Internet Engineering Task Force C. V. Vredendaal
Internet-Draft NXP Semiconductors
Intended status: Informational S. Dragone
Expires: 26 April 2023 B. Hess
T. Visegrady
M. Osborne
IBM Research GmbH
D. Bong
Utimaco IS GmbH
J. Bos
NXP Semiconductors
23 October 2022
Quantum Safe Cryptography Key Information for CRYSTALS-Dilithium
draft-uni-qsckeys-dilithium-00
Abstract
This proposal defines key management approaches for the Quantum Safe
Cryptographic (QSC) algorithm CRYSTALS-Dilithium which has been
selected for standardization by the NIST Post Quantum Cryptography
(PQC) process. This includes key identification, key serialization,
and key compression. The purpose is to provide guidance such that
the adoption of quantum safe algorithms is not hampered with the
fragmented evolution of necessary key management standards. Early
definition of key material standards will help expedite the adoption
of new quantum safe algorithms and at the same time as improving
interoperability between implementations and minimizing divergence
across standards.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at https://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on 26 April 2023.
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Copyright Notice
Copyright (c) 2022 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 (https://trustee.ietf.org/
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Please review these documents carefully, as they describe your rights
and restrictions with respect to this document. Code Components
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provided without warranty as described in the Revised BSD License.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Requirements Language . . . . . . . . . . . . . . . . . . 3
1.2. Algorithm Identification . . . . . . . . . . . . . . . . 3
1.3. Algorithm and Algorithm Parameter Object Identifier . . . 3
2. Overview of CRYSTALS-Dilithium and parameter OIDs . . . . . . 4
2.1. Key Formats . . . . . . . . . . . . . . . . . . . . . . . 5
2.2. Public Key Format based on RFC5280 . . . . . . . . . . . 6
2.3. Overview of Memo Definitions - PQC Key Formats . . . . . 6
3. CRYSTALS-Dilithium . . . . . . . . . . . . . . . . . . . . . 6
3.1. Algorithm Parameter Identifiers . . . . . . . . . . . . . 7
3.2. Key Details . . . . . . . . . . . . . . . . . . . . . . . 10
3.3. Private Key Full Encoding . . . . . . . . . . . . . . . . 10
3.4. Private Key Partial Encoding Option 1 . . . . . . . . . . 11
3.5. Private key Partial Encoding Option 2 . . . . . . . . . . 12
3.6. Public Key Full Encoding . . . . . . . . . . . . . . . . 12
4. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 13
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 13
6. Security Considerations . . . . . . . . . . . . . . . . . . . 13
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 13
7.1. Normative References . . . . . . . . . . . . . . . . . . 13
7.2. Informative References . . . . . . . . . . . . . . . . . 13
Appendix A. Additional Stuff . . . . . . . . . . . . . . . . . . 14
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 14
1. Introduction
QSC algorithms being standardized in the NIST PQC Process have
evolved through several rounds and iterations. Keys are neither
easily identifiable nor compatible across rounds. It is also
expected that algorithms will evolve after final candidates have been
selected. The lack of binary compatibility between algorithm
versions and variants means that it is important to clearly identify
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key material. Parallel to the NIST process, industry is evaluating
the impact of adopting new PQC algorithms, in particular key
management. Here it is important to define and standardize key
serialization and encoding formats. Finally, we have seen that many
platforms and protocols are very constrained when it comes to the
amount of memory or space available for key objects. This makes it
important to define and standardize key compression formats. This
proposal addresses aspects of key identification, key serialization,
and key compression for the future primary NIST PQC Digital Signature
standard, CRYSTALS-Dilithium. For the other schemes, see draft-uni-
qsckeys-kyber, draft-uni-qsckeys-falcon, draft-uni-qsckeys-
sphincsplus and the previous Internet-Draft [draft-uni-qsckeys-01].
This proposal will be updated when the final NIST standard for
CRYSTALS-Dilithium becomes available.
1.1. Requirements Language
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [RFC2119] .
1.2. Algorithm Identification
Algorithm identification is important for several reasons:
* Managing a smooth transition from early adoption algorithm
versions to production versions where there is no compatibility.
