Internet Engineering Task Force H. Kario, Ed.
Internet-Draft Red Hat, Inc.
Updates: 8017 (if approved) 22 November 2023
Intended status: Informational
Expires: 25 May 2024
Implementation Guidance for the PKCS #1 RSA Cryptography Specification
draft-kario-rsa-guidance-02
Abstract
This document specifies additions and amendments to RFC 8017.
Specifically, it provides guidance to implementers of the standard to
protect against side-channel attacks. It also deprecates the RSAES-
PKCS-v1_5 encryption scheme, but provides an alternative depadding
algorithm that protects against side-channel attacks raising from
users of vulnerable APIs. The purpose of this specification is to
increase security of RSA implementations.
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
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This Internet-Draft will expire on 25 May 2024.
Copyright Notice
Copyright (c) 2023 IETF Trust and the persons identified as the
document authors. All rights reserved.
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Provisions Relating to IETF Documents (https://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
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3. Requirements Language . . . . . . . . . . . . . . . . . . . . 3
4. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 3
5. Side channel attacks . . . . . . . . . . . . . . . . . . . . 4
6. General recommendations . . . . . . . . . . . . . . . . . . . 5
7. Side-channel free modular exponentiation . . . . . . . . . . 5
7.1. General recommendations . . . . . . . . . . . . . . . . . 5
7.2. Montgomery ladder . . . . . . . . . . . . . . . . . . . . 6
7.3. Montgomery reduction in multiplication . . . . . . . . . 6
8. Base blinding . . . . . . . . . . . . . . . . . . . . . . . . 6
9. Exponent blinding . . . . . . . . . . . . . . . . . . . . . . 7
10. Depadding . . . . . . . . . . . . . . . . . . . . . . . . . . 8
10.1. IRPRF . . . . . . . . . . . . . . . . . . . . . . . . . 9
10.2. Implicit rejection . . . . . . . . . . . . . . . . . . . 10
11. Non-fixes . . . . . . . . . . . . . . . . . . . . . . . . . . 12
11.1. Random delays . . . . . . . . . . . . . . . . . . . . . 12
11.2. Returing random value from API . . . . . . . . . . . . . 12
12. Deprecated Algorithms . . . . . . . . . . . . . . . . . . . . 13
13. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 13
14. Security Considerations . . . . . . . . . . . . . . . . . . . 13
15. References . . . . . . . . . . . . . . . . . . . . . . . . . 13
15.1. Normative References . . . . . . . . . . . . . . . . . . 13
15.2. Informative References . . . . . . . . . . . . . . . . . 13
Appendix A. Test Vectors . . . . . . . . . . . . . . . . . . . . 15
A.1. 2048 bit key . . . . . . . . . . . . . . . . . . . . . . 15
A.2. 2049 bit key . . . . . . . . . . . . . . . . . . . . . . 16
A.3. 3072 bit key . . . . . . . . . . . . . . . . . . . . . . 16
A.4. 4096 bit key . . . . . . . . . . . . . . . . . . . . . . 16
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 16
1. Introduction
The PKCS #1 [RFC8017] describes the RSA cryptosystem, providing
guidance on implementing encryption schemes and signature schemes.
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Unfortunately, straight-forward implementation of the RSA encryption
schemes leave it vulnerable to side-channel attacks. Protections
against them are not documented in RFC 8017, and attacks are
mentioned only in passing.
2. Rationale
The RSAES-PKCS-v1_5 encryption scheme is known to be problematic
since 1998, when Daniel Bleichenbacher published his attack
[Bleichenbacher98]. Side-channel attacks against public key
algorithms, including RSA, are known to be possible since 1996 thanks
to work by Paul Kocher [Kocher96].
Despite those results, side-channel attacks against RSA
implementations have proliferated for the next 25 years. Including
attacks against simple exponentiation implementations
[Dhem98][Schindler01], implementations that use the Chinese Remainder
Theorem optimisation [Schindler00][Brumley03] [Aciicmez05], and
implementations that use either base or exponent blinding exclusively
[Aciicmez07][Aciicmez08] [Schindler14].
Similarly, side-channel free handling of the errors from the RSAES-
PKCS-v1_5 decryption operation is something that implementations
struggle with [Bock18][Kario23].
We thus provide guidance how to implement those algorithms in a way
that should be secure against at least the simple timing side channel
attacks.
3. 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].
