rfc7638
Internet Engineering Task Force (IETF) M. Jones
Request for Comments: 7638 Microsoft
Category: Standards Track N. Sakimura
ISSN: 2070-1721 Nomura Research Institute
September 2015
JSON Web Key (JWK) Thumbprint
Abstract
This specification defines a method for computing a hash value over a
JSON Web Key (JWK). It defines which fields in a JWK are used in the
hash computation, the method of creating a canonical form for those
fields, and how to convert the resulting Unicode string into a byte
sequence to be hashed. The resulting hash value can be used for
identifying or selecting the key represented by the JWK that is the
subject of the thumbprint.
Status of This Memo
This is an Internet Standards Track document.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Further information on
Internet Standards is available in Section 2 of RFC 5741.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
http://www.rfc-editor.org/info/rfc7638.
Copyright Notice
Copyright (c) 2015 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
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.
Jones & Sakimura Standards Track [Page 1]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Notational Conventions . . . . . . . . . . . . . . . . . 2
2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. JSON Web Key (JWK) Thumbprint . . . . . . . . . . . . . . . . 3
3.1. Example JWK Thumbprint Computation . . . . . . . . . . . 4
3.2. JWK Members Used in the Thumbprint Computation . . . . . 6
3.2.1. JWK Thumbprint of a Private Key . . . . . . . . . . . 6
3.2.2. Why Not Include Optional Members? . . . . . . . . . . 7
3.3. Order and Representation of Members in Hash Input . . . . 7
3.4. Selection of Hash Function . . . . . . . . . . . . . . . 8
3.5. JWK Thumbprints of Keys Not in JWK Format . . . . . . . . 8
4. Practical JSON and Unicode Considerations . . . . . . . . . . 8
5. Relationship to Digests of X.509 Values . . . . . . . . . . . 9
6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 10
7. Security Considerations . . . . . . . . . . . . . . . . . . . 10
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.1. Normative References . . . . . . . . . . . . . . . . . . 11
8.2. Informative References . . . . . . . . . . . . . . . . . 12
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 13
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 13
1. Introduction
This specification defines a method for computing a hash value
(a.k.a. digest) over a JSON Web Key (JWK) [JWK]. It defines which
fields in a JWK are used in the hash computation, the method of
creating a canonical form for those fields, and how to convert the
resulting Unicode string into a byte sequence to be hashed. The
resulting hash value can be used for identifying or selecting the key
represented by the JWK that is the subject of the thumbprint, for
instance, by using the base64url-encoded JWK Thumbprint value as a
"kid" (key ID) value.
1.1. Notational Conventions
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
"Key words for use in RFCs to Indicate Requirement Levels" [RFC2119].
The interpretation should only be applied when the terms appear in
all capital letters.
Jones & Sakimura Standards Track [Page 2]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
2. Terminology
This specification uses the same terminology as the "JSON Web Key
(JWK)" [JWK], "JSON Web Signature (JWS)" [JWS], and "JSON Web
Algorithms (JWA)" [JWA] specifications.
This term is defined by this specification:
JWK Thumbprint
The digest value for a JWK.
3. JSON Web Key (JWK) Thumbprint
The thumbprint of a JSON Web Key (JWK) is computed as follows:
1. Construct a JSON object [RFC7159] containing only the required
members of a JWK representing the key and with no whitespace or
line breaks before or after any syntactic elements and with the
required members ordered lexicographically by the Unicode
[UNICODE] code points of the member names. (This JSON object is
itself a legal JWK representation of the key.)
2. Hash the octets of the UTF-8 representation of this JSON object
with a cryptographic hash function H. For example, SHA-256 [SHS]
might be used as H. See Section 3.4 for a discussion on the
choice of hash function.
The resulting value is the JWK Thumbprint with H of the JWK. The
details of this computation are further described in subsequent
sections.
