Key Stream (1): 18 3C 56 28 8E 3C E9 AA 22 16 56 CB 23 A6 9A 4F
Ciphertext : 4B 55 38 4F E2 59 C9 C8 4E 79 35 A0 03 CB E9 28
Test Vector #5: Encrypting 32 octets using AES-CTR with 192-bit key
AES Key : 7C 5C B2 40 1B 3D C3 3C 19 E7 34 08 19 E0 F6 9C
: 67 8C 3D B8 E6 F6 A9 1A
AES-CTR IV : 02 0C 6E AD C2 CB 50 0D
Nonce : 00 96 B0 3B
Plaintext : 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
: 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
Counter Block (1): 00 96 B0 3B 02 0C 6E AD C2 CB 50 0D 00 00 00 01
Key Stream (1): 45 33 41 FF 64 9E 25 35 76 D6 A0 F1 7D 3C C3 90
Counter Block (2): 00 96 B0 3B 02 0C 6E AD C2 CB 50 0D 00 00 00 02
Key Stream (2): 94 81 62 0F 4E C1 B1 8B E4 06 FA E4 5E E9 E5 1F
Ciphertext : 45 32 43 FC 60 9B 23 32 7E DF AA FA 71 31 CD 9F
: 84 90 70 1C 5A D4 A7 9C FC 1F E0 FF 42 F4 FB 00
Test Vector #6: Encrypting 36 octets using AES-CTR with 192-bit key
AES Key : 02 BF 39 1E E8 EC B1 59 B9 59 61 7B 09 65 27 9B
: F5 9B 60 A7 86 D3 E0 FE
AES-CTR IV : 5C BD 60 27 8D CC 09 12
Nonce : 00 07 BD FD
Plaintext : 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
: 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
: 20 21 22 23
Counter Block (1): 00 07 BD FD 5C BD 60 27 8D CC 09 12 00 00 00 01
Key Stream (1): 96 88 3D C6 5A 59 74 28 5C 02 77 DA D1 FA E9 57
Counter Block (2): 00 07 BD FD 5C BD 60 27 8D CC 09 12 00 00 00 02
Key Stream (2): C2 99 AE 86 D2 84 73 9F 5D 2F D2 0A 7A 32 3F 97
Counter Block (3): 00 07 BD FD 5C BD 60 27 8D CC 09 12 00 00 00 03
Key Stream (3): 8B CF 2B 16 39 99 B2 26 15 B4 9C D4 FE 57 39 98
Ciphertext : 96 89 3F C5 5E 5C 72 2F 54 0B 7D D1 DD F7 E7 58
: D2 88 BC 95 C6 91 65 88 45 36 C8 11 66 2F 21 88
: AB EE 09 35
Test Vector #7: Encrypting 16 octets using AES-CTR with 256-bit key
AES Key : 77 6B EF F2 85 1D B0 6F 4C 8A 05 42 C8 69 6F 6C
: 6A 81 AF 1E EC 96 B4 D3 7F C1 D6 89 E6 C1 C1 04
AES-CTR IV : DB 56 72 C9 7A A8 F0 B2
Nonce : 00 00 00 60
Plaintext String : ’Single block msg’
Plaintext : 53 69 6E 67 6C 65 20 62 6C 6F 63 6B 20 6D 73 67
Counter Block (1): 00 00 00 60 DB 56 72 C9 7A A8 F0 B2 00 00 00 01
Key Stream (1): 47 33 BE 7A D3 E7 6E A5 3A 67 00 B7 51 8E 93 A7
Ciphertext : 14 5A D0 1D BF 82 4E C7 56 08 63 DC 71 E3 E0 C0
Test Vector #8: Encrypting 32 octets using AES-CTR with 256-bit key
AES Key : F6 D6 6D 6B D5 2D 59 BB 07 96 36 58 79 EF F8 86
: C6 6D D5 1A 5B 6A 99 74 4B 50 59 0C 87 A2 38 84
AES-CTR IV : C1 58 5E F1 5A 43 D8 75
Nonce : 00 FA AC 24
Plaintext : 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
: 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
Counter block (1): 00 FA AC 24 C1 58 5E F1 5A 43 D8 75 00 00 00 01
Key stream (1): F0 5F 21 18 3C 91 67 2B 41 E7 0A 00 8C 43 BC A6
Counter block (2): 00 FA AC 24 C1 58 5E F1 5A 43 D8 75 00 00 00 02
Key stream (2): A8 21 79 43 9B 96 8B 7D 4D 29 99 06 8F 59 B1 03
Ciphertext : F0 5E 23 1B 38 94 61 2C 49 EE 00 0B 80 4E B2 A9
: B8 30 6B 50 8F 83 9D 6A 55 30 83 1D 93 44 AF 1C
Test Vector #9: Encrypting 36 octets using AES-CTR with 256-bit key
AES Key : FF 7A 61 7C E6 91 48 E4 F1 72 6E 2F 43 58 1D E2
: AA 62 D9 F8 05 53 2E DF F1 EE D6 87 FB 54 15 3D
