates will be applied to all names claimed
// in the chain, not just opts.DNSName. Thus it is invalid for a leaf to claim
// example.com if an intermediate doesn't permit it, even if example.com is not
// the name being validated. Note that DirectoryName constraints are not
// supported.
//
// Extended Key Usage values are enforced down a chain, so an intermediate or
// root that enumerates EKUs prevents a leaf from asserting an EKU not in that
// list.
//
// WARNING: this function doesn't do any revocation checking.
func (c *Certificate) Verify(opts VerifyOptions) (chains [][]*Certificate, err error) {
	// Platform-specific verification needs the ASN.1 contents so
	// this makes the behavior consistent across platforms.
	if len(c.Raw) == 0 {
		return nil, errNotParsed
	}
	if opts.Intermediates != nil {
		for _, intermediate := range opts.Intermediates.certs {
			if len(intermediate.Raw) == 0 {
				return nil, errNotParsed
			}
		}
	}

	// Use Windows's own verification and chain building.
	if opts.Roots == nil && runtime.GOOS == "windows" {
		return c.systemVerify(&opts)
	}

	if opts.Roots == nil {
		opts.Roots = systemRootsPool()
		if opts.Roots == nil {
			return nil, SystemRootsError{systemRootsErr}
		}
	}

	err = c.isValid(leafCertificate, nil, &opts)
	if err != nil {
		return
	}

	if len(opts.DNSName) > 0 {
		err = c.VerifyHostname(opts.DNSName)
		if err != nil {
			return
		}
	}

	requestedKeyUsages := make([]ExtKeyUsage, len(opts.KeyUsages))
	copy(requestedKeyUsages, opts.KeyUsages)
	if len(requestedKeyUsages) == 0 {
		requestedKeyUsages = append(requestedKeyUsages, ExtKeyUsageServerAuth)
	}

	// If no key usages are specified, then any are acceptable.
	checkEKU := !opts.DisableEKUChecks && len(c.ExtKeyUsage) > 0

	for _, eku := range requestedKeyUsages {
		if eku == ExtKeyUsageAny {
			checkEKU = false
			break
		}
	}

	if checkEKU {
		foundMatch := false
	NextUsage:
		for _, eku := range requestedKeyUsages {
			for _, leafEKU := range c.ExtKeyUsage {
				if ekuPermittedBy(eku, leafEKU, checkingAgainstLeafCert) {
					foundMatch = true
					break NextUsage
				}
			}
		}

		if !foundMatch {
			msg := "leaf contains the following, recognized EKUs: "

			for i, leafEKU := range c.ExtKeyUsage {
				oid, ok := oidFromExtKeyUsage(leafEKU)
				if !ok {
					continue
				}

				if i > 0 {
					msg += ", "
				}
				msg += formatOID(oid)
			}

			return nil, CertificateInvalidError{c, IncompatibleUsage, msg}
		}
	}

	var candidateChains [][]*Certificate
	if opts.Roots.contains(c) {
		candidateChains = append(candidateChains, []*Certificate{c})
	} else {
		if candidateChains, err = c.buildChains(make(map[int][][]*Certificate), []*Certificate{c}, &opts); err != nil {
			return nil, err
		}
	}

	return candidateChains, nil
}

func appendToFreshChain(chain []*Certificate, cert *Certificate) []*Certificate {
	n := make([]*Certificate, len(chain)+1)
	copy(n, chain)
	n[len(chain)] = cert
	return n
}

func (c *Certificate) buildChains(cache map[int][][]*Certificate, currentChain []*Certificate, opts *VerifyOptions) (chains [][]*Certificate, err error) {
	possibleRoots, failedRoot, rootErr := opts.Roots.findVerifiedParents(c)
nextRoot:
	for _, rootNum := range possibleRoots {
		root := opts.Roots.certs[rootNum]

		for _, cert := range currentChain {
			if cert.Equal(root) {
				continue nextRoot
			}
		}