4. Notation
In this document we reuse the notation from RFC 8017, in addition, we
define the following:
AL alternative message length, non-negative integer, 0 <= AL <= k -
11
AM alternative encoded message, an octet string
bb base blinding factor, a positive integer
bbInv base un-blinding factor, a positive integer,
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bbInv = bb^(-1) mod n
D octet string representation of d
DH an octet string of a SHA-256 hash of D
KDK an octet string containing a Key Derivation Key for a specific
ciphertext C
l length in octets of the message M
b_i an exponent blinding factor for i-th prime, non-negative
integer.
5. Side channel attacks
Cryptographic implementations may provide a lot of indirect signals
to the attacker that includes information about the secret processed
data. Depending on type of information, those leaks can be used to
decrypt data or retrieve private keys. Most common side-channels
that leak information about secret data are:
1. Different errors returned
2. Different processing times of operations
3. Different patterns of jump instructions and memory accesses
4. Use of hardware instructions that take different amount time to
execute depending on operands or result
Some of those leaks may be detectable over the network, while others
may require closer access to the attacked system. With closer
access, the attacker may be able to measure power usage,
electromagnetic emanations, or sounds and correlate them with
specific bits of secret information.
Recent research into network based side channel detection has shown
that even very small side channels (of just few clock cycles) can be
reliably detected over the network. The detectability depends on the
sample size the attacker is able to collect, not on size of the side-
channel.
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6. General recommendations
As a general rule, all operations that process secret information (be
it parts of the private key or parts of encrypted message) MUST be
performed with code that doesn't have secret data dependent branch
instructions, secret data dependent memory accesses, or uses non-
constant time machine instructions (which ones are those is
architecture dependant, but division is commonly non-constant time).
Special care should be placed around the code that handles the
conversion of the numerical representation to the octet string
representation in RSA decryption operations.
All operations that use private keys SHOULD additionally employ both
base blinding and exponent blinding as protections against leaks
inside modular exponentiation code.
7. Side-channel free modular exponentiation
The underlying modular exponentiation algorithm MUST be constant time
with regards to the exponent in all uses of the private key.
For private key decryption the modular exponentiation algorithm MUST
be constant time with regards to the output of the exponentiation.
In case the Chinese remainder theorem optimisation is used the
modular exponentiation algorithm must also be constant time with
regards to the used moduli.
7.1. General recommendations
It's especially important to make sure that all values that are
secret to the attacker are stored in memory buffers that have sizes
determined by the public modulus.
For example, the private exponents should be stored in memory buffers
that have sizes determined by the public modulus value, not the
numerical values of the exponents themselves.
Similarly, the size of the output buffer for multiplication should
always be equal to the sum of buffer sizes of multiplicands. The
output size of the modular reduction operation should similarly be
equal to the size of the modulus and not depend on bit size of the
output.
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7.2. Montgomery ladder
For the modular exponentiation algorithm to be side-channel free
every step of the calculation MUST NOT depend on the bits of the
exponent. In particular, use of simple square and multiply algorithm
will leak information about bits of the exponent through lack of
multiplication operation in individual exponentiation steps.
The recommended workaround against it, is the use of the Montgomery
ladder construction.
While that approach ensures that both the square and multiply
operations are performed, the fact that the results of them are
placed in different memory locations based on bits of the secret
exponent will provide enough information for an attacker to recover
the bits of the exponent. To counteract it, the implementation
should ensure that both memory locations are accessed and updated on
every step.
7.3. Montgomery reduction in multiplication
As multiplication operations quickly make the intermediate values in
modular exponentiation large, performing a modular reduction after
every multiplication or squaring operation is a common optimisation.
To further optimise the modular reduction, the Montgomery modular
multiplication is used for performing the combined multiply-and-
reduce operation. The last step of that operation is conditional on
the value of the output. A side-channel free implementation should
perfom the subtraction in all cases and then copy the result or the
first operand of the subtraction based on sign of the result of the
subtraction in side-channel free manner.
8. Base blinding
As a protection against multiple attacks, it's RECOMMENDED to perform
all operations involving the private key with the use of blinding
[Kocher96].
It should be noted that for decryption operations the unblinding
operation MUST be performed using side-channel free code that does
not leak information about the result of this multiplication and
reduction modulo operation.
To implement base blinding, select a number bb uniformly at random
such that it is relatively prime to n and smaller than n.
Compute multiplicative inverse of bb modulo n.
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bbInv = bb^(-1) mod n
In the RSADP() operation, after performing step 1, multiply c by bb
mod n. Use the result as new c for all the remaining operations.
Before returning the value m in step 3, multiply it by bbInv mod n.
Note: multiplication by bbInv and reduction modulo n MUST be
performed using side-channel free code with respect to value m.