* Supporting different algorithm versions from different NIST rounds
* Identifying different key serialization strategies
* Identifying compressed and uncompressed keys
The current standardization of quantum safe algorithms does not
address the definition of serialization structures for keys. As a
result, it has become commonplace for the cryptographic community
working on and with these algorithms to define their own approaches.
This leads to proprietary and internal representations for key
material. This has certain advantages in terms of ease of
experimentation while focusing on finding the best-performing QSC
algorithms. In terms of longer-term support where algorithm versions
change this is a problem. This proposal defines in section 2 a long-
term structured key representation format useful to address the goals
outlined above.
1.3. Algorithm and Algorithm Parameter Object Identifier
Algorithm and algorithm parameter information shall have ASN.1 type
AlgorithmIdentifier as given in [RFC5280] and shall be extended by an
pqcAlgorithmParameterName type in the optional parameters field:
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AlgorithmIdentifier ::= SEQUENCE {
algorithm OBJECT IDENTIFIER, - OID: algorithm and algo parameter
parameters pqcAlgorithmParameterName OPTIONAL
}
pqcAlgorithmParameterName ::= PrintableString
2. Overview of CRYSTALS-Dilithium and parameter OIDs
CRYSTALS-Dilithium consists of six parameter sets. This memo
attributes a name and a placeholder for an OID to the different
parameter sets of CRYSTALS-Dilithium. The following table gives an
overview of the possible OIDs in the algorithm field and possible
parameters set names in the parameters field of the
AlgorithmIdentifier type. Each name or OID represents a single
parameter set of given security. Details can be found in the next
section.
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|=========+=====+===============================================|
| CRYSTALS-Dilithium (PQC Digital Signature) |
|=========+=====+===============================================|
| dilithium-4x4-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1|{..*.. pqc-ds-dilithium dilithium-4x4-r3} |
| |dot | |
|---------------+-----+-----------------------------------------|
| dilithium-4x4-aes-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1| {..*.. pqc-ds-dilithium dilithium-4x4-aes-r3} |
| | dot | |
|---------+-----+-----------------------------------------------|
| dilithium-6x5-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1| {..*.. pqc-ds-dilithium dilithium-6x5-r3} |
| | Dot | |
|---------+-----+-----------------------------------------------|
| dilithium-6x5-aes-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1| {..*.. pqc-ds-dilithium dilithium-6x5-aes-r3} |
| | Dot | |
|---------+-----+-----------------------------------------------|
| dilithium-8x7-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1| {..*.. pqc-ds-dilithium dilithium-8x7-r3} |
| |Dot | |
|---------+-----+-----------------------------------------------|
| dilithium-8x7-aes-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1| {..*.. pqc-ds-dilithium dilithium-8x7-aes-r3} |
| |dot. | |
|=========+=====+===============================================|
Figure 1
2.1. Key Formats
The private key format defined is from PKCS#8 [RFC5208] . PKCS#8
PrivateKeyInfo is defined as:
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PrivateKeyInfo ::= SEQUENCE {
version INTEGER -- PKCS#8 syntax ver
privateKeyAlgorithm AlgorithmIdentifier -- see chapter above
privateKey OCTET STRING, -- see chapter below
attributes [0] IMPLICIT Attributes OPTIONAL
}
Distributing a PQC private key requires a PKCS#8 PrivateKeyInfo with
a joined PQC algorithm and algorithm parameter OID in the algorithm
field of AlgorithmIdentifier and a PQC algorithm specific private key
object in the privateKey field of PrivateKeyInfo. Both objects are
defined in the specific algorithm sections of this document. For an
overview see tables above and below.
2.2. Public Key Format based on [RFC5280]
RFC5280 subjectPublicKeyInfo is defined in as:
SubjectPublicKeyInfo := SEQUENCE {
algorithm AlgorithmIdentifier -- see chapter above
subjectPublicKey BIT STRING -- see chapter below
}
Distributing a PQC public key requires a [RFC5480]
subjectPublicKeyInfo with a joined PQC algorithm and algorithm
parameter OID in the algorithm field of AlgorithmIdentifier and a PQC
algorithm specific public key object in the subjectPublicKey field of
subjectPublicKeyInfo. Both objects are defined in the specific
algorithm sections of this document. For an overview see tables
above and below.