Jones & Sakimura Standards Track [Page 3]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
3.1. Example JWK Thumbprint Computation
This section demonstrates the JWK Thumbprint computation for the JWK
below (with the long line broken for display purposes only):
{
"kty": "RSA",
"n": "0vx7agoebGcQSuuPiLJXZptN9nndrQmbXEps2aiAFbWhM78LhWx4cbbfAAt
VT86zwu1RK7aPFFxuhDR1L6tSoc_BJECPebWKRXjBZCiFV4n3oknjhMstn6
4tZ_2W-5JsGY4Hc5n9yBXArwl93lqt7_RN5w6Cf0h4QyQ5v-65YGjQR0_FD
W2QvzqY368QQMicAtaSqzs8KJZgnYb9c7d0zgdAZHzu6qMQvRL5hajrn1n9
1CbOpbISD08qNLyrdkt-bFTWhAI4vMQFh6WeZu0fM4lFd2NcRwr3XPksINH
aQ-G_xBniIqbw0Ls1jF44-csFCur-kEgU8awapJzKnqDKgw",
"e": "AQAB",
"alg": "RS256",
"kid": "2011-04-29"
}
As defined in "JSON Web Key (JWK)" [JWK] and "JSON Web Algorithms
(JWA)" [JWA], the required members for an RSA public key are:
o "kty"
o "n"
o "e"
Therefore, these are the members used in the thumbprint computation.
Their lexicographic order, per Section 3.3, is:
o "e"
o "kty"
o "n"
Therefore, the JSON object constructed as an intermediate step in the
computation is as follows (with the line broken for display purposes
only):
{"e":"AQAB","kty":"RSA","n":"0vx7agoebGcQSuuPiLJXZptN9nndrQmbXEps2
aiAFbWhM78LhWx4cbbfAAtVT86zwu1RK7aPFFxuhDR1L6tSoc_BJECPebWKRXjBZCi
FV4n3oknjhMstn64tZ_2W-5JsGY4Hc5n9yBXArwl93lqt7_RN5w6Cf0h4QyQ5v-65Y
GjQR0_FDW2QvzqY368QQMicAtaSqzs8KJZgnYb9c7d0zgdAZHzu6qMQvRL5hajrn1n
91CbOpbISD08qNLyrdkt-bFTWhAI4vMQFh6WeZu0fM4lFd2NcRwr3XPksINHaQ-G_x
BniIqbw0Ls1jF44-csFCur-kEgU8awapJzKnqDKgw"}
Jones & Sakimura Standards Track [Page 4]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
The octets of the UTF-8 representation of this JSON object are:
[123, 34, 101, 34, 58, 34, 65, 81, 65, 66, 34, 44, 34, 107, 116, 121,
34, 58, 34, 82, 83, 65, 34, 44, 34, 110, 34, 58, 34, 48, 118, 120,
55, 97, 103, 111, 101, 98, 71, 99, 81, 83, 117, 117, 80, 105, 76, 74,
88, 90, 112, 116, 78, 57, 110, 110, 100, 114, 81, 109, 98, 88, 69,
112, 115, 50, 97, 105, 65, 70, 98, 87, 104, 77, 55, 56, 76, 104, 87,
120, 52, 99, 98, 98, 102, 65, 65, 116, 86, 84, 56, 54, 122, 119, 117,
49, 82, 75, 55, 97, 80, 70, 70, 120, 117, 104, 68, 82, 49, 76, 54,
116, 83, 111, 99, 95, 66, 74, 69, 67, 80, 101, 98, 87, 75, 82, 88,
106, 66, 90, 67, 105, 70, 86, 52, 110, 51, 111, 107, 110, 106, 104,
77, 115, 116, 110, 54, 52, 116, 90, 95, 50, 87, 45, 53, 74, 115, 71,
89, 52, 72, 99, 53, 110, 57, 121, 66, 88, 65, 114, 119, 108, 57, 51,
108, 113, 116, 55, 95, 82, 78, 53, 119, 54, 67, 102, 48, 104, 52, 81,
121, 81, 53, 118, 45, 54, 53, 89, 71, 106, 81, 82, 48, 95, 70, 68,
87, 50, 81, 118, 122, 113, 89, 51, 54, 56, 81, 81, 77, 105, 99, 65,
116, 97, 83, 113, 122, 115, 56, 75, 74, 90, 103, 110, 89, 98, 57, 99,
55, 100, 48, 122, 103, 100, 65, 90, 72, 122, 117, 54, 113, 77, 81,
118, 82, 76, 53, 104, 97, 106, 114, 110, 49, 110, 57, 49, 67, 98, 79,
112, 98, 73, 83, 68, 48, 56, 113, 78, 76, 121, 114, 100, 107, 116,