As calculating multiplicative inverse is expensive, implementations
MAY calculate new values of bb and bbInv by squaring them:
new bb = bb^2 mod n
new bbInv = bbInv^2 mod n
A given pair of blinding factors (bb, bbInv) MUST NOT be used for
more than one RSADP() operation.
Unless the multiplication (squaring) and reduction modulo operations
are verified to be side-channel free, it's RECOMMENDED to generate
completely new blinding parameters every few hundred private key
operations.
9. Exponent blinding
To further protect against private key leaks, it's RECOMMENDED to
perform the blinding of the used exponents [Kocher96].
When performing the RSADP() operation, the blinding depends on the
form of the private key.
If the key is in the first form, the pair (n, d), then the exponent d
should be modified by adding a multiple of Euler phi(n): m = c^(d +
b*phi(n)) mod n. Where b is a 64 bit long uniform random number.
A new value b MUST be selected for every RSADP() operation.
If the key is the second form, the quintuple (p, q, dP, dQ, qInv)
with optional sequence of triplets (r_i, d_i, t_i), i = 3, ..., u,
then each exponent used MUST be blinded individually.
1. The m_1 = c^(dP + b_1 * phi(p)) mod p
2. The m_2 = c^(dQ + b_2 * phi(q)) mod q
3. If u > 3, then m_i = c^(d_i + b_i * phi(r_i)) mod (r_i)
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Where b_1, b_2, ..., b_i are all uniformly selected random numbers at
least 64 bits long (or at least 2 machine word sizes, whichever is
greater).
As Euler phi(p) for an argument p that's a prime is equal p - 1, it's
simple to calculate in this case.
Note: the selection of random b_i values, multiplication of them by
the result of phi() function, and addition to the exponent MUST be
performed with side-channel free code.
Use of smaller blinding factor is NOT RECOMMENDED, as values shorter
than 64 bits have been shown to still be vulnerable to side-channel
attacks[Bauer12][Schindler11].
The b_1, b_2, ..., b_i factors MUST NOT be reused for multiple
RSADP() operations.
10. Depadding
In case of RSA-OAEP, the padding is self-verifying, thus the
depadding operation needs to follow the standard algorithm to provide
a safe API to users.
It MUST ignore the value of the very fist octet of padding and
process the remaining bytes as if it was equal zero.
The RSAES-PKCS-v1_5 encryption scheme is considered deprecated, and
should be used only to process legacy data. It MUST NOT be used as
part of online protocols or API endpoints.
For implementations that can't remove support for this padding mode
it's RECOMMENDED to implement an implicit rejection mechanism that
completely hides from the calling code whether the padding check
failed or not.
It should be noted that the algorithm MUST be implemented as stated,
otherwise in case of heteregonous environments where two
implementations use the same key but implement the implicit rejection
differently, it may be possible for the attacker to compare behaviour
between the implementations to guess if the padding check failed or
not.
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The basic idea of the implicit rejection is to prepare a random but
deterministic message to be returned in case the standard RSAES-PKCS-
v1_5 padding checks fail. To do that, use the private key and the
provided ciphertext to derive a static, but unknown to the attacker,
random value. It's a combination of the method documented in the TLS
1.2 (RFC 5246[RFC5246]) and the deterministic (EC)DSA signatures (RFC
6979 [RFC6979]).
10.1. IRPRF
For the calculation of the random message for implicit rejection we
define a Pseudo-Random Function (PRF) as follows:
IRPRF( KDK, label, length )
Input:
KDK the key derivation key
label a label making the output unique for a given KDK
length requested length of output in octets
Output: derived key, an octet string
Steps:
1. If KDK is not 32 octets long, or if length is larger than 8192
return error and stop.
2. The returned value is created by concatenation of subsequent
calls to a SHA-256 HMAC function with the KDK as the HMAC key and
following octet string as the message:
P_i = I || label || bitLength
3. Where the I is an iterator value encoded as two octet long big
endian integer, label is the passed in label, and bitLength is
the length times 8 (to represent number of bits of output)
encoded as two octet big endian integer. The iterator is
initialised to 0 on first call, and then incremented by 1 for
every subsequent HMAC call.
4. The HMAC is iterated until the concatenated output is shorter
than length
5. The output is the length left-most octets of the concatenated
HMAC output
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10.2. Implicit rejection
For implementations that cannot remove support for the RSAES-PKCS-
v1_5 encryption scheme nor provide a usage-specific API, it's
possible to implement an implicit rejection algorithm as a protection
measure. It should be noted that implementing it correctly is hard,
thus it's RECOMMENDED instead to disable support for RSAES-PKCS-v1_5
padding instead.