2.3. Overview of Memo Definitions - PQC Key Formats
The privateKey field in the PrivateKeyInfo type [RFC5480] is an OCTET
STRING whose contents are the value of the private key. The
interpretation of the content differs from PQC algorithm to
algorithm. The subjectPublicKey field in the subjectPublicKeyInfo
type [RFC5480] is a BIT STRING whose contents are the value of the
public key. Here also the interpretation of the content differs from
PQC algorithm to algorithm.
3. CRYSTALS-Dilithium
CRYSTALS-Dilithium is a digital signature scheme that is based on the
hardness of lattice problems over module lattices.
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* Project Website: https://pq-crystals.org/dilithium/index.shtml
* NIST Round 3 Submission (version 3.1):
https://csrc.nist.gov/CSRC/media/Projects/post-quantum-
cryptography/documents/round-3/submissions/Dilithium-Round3.zip,
https://pq-crystals.org/dilithium/data/dilithium-specification-
round3-20210208.pdf
3.1. Algorithm Parameter Identifiers
CRYSTALS-Dilithium uses OIDs to identify parameters sets.
|=========================+=====================================|
| dilithium-4x4-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-4x4-r3} |
| | <.> |
| NIST Level Security | Level 2 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n+1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=39 |
| | challenge entropy=192 |
| | gamma coefficient range: gamma1=2^17|
| | low-order rounding range: gamma2=(q-|
| | 1)/88 |
| | Private key Range eta=2 |
| | Dimensions of A: (k,l)=(4,4) |
| | Max # of 1's in the hint h: w=80 |
| | Repetitions=4.25 |
|=========================+=====================================|
| dilithium-4x4-aes-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-4x4-aes-r3} |
| | <.> |
| NIST Level Security | Level 2 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n + 1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=39 |
| | challenge entropy=192 |
| | y coefficient range: gamma1=2^17 |
| | low-order rounding range:gamma2=(q- |
| | -1)/88 |
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| | Private key Range eta=2 |
| | Dimensions of A: (k,l)=(4,4) |
| | Max # of 1's in the hint h: w=80 |
| | Repetitions=4.25 |
|=========================+=====================================|
| dilithium-6x5-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-6x5-r3} |
| | <.> |
| NIST Level Security | Level 3 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n + 1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=49 |
| | challenge entropy=225 |
| | y coefficient range: gamma1=2^19 |
| | low-order rounding range:gamma2=(q- |
| | -1)/32 |
| | Private key Range eta=4 |
| | Dimensions of A: (k,l)=(6,5) |
| | Max # of 1's in the hint h: w=55 |
| | Repetitions=5.1 |
|=========================+=====================================|
| dilithium-6x5-aes-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-6x5-aes-r3} |
| | <.> |
| NIST Level Security | Level 3 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n +1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=49 |
| | challenge entropy=225 |
| | y coefficient range: gamma1=2^19 |
| | low-order rounding range:gamma2=(q- |
| | -1)/32 |
| | Private key Range eta=4 |
| | Dimensions of A: (k,l)=(6,5) |
| | Max # of 1's in the hint h: w=55 |
| | Repetitions=5.1 |
|=========================+=====================================|
| dilithium-8x7-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-8x7-r3} |
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| | <.> |
| NIST Level Security | Level 5 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n + 1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=60 |
| | challenge entropy=257 |
| | y coefficient range: gamma1=2^19 |
| | low-order rounding range:gamma2=(q- |
| | -1)/32 |
| | Private key Range eta=2 |
| | Dimensions of A: (k,l)=(8,7) |
| | Max # of 1's in the hint h: w=75 |
| | Repetitions=3.85 |
|=========================+=====================================|
| dilithium-8x7-aes-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-8x7-aes-r3} |
| | <.> |
| NIST Level Security | Level 5 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n + 1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=60 |
| | challenge entropy=257 |
| | y coefficient range: gamma1=2^19 |
| | low-order rounding range:gamma2=(q- |
| | -1)/32 |
| | Private key Range eta=2 |
| | Dimensions of A: (k,l)=(8,7) |
| | Max # of 1's in the hint h: w=75 |
| | Repetitions=3.85 |
|=========================+=====================================|
Figure 2
The AES variants listed above differ from the other variants in that
they use AES, rather than SHAKE internally to expand the key
parameters from an initial seed. While the parameters listed in the
table are the same, the key-pairs will not be compatible with the
'aes' variants.