45, 98, 70, 84, 87, 104, 65, 73, 52, 118, 77, 81, 70, 104, 54, 87,
101, 90, 117, 48, 102, 77, 52, 108, 70, 100, 50, 78, 99, 82, 119,
114, 51, 88, 80, 107, 115, 73, 78, 72, 97, 81, 45, 71, 95, 120, 66,
110, 105, 73, 113, 98, 119, 48, 76, 115, 49, 106, 70, 52, 52, 45, 99,
115, 70, 67, 117, 114, 45, 107, 69, 103, 85, 56, 97, 119, 97, 112,
74, 122, 75, 110, 113, 68, 75, 103, 119, 34, 125]
Using SHA-256 [SHS] as the hash function H, the JWK SHA-256
Thumbprint value is the SHA-256 hash of these octets, specifically:
[55, 54, 203, 177, 120, 124, 184, 48, 156, 119, 238, 140, 55, 5, 197,
225, 111, 251, 158, 133, 151, 21, 144, 31, 30, 76, 89, 177, 17, 130,
245, 123]
The base64url encoding [JWS] of this JWK SHA-256 Thumbprint value
(which might, for instance, be used as a "kid" (key ID) value) is:
NzbLsXh8uDCcd-6MNwXF4W_7noWXFZAfHkxZsRGC9Xs
Jones & Sakimura Standards Track [Page 5]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
3.2. JWK Members Used in the Thumbprint Computation
Only the required members of a key's representation are used when
computing its JWK Thumbprint value. As defined in "JSON Web Key
(JWK)" [JWK] and "JSON Web Algorithms (JWA)" [JWA], the required
members for an elliptic curve public key for the curves specified in
Section 6.2.1.1 of RFC 7518 [JWA], in lexicographic order, are:
o "crv"
o "kty"
o "x"
o "y"
The required members for an RSA public key, in lexicographic order,
are:
o "e"
o "kty"
o "n"
The required members for a symmetric key, in lexicographic order,
are:
o "k"
o "kty"
As other "kty" (key type) values are defined, the specifications
defining them should be similarly consulted to determine which
members, in addition to "kty", are required.
3.2.1. JWK Thumbprint of a Private Key
The JWK Thumbprint of a JWK representing a private key is computed as
the JWK Thumbprint of a JWK representing the corresponding public
key. This has the intentional benefit that the same JWK Thumbprint
value can be computed both by parties using either the public or
private key. The JWK Thumbprint can then be used to refer to both
keys of the key pair. Application context can be used to determine
if the public or private key is the one being referred to by the JWK
Thumbprint.
This specification defines the method of computing JWK Thumbprints of
JWKs representing private keys for interoperability reasons -- so
that different implementations computing JWK Thumbprints of private
keys will produce the same result.
Jones & Sakimura Standards Track [Page 6]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
3.2.2. Why Not Include Optional Members?
Optional members of JWKs are intentionally not included in the JWK
Thumbprint computation so that their absence or presence in the JWK
does not alter the resulting value. The JWK Thumbprint value is a
digest of the members required to represent the key as a JWK -- not
of additional data that may also accompany the key.