		err = root.isValid(rootCertificate, currentChain, opts)
		if err != nil {
			continue
		}
		chains = append(chains, appendToFreshChain(currentChain, root))
	}

	possibleIntermediates, failedIntermediate, intermediateErr := opts.Intermediates.findVerifiedParents(c)
nextIntermediate:
	for _, intermediateNum := range possibleIntermediates {
		intermediate := opts.Intermediates.certs[intermediateNum]
		for _, cert := range currentChain {
			if cert.Equal(intermediate) {
				continue nextIntermediate
			}
		}
		err = intermediate.isValid(intermediateCertificate, currentChain, opts)
		if err != nil {
			continue
		}
		var childChains [][]*Certificate
		childChains, ok := cache[intermediateNum]
		if !ok {
			childChains, err = intermediate.buildChains(cache, appendToFreshChain(currentChain, intermediate), opts)
			cache[intermediateNum] = childChains
		}
		chains = append(chains, childChains...)
	}

	if len(chains) > 0 {
		err = nil
	}

	if len(chains) == 0 && err == nil {
		hintErr := rootErr
		hintCert := failedRoot
		if hintErr == nil {
			hintErr = intermediateErr
			hintCert = failedIntermediate
		}
		err = UnknownAuthorityError{c, hintErr, hintCert}
	}

	return
}

func matchHostnames(pattern, host string) bool {
	host = strings.TrimSuffix(host, ".")
	pattern = strings.TrimSuffix(pattern, ".")

	if len(pattern) == 0 || len(host) == 0 {
		return false
	}

	patternParts := strings.Split(pattern, ".")
	hostParts := strings.Split(host, ".")

	if len(patternParts) != len(hostParts) {
		return false
	}

	for i, patternPart := range patternParts {
		if i == 0 && patternPart == "*" {
			continue
		}
		if patternPart != hostParts[i] {
			return false
		}
	}

	return true
}

// toLowerCaseASCII returns a lower-case version of in. See RFC 6125 6.4.1. We use
// an explicitly ASCII function to avoid any sharp corners resulting from
// performing Unicode operations on DNS labels.
func toLowerCaseASCII(in string) string {
	// If the string is already lower-case then there's nothing to do.
	isAlreadyLowerCase := true
	for _, c := range in {
		if c == utf8.RuneError {
			// If we get a UTF-8 error then there might be
			// upper-case ASCII bytes in the invalid sequence.
			isAlreadyLowerCase = false
			break
		}
		if 'A' <= c && c <= 'Z' {
			isAlreadyLowerCase = false
			break
		}
	}

	if isAlreadyLowerCase {
		return in
	}

	out := []byte(in)
	for i, c := range out {
		if 'A' <= c && c <= 'Z' {
			out[i] += 'a' - 'A'
		}
	}
	return string(out)
}

// VerifyHostname returns nil if c is a valid certificate for the named host.
// Otherwise it returns an error describing the mismatch.
func (c *Certificate) VerifyHostname(h string) error {
	// IP addresses may be written in [ ].
	candidateIP := h
	if len(h) >= 3 && h[0] == '[' && h[len(h)-1] == ']' {
		candidateIP = h[1 : len(h)-1]
	}
	if ip := net.ParseIP(candidateIP); ip != nil {
		// We only match IP addresses against IP SANs.
		// https://tools.ietf.org/html/rfc6125#appendix-B.2
		for _, candidate := range c.IPAddresses {
			if ip.Equal(candidate) {
				return nil
			}
		}
		return HostnameError{c, candidateIP}
	}

	lowered := toLowerCaseASCII(h)

	if c.hasSANExtension() {
		for _, match := range c.DNSNames {
			if matchHostnames(toLowerCaseASCII(match), lowered) {
				return nil
			}
		}
		// If Subject Alt Name is given, we ignore the common name.
	} else if matchHostnames(toLowerCaseASCII(c.Subject.CommonName), lowered) {
		return nil
	}

	return HostnameError{c, h}
}