rfc3218.txt

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Network Working Group                                        E. Rescorla
Request for Comments: 3218                                    RTFM, Inc.
Category: Informational                                     January 2002


                Preventing the Million Message Attack on
                      Cryptographic Message Syntax

Status of this Memo

   This memo provides information for the Internet community.  It does
   not specify an Internet standard of any kind.  Distribution of this
   memo is unlimited.

Copyright Notice

   Copyright (C) The Internet Society (2002).  All Rights Reserved.

Abstract

   This memo describes a strategy for resisting the Million Message
   Attack.

Table of Contents

   1. Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   1
   2. Overview of PKCS-1  . . . . . . . . . . . . . . . . . . . . .   2
   2.1. The Million Message Attack  . . . . . . . . . . . . . . . .   3
   2.2. Applicability . . . . . . . . . . . . . . . . . . . . . . .   3
   2.2.1. Note on Block Cipher Padding  . . . . . . . . . . . . . .   4
   2.3. Countermeasures . . . . . . . . . . . . . . . . . . . . . .   4
   2.3.1. Careful Checking  . . . . . . . . . . . . . . . . . . . .   4
   2.3.2. Random Filling  . . . . . . . . . . . . . . . . . . . . .   5
   2.3.3. OAEP  . . . . . . . . . . . . . . . . . . . . . . . . . .   5
   2.4. Security Considerations . . . . . . . . . . . . . . . . . .   6
   3. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . .   6
   4. References  . . . . . . . . . . . . . . . . . . . . . . . . .   6
   5. Author's Address. . . . . . . . . . . . . . . . . . . . . . .   6
   6. Full Copyright Statement  . . . . . . . . . . . . . . . . . .   7

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
   technique 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



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RFC 3218      Preventing the Million Message Attack on CMS  January 2002


   attacker could convince the receiver to act as a particular kind of
   oracle. (An oracle is a program which answers queries based on
   information 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
   modulus of the recipient's public key (typically somewhere between
   512 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
   modulus.  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
   integer 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
   prevents 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 CEK 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



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   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
   single 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
   integers S and computes C'=C*(S^e) mod n.  Upon decryption, C'
   produces a 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
   correct first two bytes 00 02 and thus appear to be properly PKCS-1
   formatted.  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
   practice, 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'
   replacing 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.




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RFC 3218      Preventing the Million Message Attack on CMS  January 2002


   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
   timing -- 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
   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
   verify that all the padding bytes are correct.  If the receiver