Optional members are not included so that the JWK Thumbprint refers
to a key -- not a key with an associated set of key attributes.
Different application contexts might or might not include different
subsets of optional attributes about the key in the JWK. If these
were included in the calculation of the JWK thumbprint, the values
would be different for those JWKs, even though the keys are the same.
The benefit of including only the JWK required members is that the
JWK Thumbprint of any JWK representing the key remains the same,
regardless of any other attributes that are present.
Different kinds of thumbprints could be defined by other
specifications that might include some or all additional JWK members,
if use cases arise where such different kinds of thumbprints would be
useful. See Section 9.1 of RFC 7517 [JWK] for notes on some ways to
cryptographically bind attributes to a key.
3.3. Order and Representation of Members in Hash Input
The required members in the input to the hash function are ordered
lexicographically by the Unicode code points of the member names.
Characters in member names and member values MUST be represented
without being escaped. This means that thumbprints of JWKs that
require such characters are not defined by this specification. (This
is not expected to limit the applicability of this specification, in
practice, as the members of JWK representations are not expected to
use any of these characters.) The characters specified as requiring
escaping by Section 7 of [RFC7159] are quotation mark, reverse
solidus (a.k.a. backslash), and the control characters U+0000 through
U+001F.
If the JWK key type uses members whose values are themselves JSON
objects, then the members of those objects MUST likewise be
lexicographically ordered. (As of the time of this writing, none are
defined that do.)
If the JWK key type uses members whose values are JSON numbers, and
if those numbers are integers, then they MUST be represented as a
JSON number as defined in Section 6 of [RFC7159] without including a
fraction part or exponent part. For instance, the value "1.024e3"
Jones & Sakimura Standards Track [Page 7]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
MUST be represented as "1024". This means that thumbprints of JWKs
using numbers that are not integers are not defined by this
specification. Also, as noted in "The I-JSON Message Format"
[RFC7493], implementations cannot expect an integer whose absolute
value is greater than 9007199254740991 (i.e., that is outside the
range [-(2**53)+1, (2**53)-1]) to be treated as an exact value. (As
of the time of this writing, none are defined that use JSON numbers.)
See Section 4 for a discussion of further practical considerations
pertaining to the representation of the hash input.
3.4. Selection of Hash Function
A specific hash function must be chosen by an application to compute
the hash value of the hash input. For example, SHA-256 [SHS] might
be used as the hash function by the application. While SHA-256 is a
good default choice at the time of this writing, the hash function of
choice can be expected to change over time as the cryptographic
landscape evolves.
Note that in many cases, only the party that creates a key will need
to know the hash function used. A typical usage is for the producer
of the key to use the base64url-encoded JWK Thumbprint value as a
"kid" (key ID) value. In this case, the consumer of the "kid" treats
it as an opaque value that it uses to select the key.
However, in some cases, multiple parties will be reproducing the JWK
Thumbprint calculation and comparing the results. In these cases,
the parties will need to know which hash function was used and use
the same one.
3.5. JWK Thumbprints of Keys Not in JWK Format
Note that a key need not be in JWK format to create a JWK Thumbprint
of it. The only prerequisites are that the JWK representation of the
key be defined and the party creating the JWK Thumbprint be in
possession of the necessary key material. These are sufficient to
create the hash input from the JWK representation of the key, as
described in Section 3.3.
4. Practical JSON and Unicode Considerations
Implementations will almost certainly use functionality provided by
the platform's JSON support when parsing the JWK and emitting the
JSON object used as the hash input. As a practical consideration,
future JWK member names and values should be avoided for which
different platforms or libraries might emit different
representations. As of the time of this writing, all defined JWK
Jones & Sakimura Standards Track [Page 8]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
member names and values use only printable ASCII characters, which
should not exhibit this problem. Note however, that JSON.stringify()
cannot be counted on to lexicographically sort the members of JSON
objects, so while it could be used to emit some kinds of member
values, different code is likely to be needed to perform the sorting.