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3.2. Key Details
Public key. The public-key consists of two parameters:
* rho: nonce
* t1: a vector encoded in 320*k bytes
The size necessary to hold all public key elements accounts to
32+320*k bytes.
Private key. The private key consists of 6 parameters:
* rho: nonce
* K: a key/seed/D
* tr: PRF bytes
* s1: vector (L)
* s2: vector (K)
* t0: k polynomials
If the private key is fully populated, it consists of 6 parameters.
The size necessary to hold all private key elements accounts to
32+32+32+32*[(k+l)*ceiling(log(2*eta+1))+13*k] bytes. The resulting
public key and private key sizes can be found in the table below.
|=========================+========+=========+=========+=========|
| Algorithm | Public | Private | Partial | Partial |
| | Key | Key SK | SK (V1) | SK (V2) |
| | Length | Length | Length | Length |
|=========================+========+=========+=========+=========+
| dilithium-4x4-r3 | 1312 | 2528 | 64 | 32 |
| dilithium-4x4-aes-r3 | 1312 | 2528 | 64 | 32 |
| dilithium-6x5-r3 | 1952 | 4000 | 64 | 32 |
| dilithium-6x5-aes-r3 | 1952 | 4000 | 64 | 32 |
| dilithium-8x7-r3 | 2592 | 4864 | 64 | 32 |
| dilithium-8x7-aes-r3 | 2592 | 4864 | 64 | 32 |
|=========================+========+=========+=========+=========|
Figure 3
3.3. Private Key Full Encoding
Encoding a CRYSTALS-Dilithium private key with PKCS#8 must include
the following two fields:
* dilithium-(kxl)-r3 in the algorithm field of AlgorithmIdentifier
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* DilithiumPrivateKey in the privateKey field, which is an OCTET
STRING.
CRYSTALS-Dilithium public keys are optionally distributed in the
PublicKey field of the PrivateKeyInfo structure.
ASN.1 Encoding for a CRYSTALS-Dilithium private key when fully
populated:
DilithiumPrivateKey ::= SEQUENCE {
version INTEGER {v0(0)} -- version (round 3)
nonce BIT STRING, -- rho
key BIT STRING, -- key/seed/D
tr BIT STRING, -- PRF bytes (CRH in spec)
s1 BIT STRING, -- vector(L)
s2 BIT STRING, -- vector(K)
t0 BIT STRING,
publicKey [0] IMPLICIT DilithiumPublicKey OPTIONAL
-- see next section
}
3.4. Private Key Partial Encoding Option 1
In option 1 ofCRYSTALS-Dilithium partial encoding the rho (nonce) and
the seed (key) are used to regenerate the full key. Note: There are
a number of alternative ways to encode a partially filled structure
that include defining fields as optional and defining fields as
'EMPTY'. As an example partial RSA keys are encoded using EMPTY
fields. It can be argued that defining fields as EMPTY significantly
simplifies the implementation of parsing ASN.1 frames. The ASN.1
format for the partially populated versions is the same as for the
fully populated version. The ASN.1 encoding for the first variant
(rho and seed) is defined as follows:
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DilithiumPrivateKey ::= SEQUENCE {
version INTEGER {v0(0)} -- version (round 3)
nonce BIT STRING, -- rho
key BIT STRING, -- key/seed/D
tr BIT STRING, -- EMPTY
s1 BIT STRING, -- EMPTY
s2 BIT STRING, -- EMPTY
t0 BIT STRING, -- EMPTY
publicKey [0] IMPLICIT DilithiumPublicKey OPTIONAL
-- see next section
}
3.5. Private key Partial Encoding Option 2
In option 2 of CRYSTALS-Dilithium partial encoding only zeta (nonce)
is used to regenerate the full key. The ASN.1 encoding for this is
defined as follows:
DilithiumPrivateKey ::= SEQUENCE {
version INTEGER {v0(0)} -- version (round 3)
nonce BIT STRING, -- zeta
key BIT STRING, -- EMPTY
tr BIT STRING, -- EMPTY
s1 BIT STRING, -- EMPTY
s2 BIT STRING, -- EMPTY
t0 BIT STRING, -- EMPTY
publicKey [0] IMPLICIT DilithiumPublicKey OPTIONAL
-- see next section
}
3.6. Public Key Full Encoding
Components are individual OCTET STRINGs, without unused bits, encoded
with the exact size. There is no removal of leading zeroes.