AES-CTR IV : 51 A5 1D 70 A1 C1 11 48
Nonce : 00 1C C5 B7
Plaintext : 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
: 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
: 20 21 22 23
Counter block (1): 00 1C C5 B7 51 A5 1D 70 A1 C1 11 48 00 00 00 01
Key stream (1): EB 6D 50 81 19 0E BD F0 C6 7C 9E 4D 26 C7 41 A5
Counter block (2): 00 1C C5 B7 51 A5 1D 70 A1 C1 11 48 00 00 00 02
Key stream (2): A4 16 CD 95 71 7C EB 10 EC 95 DA AE 9F CB 19 00
Counter block (3): 00 1C C5 B7 51 A5 1D 70 A1 C1 11 48 00 00 00 03
Key stream (3): 3E E1 C4 9B C6 B9 CA 21 3F 6E E2 71 D0 A9 33 39
Ciphertext : EB 6C 52 82 1D 0B BB F7 CE 75 94 46 2A CA 4F AA
: B4 07 DF 86 65 69 FD 07 F4 8C C0 B5 83 D6 07 1F
: 1E C0 E6 B8
7. Security Considerations
When used properly, AES-CTR mode provides strong confidentiality.
Bellare, Desai, Jokipii, Rogaway show in [BDJR] that the privacy
guarantees provided by counter mode are at least as strong as those
for CBC mode when using the same block cipher.
Unfortunately, it is very easy to misuse this counter mode. If
counter block values are ever used for more that one packet with the
same key, then the same key stream will be used to encrypt both
packets, and the confidentiality guarantees are voided.
What happens if the encryptor XORs the same key stream with two
different plaintexts? Suppose two plaintext byte sequences P1, P2,
P3 and Q1, Q2, Q3 are both encrypted with key stream K1, K2, K3. The
two corresponding ciphertexts are:
(P1 XOR K1), (P2 XOR K2), (P3 XOR K3)
(Q1 XOR K1), (Q2 XOR K2), (Q3 XOR K3)
If both of these two ciphertext streams are exposed to an attacker,
then a catastrophic failure of confidentiality results, since:
(P1 XOR K1) XOR (Q1 XOR K1) = P1 XOR Q1
(P2 XOR K2) XOR (Q2 XOR K2) = P2 XOR Q2
(P3 XOR K3) XOR (Q3 XOR K3) = P3 XOR Q3
Once the attacker obtains the two plaintexts XORed together, it is
relatively straightforward to separate them. Thus, using any stream
cipher, including AES-CTR, to encrypt two plaintexts under the same
key stream leaks the plaintext.
Therefore, stream ciphers, including AES-CTR, should not be used with
static keys. It is inappropriate to use AES-CTR with static keys.
Extraordinary measures would be needed to prevent reuse of a counter
block value with the static key across power cycles. To be safe, ESP
implementations MUST use fresh keys with AES-CTR. The Internet Key
Exchange (IKE) protocol [IKE] can be used to establish fresh keys.
IKE can also be used to establish the nonce at the beginning of the
security association.
When IKE is used to establish fresh keys between two peer entities,
separate keys are established for the two traffic flows. When a
mechanism other than IKE is used to establish fresh keys, and that
mechanism establishes only a single key to encrypt packets, then
there is a high probability that the peers will select the same IV
values for some packets. Thus, to avoid counter block collisions,
ESP implementations that permit use of the same key for encrypting
outbound traffic and decrypting incoming traffic with the same peer
MUST ensure that the two peers assign different Nonce values to the
security association.