In particular, while the operation of lexicographically ordering
member names by their Unicode code points is well defined, different
platform sort functions may produce different results for non-ASCII
characters, in ways that may not be obvious to developers. If
writers of future specifications defining new JWK key type values
choose to restrict themselves to printable ASCII member names and
values (which are for machine and not human consumption anyway), some
future interoperability problems might be avoided.
However, if new JWK members are defined that use non-ASCII member
names or values, their definitions should specify the exact Unicode
code point sequences used to represent them. This is particularly
important in cases in which Unicode normalization could result in the
transformation of one set of code points into another under any
circumstances.
Use of escaped characters in JWKs for which JWK Thumbprints will be
computed should be avoided. Use of escaped characters in the hash
input JWKs derived from these original JWKs is prohibited.
There is a natural representation to use for numeric values that are
integers. However, this specification does not attempt to define a
standard representation for numbers that are not integers or that
contain an exponent component. This is not expected to be a problem
in practice, as the required members of JWK representations are
expected to use only numbers that are integers.
Use of number representations containing fraction or exponent parts
in JWKs for which JWK Thumbprints will be computed should be avoided.
All of these practical considerations are really an instance of Jon
Postel's principle: "Be liberal in what you accept, and conservative
in what you send."
5. Relationship to Digests of X.509 Values
JWK Thumbprint values are computed on the JWK members required to
represent a key, rather than all members of a JWK that the key is
represented in. Thus, they are more analogous to applications that
use digests of X.509 Subject Public Key Info (SPKI) values, which are
defined in Section 4.1.2.7 of [RFC5280], than to applications that
use digests of complete certificate values, as the "x5t" (X.509
Jones & Sakimura Standards Track [Page 9]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
certificate SHA-1 thumbprint) [JWS] value defined for X.509
certificate objects does. While logically equivalent to a digest of
the SPKI representation of the key, a JWK Thumbprint is computed over
a JSON representation of that key, rather than over an ASN.1
representation of it.
6. IANA Considerations
This specification adds to the instructions for the Designated
Experts of the following IANA registries, all of which are in the
"JSON Object Signing and Encryption (JOSE)" registry [IANA.JOSE]:
o JSON Web Key Types
o JSON Web Key Elliptic Curve
o JSON Web Key Parameters
IANA has added a link to this specification in the Reference sections
of these registries.
For these registries, because of the practical JSON and Unicode
considerations described in Section 4, the Designated Experts must
either:
(a) require that JWK member names and values being registered use
only printable ASCII characters excluding double quote ('"') and
backslash ('\') (the Unicode characters with code points U+0021,
U+0023 through U+005B, and U+005D through U+007E), or
(b) if new JWK members or values are defined that use other code
points, require that their definitions specify the exact Unicode code
point sequences used to represent them. Furthermore, proposed
registrations that use Unicode code points that can only be
represented in JSON strings as escaped characters must not be
accepted.
7. Security Considerations
The JSON Security Considerations and Unicode Comparison Security
Considerations described in Sections 10.12 and 10.13 of "JSON Web
Signature (JWS)" [JWS] also apply to this specification.
Also, as described in Section 4, some implementations may produce
incorrect results if esoteric or escaped characters are used in the
member names. The security implications of this appear to be limited
for JWK Thumbprints of public keys, because while it may result in
implementations failing to identify the intended key, it should not
leak information. The information in a public key is already public
in nature, by definition.
Jones & Sakimura Standards Track [Page 10]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
A hash of a symmetric key has the potential to leak information about
the key value. Thus, the JWK Thumbprint of a symmetric key should
typically be concealed from parties not in possession of the
symmetric key, unless in the application context, the cryptographic
hash used, such as SHA-256, is known to provide sufficient protection
against disclosure of the key value.