To implement implicit rejection, the RSAES-PKCS1-V1_5-DECRYPT from
section 7.2.2 of RFC 8017 needs to be implemented as follows:
1. Length checking: If the length of the ciphertext C is not k
octets (or if k < 11), output "decryption error" and stop.
2. RSA decryption:
a. Convert the ciphertext C to an integer ciphertext
representative c:
c = OS2IP (C).
b. Apply the RSADP decryption primitive to the RSA private key
(n, d) and the ciphertext representative c to produce an
integer message representative m:
m = RSADP ((n, d), c).
Note: the RSADP MUST be constant-time with respect of message
m.
If RSADP outputs "ciphertext representative out of range"
(meaning that c >= n), output "decryption error" and stop.
c. Convert the message representative m to an encoded message EM
of length k octets:
EM = I2OSP (m, k).
Note: I2OSP MUST be constant-time with respect of m.
3. Derivation of alternative message
1. Derive the Key Derivation Key (KDK)
a. Convert the private expoent d to a string of length k
octets:
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D = I2OSP (d, k).
b. Hash the private exponent using the SHA-256 algorithm:
DH = SHA256 (D).
Note: This value MAY be cached between the decryption
operations, but MUST be considered private-key
equivalent.
c. Use the DH as the SHA-256 HMAC key and the provided
ciphertext C as the message. If the ciphertext C is not
k octets long, it MUST be left padded with octets of
value zero.
KDK = HMAC (DH, C, SHA256).
2. Create the candidate lengths and the random message
a. Use the IRPRF with key KDK, "length" as six octet label
encoded with UTF-8, to generate 256 octet output.
Interpret this output as 128 two octet long big-endian
numbers.
CL = IRPRF (KDK, "length", 256).
b. Use the IRPRF with key KDK, "message" as a seven octet
label encoded with UTF-8 to generate k octet long output
to be used as the alternative message:
AM = IRPRF (KDK, "message", k).
3. Select the alternative length for the alternative message.
Note: this must be performed in side-channel free way.
a. Iterate over the 128 candidate CL lengths. For each zero
out high order bits so that they have the same bit length
as the maximum valid message size (k - 11).
b. Select the last length that's not larger than k - 11, use
0 if none are. Save it as AL.
4. EME-PKCS1-v1_5 decoding: Separate the encoded message EM into an
octet string PS consisting of nonzero octets and a message M as
EM = 0x00 || 0x02 || PS || 0x00 || M.
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If the first octet of EM does not have hexadecimal value 0x00, if
the second octet of EM does not have hexadecimal value 0x02, if
there is no octet with hexadecimal value 0x00 to separate PS from
M, or if the length of PS is less than 8 octets, the check
variable must remember if any of those checks failed.
Irrespective of the check variable value, the code should also
return length of message M: L. If there is no octet with
hexadecimal value 0x00 to separate PS from M, then L should equal
0.
Note: All those checks MUST be performed irrespective if previous
checks failed or not. A common technique for that is to have a
check variable that is OR-ed with the results of subsequent
checks.
5. Decision which message to return: in case the check variable is
set, the code should return the last AL octets of AM, in case the
check variable is unset the code should return the last L octets
of EM.
Note: The decision which length to use MUST be performed in side-
channel free manner. While the length of the returned message is
not considered sensitive, the read memory location is. As such,
when returning message M both EM and AM memory locations MUST be
read.
11. Non-fixes
While there are infinite ways to implement those algorithms
incorrectly few common ideas to work-around side-channel attacks are
repeated. We list few of them as examples of approaches that don't
work and thus MUST NOT be used.
11.1. Random delays
«describe that adding random delays doesn't work»
11.2. Returing random value from API
«describe why returning a random message, even of user-specified
length is not a universal solution»
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12. Deprecated Algorithms
Current protocol deployments MUST NOT use encryption with RSAES-PKCS-
v1_5 padding. Support for RSAES-PKCS-v1_5 SHOULD be disabled in
default configuration of any implementation of RSA cryptosystem. All
new protocols MUST NOT specify RSAES-PKCS-v1_5 as a valid encryption
padding for RSA keys.
13. IANA Considerations
This memo includes no request to IANA.
14. Security Considerations
This whole document specifies security considerations for RSA
implementations.
15. References
15.1. Normative References
[RFC8017] Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch,
"PKCS #1: RSA Cryptography Specifications Version 2.2",
RFC 8017, DOI 10.17487/RFC8017, November 2016,
.