Data forgery is trivial with CTR mode. The demonstration of this
attack is similar to the key stream reuse discussion above. If a
known plaintext byte sequence P1, P2, P3 is encrypted with key stream
K1, K2, K3, then the attacker can replace the plaintext with one of
his own choosing. The ciphertext is:
(P1 XOR K1), (P2 XOR K2), (P3 XOR K3)
The attacker simply XORs a selected sequence Q1, Q2, Q3 with the
ciphertext to obtain:
(Q1 XOR (P1 XOR K1)), (Q2 XOR (P2 XOR K2)), (Q3 XOR (P3 XOR K3))
Which is the same as:
((Q1 XOR P1) XOR K1), ((Q2 XOR P2) XOR K2), ((Q3 XOR P3) XOR K3)
Decryption of the attacker-generated ciphertext will yield exactly
what the attacker intended:
(Q1 XOR P1), (Q2 XOR P2), (Q3 XOR P3)
Accordingly, ESP implementations MUST use of AES-CTR in conjunction
with ESP authentication.
Additionally, since AES has a 128-bit block size, regardless of the
mode employed, the ciphertext generated by AES encryption becomes
distinguishable from random values after 2^64 blocks are encrypted
with a single key. Since ESP with Enhanced Sequence Numbers allows
for up to 2^64 packets in a single security association, there is
real potential for more than 2^64 blocks to be encrypted with one
key. Therefore, implementations SHOULD generate a fresh key before
2^64 blocks are encrypted with the same key. Note that ESP with 32-
bit Sequence Numbers will not exceed 2^64 blocks even if all of the
packets are maximum-length IPv6 jumbograms [JUMBO].
There are fairly generic precomputation attacks against all block
cipher modes that allow a meet-in-the-middle attack against the key.
These attacks require the creation and searching of huge tables of
ciphertext associated with known plaintext and known keys. Assuming
that the memory and processor resources are available for a
precomputation attack, then the theoretical strength of AES-CTR (and
any other block cipher mode) is limited to 2^(n/2) bits, where n is
the number of bits in the key. The use of long keys is the best
countermeasure to precomputation attacks. Therefore, implementations
that employ 128-bit AES keys should take precautions to make the
precomputation attacks more difficult. The unpredictable nonce value
in the counter block significantly increases the size of the table
that the attacker must compute to mount a successful attack.
8. Design Rationale
In the development of this specification, the use of the ESP sequence
number field instead of an explicit IV field was considered. This
selection is not a cryptographic security issue, as either approach
will prevent counter block collisions.
In a very conservative model of encryption security, at most 2^64
blocks ought to be encrypted with AES-CTR under a single key. Under
this constraint, no more than 64 bits are needed to identify each
packet within a security association. Since the ESP extended
sequence number is 64 bits, it is an obvious candidate for use as an
implicit IV. This would dictate a single method for the assignment
of per-packet value in the counter block. The use of an explicit IV
does not dictate such a method, which is desirable for several
reasons.
1. Only the encryptor can ensure that the value is not used for more
than one packet, so there is no advantage to selecting a mechanism
that allows the decryptor to determine whether counter block
values collide. Damage from the collision is done, whether the
decryptor detects it or not.
2. Allows adders, LFSRs, and any other technique that meets the time
budget of the encryptor, so long as the technique results in a
unique value for each packet. Adders are simple and
straightforward to implement, but due to carries, they do not
execute in constant time. LFSRs offer an alternative that
executes in constant time.
3. Complexity is in control of the implementer. Further, the
decision made by the implementer of the encryptor does not make
the decryptor more (or less) complex.
4. When the encryptor has more than one cryptographic hardware
device, an IV prefix can be assigned to each device, ensuring that
collisions will not occur. Yet, since the decryptor does not need
to examine IV structure, the decryptor is unaffected by the IV
structure selected by the encryptor. One cannot make use of the
same technique with the ESP sequence numbers, because the
semantics for them require sequential value generation.
5. Assurance boundaries are very important to implementations that
will be evaluated against the FIPS Pub 140-1 or FIPS Pub 140-2
[SECRQMTS]. The assignment of the per-packet counter block value
needs to be inside the assurance boundary. Some implementations
assign the sequence number inside the assurance boundary, but
others do not. A sequence number collision does not have the dire
consequences, but, as described in section 6, a collision in
counter block values has disastrous consequences.
