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INTERNET-DRAFT E. Rescorla
<draft-ietf-smime-pkcs1-01.txt> RTFM, Inc.
(September 2001 (Expires March 2002)
Preventing the Million Message Attack on CMS
Status of this Memo
This document is an Internet-Draft and is in full conformance with
all provisions of Section 10 of RFC2026. Internet-Drafts are working
documents of the Internet Engineering Task Force (IETF), its areas,
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1. Introduction
When data is encrypted using RSA it must be padded out to the length
of the modulus--typically 512 to 2048 bits. The most popular tech-
nique for doing this is described in [PKCS-1-v1.5]. However, in 1998
Bleichenbacher described an adaptive chosen ciphertext attack on SSL
[MMA]. This attack, called the Million Message Attack, allowed the
recovery of a single PKCS-1 encrypted block, provided that the
attacker could convince the receiver to act as a particular kind of
oracle. (An oracle is a program which answers queries based on infor-
mation unavailable to the requester (in this case the private key)).
The MMA is also possible against [CMS]. Mail list agents are the
most likely CMS implementations to be targets for the MMA, since mail
list agents are automated servers that automatically respond to a
large number of messages. This document describes a strategy for
resisting such attacks.
2. Overview of PKCS-1
The first stage in RSA encryption is to map the message to be
encrypted (in CMS a symmetric Content-Encryption Key (CEK)) into an
integer the same length as (but numerically less than) the RSA modu-
lus of the recipient's public key (typically somewhere between 512
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and 2048 bits). PKCS-1 describes the most common procedure for this
transformation.
We start with an "encryption block" of the same length as the modu-
lus. The rightmost bytes of the block are set to the message to be
encrypted. The first two bytes are a zero byte and a "block type"
byte. For encryption the block type is 2. The remaining bytes are
used as padding. The padding is constructed by generating a series of
non-zero random bytes. The last padding byte is zero, which allows
the padding to be distinguished from the message.
|--------------------------------------------------------|
| 0 | 2 | Nonzero random bytes | 0 | Message |
|--------------------------------------------------------|
Once the block has been formatted, the sender must then convert the
block into an integer. This is done by treating the block as an inte-
ger in big-endian form. Thus, the resulting number is less than the
modulus (because the first byte is zero), but within a factor of 2^16
(because the second byte is 2).
In CMS, the message is always a randomly generated symmetric content-
encryption key (CEK). Depending on the cipher being used it might be
anywhere from 8 to 32 bytes.
There must be at least 8 bytes of non-zero padding. The padding pre-
vents an attacker from verifying guesses about the encrypted message.
Imagine that the attacker wishes to determine whether or not two RSA-
encrypted keys are the same. Because there are at least 255^8 (about
2^64) different padding values with high probability two encryptions
of the same message will be different. The padding also prevents the
attacker from verifying guessed CEKs by trial-encrypting them with
the recipient's RSA key since he must try each potential pad for
every guess. Note that a lower cost attack would be to exhaustively
search the CEK space by trial-decrypting the content and examining
the plaintext to see if it appears reasonable.
2.1. The Million Message Attack
The purpose of the Million Message Attack (MMA) is to recover a sin-
gle plaintext (formatted block) given the ciphertext (encrypted
block). The attacker first captures the ciphertext in transit and
then uses the recipient as an oracle to recover the plaintext by
sending transformed versions of the ciphertext and observing the
recipient's response.
Call the ciphertext C. The attacker then generates a series of inte-
gers S and computes C'=C(S^e) mod n. Upon decryption, C' produces a
Rescorla [Page 2] Internet-Draft Security Considerations Guidelines
corresponding plaintext M'. Most values of M' will appear to be
garbage but some values of M' (about one in 2^16) will have the cor-
rect first two bytes 00 02 and thus appear to be properly PKCS-1 for-
matted. The attack proceeds by finding a sequence of values S such
that the resulting M' is properly PKCS-1 formatted. This information
can be used to discover M. Operationally, this attack usually
requires about 2^20 messages and responses. Details can be found in
[MMA].
2.2. Applicability
Since the MMA requires so many messages, it must be mounted against a
victim who is willing to process a large number of messages. In prac-
tice, no human is willing to read this many messages and so the MMA
can only be mounted against an automated victim.
The MMA also requires that the attacker be able to distinguish cases
where M' was PKCS-1 formatted from cases where it was not. In the
case of CMS the attacker will be sending CMS messages with C' replac-
ing the wrapped CEK. Thus, there are five possibilities:
1. M' is improperly formatted.
2. M' is properly formatted but the CEK is prima facie bogus
(wrong length, etc.)
3. M' is properly formatted and the CEK appears OK. A signature
or MAC is present so integrity checking fails.
4. M' is properly formatted and no integrity check is applied.
In this case there is some possibility (approximately 1/32) that
the CBC padding block will verify properly. (The actual probability
depends highly on the receiving implementation. See "Note on
Block Cipher Padding" below). The message will
appear OK at the CMS level but will be bogus at the application
level.
5. M' is properly formatted and the resulting CEK is correct.
This is extremely improbable but not impossible.
The MMA requires the attacker to be able to distinguish case 1 from
cases 2-4. (He can always distinguish case 5, of course). This might
happen if the victim returned different errors for each case. The
attacker might also be able to distinguish these cases based on tim-
ing--decrypting the message and verifying the signature takes some
time. If the victim responds uniformly to all four errors then no
attack is possible.