15.2. Informative References
[Aciicmez05]
Acıiçmez, O., Schindler, W., and Ç. K. Koç, "Improving
Brumley and Boneh timing attack on unprotected SSL
implementations", Proceedings of the 12th ACM conference
on Computer and communications security CCS '05, 2005,
.
[Aciicmez07]
Acıiçmez, O. and W. Schindler, "A Major Vulnerability in
RSA Implementations due to MicroArchitectural Analysis
Threat", Cryptology ePrint Archive Paper 2007/336, 2007,
.
[Aciicmez08]
Acıiçmez, O. and W. Schindler, "A Vulnerability in RSA
Implementations Due to Instruction Cache Analysis and Its
Demonstration on OpenSSL", Lecture Notes in Computer
Science vol 4964, 2007,
.
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[Bauer12] Bauer, S., "Attacking Exponent Blinding in RSA without
CRT", Lecture Notes in Computer Science vol 7275, 2012,
.
[Bleichenbacher98]
Bleichenbacher, D., "Chosen Ciphertext Attacks Against
Protocols Based on the RSA Encryption Standard PKCS#1",
Lecture Notes in Computer Science vol 1462,
.
[Bock18] Böck, H., Somorovsky, J., and C. Young, "Return Of
Bleichenbacher's Oracle Threat (ROBOT)", 27th USENIX
Security Symposium USENIX Security 18, 2018,
.
[Brumley03]
Brumley, D. and D. Boneh, "Remote timing attacks are
practical", Computer Networks Volume 48, Issue 5, 2003,
.
[Dhem98] Dhem, J., Koeune, F., Leroux, P., Mestré, P., Quisquater,
J., and J. Willems, "A Practical Implementation of the
Timing Attack", Lecture Notes in Computer Science vol
1820, 1998, .
[Kario23] Kario, H., "Everlasting ROBOT: the Marvin Attack", 28th
European Symposium on Research in Computer Security ,
2023, .
[Kocher96] Kocher, P. C., "Timing Attacks on Implementations of
Diffie-Hellman, RSA, DSS, and Other Systems.", Lecture
Notes in Computer Science vol 1109, 1996,
.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
.
[RFC5246] Dierks, T. and E. Rescorla, "The Transport Layer Security
(TLS) Protocol Version 1.2", RFC 5246,
DOI 10.17487/RFC5246, August 2008,
.
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[RFC6979] Pornin, T., "Deterministic Usage of the Digital Signature
Algorithm (DSA) and Elliptic Curve Digital Signature
Algorithm (ECDSA)", RFC 6979, DOI 10.17487/RFC6979, August
2013, .
[Schindler00]
Schindler, W., "A Timing Attack against RSA with the
Chinese Remainder Theorem", Lecture Notes in Computer
Science vol 1965, 2000,
.
[Schindler01]
Schindler, W., Koeune, F., and J. Quisquater, "Improving
Divide and Conquer Attacks against Cryptosystems by Better
Error Detection / Correction Strategies.", Lecture Notes
in Computer Science vol 2260, 2001,
.
[Schindler11]
Schindler, W. and K. Itoh, "Exponent Blinding Does Not
Always Lift (Partial) Spa Resistance to Higher-Level
Security", Lecture Notes in Computer Science vol 6715,
2011, .
[Schindler14]
Schindler, W. and A. Wiemers, "Power attacks in the
presence of exponent blinding.", Journal of Cryptographic
Engineering 4, 2014,
.
Appendix A. Test Vectors
A.1. 2048 bit key
«provide test vectors here»
see also: https://github.com/tlsfuzzer/tlslite-
ng/blob/master/unit_tests/test_tlslite_utils_rsakey.py#L1694
proposed test vectors:
Otherwise valid, but with wrong first byte of plaintext
Otherwise valid, but with padding type specifying signature
Otherwise valid, but with PS of 7 bytes
Otherwise valid, but with PS of 0 bytes
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Otherwise valid, but with the message separator byte missing
invalid ciphertext that decrypts to a synthehic message of maximum
size
invalid ciphertext that decrypts to a 0-bytes long message
invalid ciphertext that needs to use the second-to-last synthethic
length for the returned message
valid ciphertext that starts with a zero byte
A.2. 2049 bit key
«provide test vectors here
A.3. 3072 bit key
«provide test vectors here»
A.4. 4096 bit key
«provide test vectors here»
Author's Address
Hubert Kario (editor)
Red Hat, Inc.
Purkynova 115
61200 Brno
Czech Republic
Email: hkario@redhat.com
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