A JWK Thumbprint will only uniquely identify a particular key if a
single unambiguous JWK representation for that key is defined and
used when computing the JWK Thumbprint. (Such representations are
defined for all the key types defined in "JSON Web Algorithms (JWA)"
[JWA].) For example, if an RSA key were to use "e":"AAEAAQ"
(representing [0, 1, 0, 1]) rather than the specified correct
representation of "e":"AQAB" (representing [1, 0, 1]), then a
different thumbprint value would be produced for what could be
effectively the same key, at least for implementations that are lax
in validating the JWK values that they accept. Thus, JWK Thumbprint
values can only be relied upon to be unique for a given key if the
implementation also validates that the correct representation of the
key is used.
Even more insidious is that an attacker may supply a key that is a
transformation of a legal key in order to have it appear to be a
different key. For instance, if a legitimate RSA key uses a modulus
value N and an attacker supplies a key with modulus 3*N, the modified
key would still work about 1/3 of the time, but would appear to be a
different key. Thus, while thumbprint values are valuable for
identifying legitimate keys, comparing thumbprint values is not a
reliable means of excluding (blacklisting) the use of particular keys
(or transformations thereof).
8. References
8.1. Normative References
[IANA.JOSE] IANA, "JSON Object Signing and Encryption (JOSE)",
<http://www.iana.org/assignments/jose>.
[JWA] Jones, M., "JSON Web Algorithms (JWA)", RFC 7518,
DOI 10.17487/RFC7518, May 2015,
<http://www.rfc-editor.org/info/rfc7518>.
[JWK] Jones, M., "JSON Web Key (JWK)", RFC 7517,
DOI 10.17487/RFC7517, May 2015,
<http://www.rfc-editor.org/info/rfc7517>.
Jones & Sakimura Standards Track [Page 11]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
[JWS] Jones, M., Bradley, J., and N. Sakimura, "JSON Web
Signature (JWS)", RFC 7515, DOI 10.17487/RFC7515, May
2015, <http://www.rfc-editor.org/info/rfc7515>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<http://www.rfc-editor.org/info/rfc2119>.
[RFC7159] Bray, T., Ed., "The JavaScript Object Notation (JSON)
Data Interchange Format", RFC 7159, DOI 10.17487/RFC7159,
March 2014, <http://www.rfc-editor.org/info/rfc7159>.
[SHS] National Institute of Standards and Technology, "Secure
Hash Standard (SHS)", FIPS PUB 180-4, March 2012,
<http://csrc.nist.gov/publications/fips/fips180-4/
fips-180-4.pdf>.
[UNICODE] The Unicode Consortium, "The Unicode Standard",
<http://www.unicode.org/versions/latest/>.
8.2. Informative References
[RFC5280] Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
Housley, R., and W. Polk, "Internet X.509 Public Key
Infrastructure Certificate and Certificate Revocation
List (CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, May
2008, <http://www.rfc-editor.org/info/rfc5280>.
[RFC7493] Bray, T., Ed., "The I-JSON Message Format", RFC 7493,
DOI 10.17487/RFC7493, March 2015,
<http://www.rfc-editor.org/info/rfc7493>.
Jones & Sakimura Standards Track [Page 12]
RFC 7638 JSON Web Key (JWK) Thumbprint September 2015
Acknowledgements
James Manger and John Bradley participated in discussions that led to
the creation of this specification. Thanks also to Joel Halpern,
Barry Leiba, Adam Montville, Kathleen Moriarty, and Jim Schaad for
their reviews of this specification.
Authors' Addresses
Michael B. Jones
Microsoft
Email: mbj@microsoft.com
URI: http://self-issued.info/
Nat Sakimura
Nomura Research Institute
Email: n-sakimura@nri.co.jp
URI: http://nat.sakimura.org/
Jones & Sakimura Standards Track [Page 13]
ERRATA