6. Coupling with the sequence number is possible in those
architectures where the sequence number assignment is performed
within the assurance boundary. In this situation, the sequence
number and the IV field will contain the same value.
7. Decoupling from the sequence number is possible in those
architectures where the sequence number assignment is performed
outside the assurance boundary.
The use of an explicit IV field directly follows from the decoupling
of the sequence number and the per-packet counter block value. The
overhead associated with 64 bits for the IV field is acceptable.
This overhead is significantly less than the overhead associated with
Cipher Block Chaining (CBC) mode. As normally employed, CBC requires
a full block for the IV and, on average, half of a block for padding.
AES-CTR with an explicit IV has about one-third of the overhead as
AES-CBC, and the overhead is constant for each packet.
The inclusion of the nonce provides a weak countermeasure against
precomputation attacks. For this countermeasure to be effective, the
attacker must not be able to predict the value of the nonce well in
advance of security association establishment. The use of long keys
provides a strong countermeasure to precomputation attacks, and AES
offers key sizes that thwart these attacks for many decades to come.
A 28-bit block counter value is sufficient for the generation of a
key stream to encrypt the largest possible IPv6 jumbogram [JUMBO];
however, a 32-bit field is used. This size is convenient for both
hardware and software implementations.
9. IANA Considerations
IANA has assigned 13 as the ESP transform number for AES-CTR with an
explicit IV.
10. Intellectual Property Statement
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intellectual property or other rights that might be claimed to
pertain to the implementation or use of the technology described in
this document or the extent to which any license under such rights
might or might not be available; neither does it represent that it
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The IETF invites any interested party to bring to its attention any
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this standard. Please address the information to the IETF Executive
Director.
11. Acknowledgements
This document is the result of extensive discussions and compromises.
While not all of the participants are completely satisfied with the
outcome, the document is better for their contributions.
The author thanks the members of the IPsec working group for their
contributions to the design, with special mention of the efforts of
(in alphabetical order) Steve Bellovin, David Black, Niels Ferguson,
Charlie Kaufman, Steve Kent, Tero Kivinen, Paul Koning, David McGrew,
Robert Moskowitz, Jesse Walker, and Doug Whiting.
The author thanks and Alireza Hodjat, John Viega, and Doug Whiting
for assistance with the test vectors.
12. References
This section provides normative and informative references.
12.1. Normative References
[AES] NIST, FIPS PUB 197, "Advanced Encryption Standard (AES)",
November 2001.
[DOI] Piper, D., "The Internet IP Security Domain of
Interpretation for ISAKMP", RFC 2407, November 1998.
[ESP] Kent, S. and R. Atkinson, "IP Encapsulating Security
Payload (ESP)", RFC 2406, November 1998.
[MODES] Dworkin, M., "Recommendation for Block Cipher Modes of
Operation: Methods and Techniques", NIST Special
Publication 800-38A, December 2001.
[STDWORDS] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
12.2. Informative References
[ARCH] Kent, S. and R. Atkinson, "Security Architecture for the
Internet Protocol", RFC 2401, November 1998.
[BDJR] Bellare, M, Desai, A., Jokipii, E. and P. Rogaway, "A
Concrete Security Treatment of Symmetric Encryption:
Analysis of the DES Modes of Operation", Proceedings 38th
Annual Symposium on Foundations of Computer Science,
1997.
[HMAC-SHA] Madson, C. and R. Glenn, "The Use of HMAC-SHA-1-96 within
ESP and AH", RFC 2404, November 1998.
[IKE] Harkins, D. and D. Carrel, "The Internet Key Exchange
(IKE)", RFC 2409, November 1998.
[JUMBO] Borman, D., Deering, S. and R. Hinden, "IPv6 Jumbograms",
RFC 2675, August 1999.
[ROADMAP] Thayer, R., Doraswamy, N. and R. Glenn, "IP Security
Document Roadmap", RFC 2411, November 1998.
[SECRQMTS] National Institute of Standards and Technology. FIPS Pub
140-1: Security Requirements for Cryptographic Modules.
11 January 1994.
National Institute of Standards and Technology. FIPS Pub
140-2: Security Requirements for Cryptographic Modules.
25 May 2001. [Supercedes FIPS Pub 140-1]
13. Author’s Address
Russell Housley
Vigil Security, LLC
918 Spring Knoll Drive
Herndon, VA 20170
USA
EMail: housley@vigilsec.com
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