DilithiumPublicKey ::= SEQUENCE {
rho OCTET STRING,
t1 OCTET STRING
}
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4. Acknowledgements
This template was derived from an initial version written by Pekka
Savola and contributed by him to the xml2rfc project.
This document is part of a plan to make xml2rfc indispensable.
5. IANA Considerations
This memo includes no request to IANA.
6. Security Considerations
Any processing of the ASN.1 private key structures, such as base64
en/decoding shall be performed in "constant-time", meaning without
secret-dependent control flow and table lookups. The ASN.1
structures in this document are defined with fixed tag-lengths. The
purpose is to prevent side-channel leakage of variable lengths during
DER parsing. Any DER parsing of the private key ASN.1 key structures
shall be performed with these fixed lengths.
7. References
7.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
.
[RFC5208] Kaliski, B., "Public-Key Cryptography Standards (PKCS) #8:
Private-Key Information Syntax Specification Version 1.2",
BCP 14, RFC 5208, DOI 10.17487/RFC5208, May 2008,
.
[RFC5280] Cooper, D., "Internet X.509 Public Key Infrastructure
Certificate and Certificate Revocation List (CRL)
Profile", BCP 14, RFC RFC5280, DOI 10.17487/RFC5280, May
2008, .
[RFC5480] Turner, S., "Elliptic Curve Cryptography Subject Public
Key Information", BCP 14, RFC RFC5480,
DOI 10.17487/RFC5480, May 2009,
.
7.2. Informative References
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[draft-uni-qsckeys-01]
Vredendaal, C. V., Dragone, S., Hess, B., Visegrady, T.,
Osborne, M., Bong, D., and J. Bos, "Quantum Safe
Cryptography Key Information", Work in Progress, Internet-
Draft, draft-uni-qsckeys-01, 12 May 2022,
.
[RFC2629] Rose, M., "Writing I-Ds and RFCs using XML", RFC 2629,
DOI 10.17487/RFC2629, June 1999,
.
[RFC3552] Rescorla, E. and B. Korver, "Guidelines for Writing RFC
Text on Security Considerations", BCP 72, RFC 3552,
DOI 10.17487/RFC3552, July 2003,
.
[RFC5226] Narten, T. and H. Alvestrand, "Guidelines for Writing an
IANA Considerations Section in RFCs", RFC 5226,
DOI 10.17487/RFC5226, May 2008,
.
Appendix A. Additional Stuff
This becomes an Appendix.
Authors' Addresses
Christine van Vredendaal
NXP Semiconductors
High Tech Campus 60
5656 AE Eindhoven
Netherlands
Email: cvvrede@gmail.com
Silvio Dragone
IBM Research GmbH
Saeumerstrasse 4
CH-8803 Rueschlikon
Switzerland
Email: sid@zurich.ibm.com
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Basil Hess
IBM Research GmbH
Saeumerstrasse 4
CH-8803 Rueschlikon
Switzerland
Email: bhe@zurich.ibm.com
Tamas Visegrady
IBM Research GmbH
Saeumerstrasse 4
CH-8803 Rueschlikon
Switzerland
Email: tvi@zurich.ibm.com
Michael Osborne
IBM Research GmbH
Saeumerstrasse 4
CH-8803 Rueschlikon
Switzerland
Email: osb@zurich.ibm.com
Dieter Bong
Utimaco IS GmbH
Germanusstrasse 4
52080 Aachen
Germany
Email: dieter.bong@utimaco.com
Joppe Bos
NXP Semiconductors
High Tech Campus 60
5656 AE Eindhoven
Netherlands
Email: joppe.bos@nxp.com
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