2.2.1. Note on Block Cipher Padding
[CMS] specifies a particular kind of block cipher padding in which
the final cipher block is padded with bytes containing the length of
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the padding. For instance, a 5-byte block would be padded with three
bytes of value 03, as in:
XX XX XX XX XX 03 03 03
[CMS] does not specify how this padding is to be removed but merely
observes that it is unambiguous. An implementation might simply get
the value of the final byte and truncate appropriately or might ver-
ify that all the padding bytes are correct. If the receiver simply
truncates then the probability that a random block will appear to be
properly padded is roughly 1/8. If the receiver checks all the
padding bytes, then the probability is 1/256 + (1/256^2) + ...
(roughly 1/255).
2.3. Countermeasures
2.3.1. Careful Checking
Even without countermeasures, sufficiently careful checking can go
quite a long way to mitigating the success of the MMA. If the
receiving implementation also checks the length of the CEK and the
parity bits (if available) AND responds identically to all such
errors, the chances of a given M' being properly formatted are sub-
stantially decreased. This increases the number of probe messages
required to recover M. However, this sort of checking only increases
the workfactor and does not eliminate the attack entirely because
some messages will still be properly formatted up to the point of
keylength. However, the combination of all three kinds of checking
(padding, length, parity bits) increases the number of messages to
the point where the attack is impractical.
2.3.2. Random Filling
The simplest countermeasure is to treat misformatted messages as if
they were properly PKCS-1 formatted. When the victim detects an
improperly formatted message, instead of returning an error he sub-
stitutes a randomly generated message. In CMS, since the message is
always a wrapped content-encryption key (CEK) the victim should sim-
ply substitute a randomly generated CEK of appropriate length and
continue. Eventually this will result in a decryption or signature
verification error but this is exactly what would have happened if M'
happened to be properly formatted but contained an incorrect CEK.
Note that this approach also prevents the attacker from distinguish-
ing various failure cases via timing since all failures return
roughly the same timing behavior. (The time required to generate the
random-padding is negligible in almost all cases. If an implementa-
tion has a very slow PRNG it can generate random padding for every
message and simply discard it if the CEK decrypts correctly).
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In a layered implementation it's quite possible that the PKCS-1 check
occurs at a point in the code where the length of the expected CEK is
not known. In that case the implementation must ensure that bad
PKCS-1 padding and ok-looking PKCS-1 padding with an incorrect length
CEK behave the same. An easy way to do this is to also randomize CEKs
that are of the wrong length or otherwise improperly formatted when
they are processed at the layer that knows the length.
Note: It is a mistake to use a fixed CEK because the attacker could
then produce a CMS message encrypted with that CEK. This message
would decrypt properly (i.e. appear to be a completely valid CMS
application to the receiver), thus allowing the attacker to determine
that the PKCS-1 formatting was incorrect. In fact, the new CEK
should be cryptographically random, thus preventing the attacker from
guessing the next "random" CEK to be used.
2.3.3. OAEP
Optimal Asymmetric Encryption Padding (OAEP) [OAEP, PKCS-1-v2] is
another technique for padding a message into an RSA encryption block.
Implementations using OAEP are not susceptible to the MMA. However,
OAEP is incompatible with PKCS-1. Implementations of S/MIME and CMS
must therefore continue to use PKCS-1 for the foreseeable future if
they wish to communicate with current widely deployed implementa-
tions. OAEP is being specified for use with AES keys in CMS so this
provides an upgrade path to OAEP.
2.4. Security Considerations
This entire document describes how to avoid a certain class of
attacks when performing PKCS-1 decryption with RSA.
Acknowledgments
Thanks to Burt Kaliski and Russ Housley for their extensive and help-
ful comments.
References
CMS Housley, R., "Cryptographic Message Syntax", RFC 2630,
June 1999.
MMA Bleichenbacher, D., "Chosen Ciphertext Attacks against
Protocols based on RSA Encryption Standard PKCS #1",
Advances in Cryptology -- CRYPTO 98.
MMAUPDATE D. Bleichenbacher, B. Kaliski, and J. Staddon, "Recent
Results on PKCS #1: RSA Encryption Standard",
RSA Laboratories' Bulletin #7, June 26, 1998.
Rescorla [Page 5] Internet-Draft Security Considerations Guidelines
OAEP Bellare, M., Rogaway, P., "Optimal Asymmetric Encryption
Padding", Advances in Cryptology -- Eurocrypt 94.
PKCS-1-v1.5 Kaliski, B., "PKCS #1: RSA Encryption, Version 1.5.",
RFC 2313, March 1998.
PKCS-1-v2 Kaliski, B., "PKCS #1: RSA Encryption, Version 2.0",
RFC 2347, October 1998.
Author's Address
Eric Rescorla <ekr@rtfm.com>
RTFM, Inc.
2064 Edgewood Drive
Palo Alto, CA 94303
Phone: (650) 320-8549
Rescorla [Page 6] Internet-Draft Security Considerations Guidelines
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Overview of PKCS-1 . . . . . . . . . . . . . . . . . . . . . . . 1
2.1. The Million Message Attack . . . . . . . . . . . . . . . . . . 2
2.2. Applicability . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2.1. Note on Block Cipher Padding . . . . . . . . . . . . . . . . 3
2.3. Countermeasures . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3.1. Careful Checking . . . . . . . . . . . . . . . . . . . . . . 4
2.3.2. Random Filling . . . . . . . . . . . . . . . . . . . . . . . 4
2.3.3. OAEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.4. Security Considerations . . . . . . . . . . . . . . . . . . . . 5
2.4. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . 5
2.4. References . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . . 6
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