CFRG S. Gueron
Internet-Draft University of Haifa and Intel Corporation
Intended status: Informational A. Langley
Expires: August 27, 2017 Google
Y. Lindell
Bar Ilan University
February 23, 2017
AES-GCM-SIV: Nonce Misuse-Resistant Authenticated Encryption
draft-irtf-cfrg-gcmsiv-04
Abstract
This memo specifies two authenticated encryption algorithms that are
nonce misuse-resistant - that is that they do not fail
catastrophically if a nonce is repeated.
Status of This Memo
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described in the Simplified BSD License.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Requirements Language . . . . . . . . . . . . . . . . . . . . 3
3. POLYVAL . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4. Encryption . . . . . . . . . . . . . . . . . . . . . . . . . 4
5. Decryption . . . . . . . . . . . . . . . . . . . . . . . . . 6
6. AEADs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
7. Field operation examples . . . . . . . . . . . . . . . . . . 7
8. Worked example . . . . . . . . . . . . . . . . . . . . . . . 7
9. Security Considerations . . . . . . . . . . . . . . . . . . . 8
10. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 9
11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 9
12. References . . . . . . . . . . . . . . . . . . . . . . . . . 9
12.1. Normative References . . . . . . . . . . . . . . . . . . 9
12.2. Informative References . . . . . . . . . . . . . . . . . 10
Appendix A. The relationship between POLYVAL and GHASH . . . . . 10
Appendix B. Additional comparisons with AES-GCM . . . . . . . . 12
Appendix C. Test vectors . . . . . . . . . . . . . . . . . . . . 12
C.1. AEAD_AES_128_GCM_SIV . . . . . . . . . . . . . . . . . . 12
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 46
1. Introduction
The concept of "Authenticated encryption with additional data" (AEAD
[RFC5116]) couples confidentiality and integrity in a single
operation that is easier for practitioners to use correctly. The
most popular AEAD, AES-GCM [GCM], is seeing widespread use due to its
attractive performance.
However, most AEADs suffer catastrophic failures of confidentiality
and/or integrity when two distinct messages are encrypted with the
same nonce. While the requirements for AEADs specify that the pair
of (key, nonce) shall only ever be used once, and thus prohibit this,
in practice this is a worry.
Nonce misuse-resistant AEADs do not suffer from this problem. For
this class of AEADs, encrypting two messages with the same nonce only
discloses whether the messages were equal or not. This is the
minimum amount of information that a deterministic algorithm can leak
in this situation.
This memo specifies two nonce misuse-resistant AEADs:
"AEAD_AES_128_GCM_SIV" and "AEAD_AES_256_GCM_SIV". These AEADs are
designed to be able to take advantage of existing hardware support
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for AES-GCM and can decrypt within 5% of the speed of AES-GCM (for
multi-kilobyte messages). Encryption is, perforce, slower than AES-
GCM because two passes are required. However, measurements suggest
that it can still run at 2/3rds of the speed of AES-GCM.
We suggest that these AEADs be considered in any situation where
there is the slightest doubt about nonce uniqueness.
2. 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].
3. POLYVAL
The GCM-SIV construction is similar to GCM: the block cipher is used
in counter mode to encrypt the plaintext and a polynomial
authenticator is used to provide integrity. The authenticator in
GCM-SIV is called POLYVAL.
POLYVAL, like GHASH, operates in a binary field of size 2^128. The
field is defined by the irreducible polynomial x^128 + x^127 + x^126
+ x^121 + 1. The sum of any two elements in the field is the result
of XORing them. The product of any two elements is calculated using
standard (binary) polynomial multiplication followed by reduction
modulo the irreducible polynomial.
We define another binary operation on elements of the field: dot(a,
b), where dot(a, b) = a * b * x^-128. The value of the field element
x^-128 is equal to x^127 + x^124 + x^121 + x^114 + 1. The result,
dot(a, b), of this multiplication is another field element.
Polynomials in this field are converted to and from 128-bit strings
by taking the least-significant bit of the first byte to be the
coefficient of x^0, the most-significant bit of the first byte to the
coefficient of x^7 and so on, until the most-significant bit of the
last byte is the coefficient of x^127.
POLYVAL takes a field element, H, and a series of field elements X_1,
..., X_s. Its result is S_s, where S is defined by the iteration S_0
= 0; S_j = dot(S_{j-1} + X_j, H), for j = 0..s
We note that POLYVAL(H, X_1, X_2, ...) is equal to
ByteReverse(GHASH(ByteReverse(H) * x, ByteReverse(X_1),
ByteReverse(X_2), ...)), where ByteReverse is a function that
reverses the order of 16 bytes. See Appendix A for a more detailed
explanation.
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4. Encryption
AES-GCM-SIV encryption takes a 16- or 32-byte key-generating key, a
96-bit nonce, and arbitrary-length plaintext & additional data byte-
strings. It outputs an authenticated ciphertext that will be 16
bytes longer than the plaintext.
If the key-generating key is 16 bytes long then AES-128 is used
throughout. Otherwise AES-256 is used throughout.
The first step of encryption is to generate per-nonce, record-
authentication and record-encryption keys. The record-authentication
key is 128-bit and the record-encryption key is either 128- (for AES-
128) or 256-bit (for AES-256).
These keys are generated by encrypting a series of plaintext blocks
that contain a 32-bit, little-endian counter followed by the nonce,
and then discarding the second half of the resulting ciphertext. In
the AES-128 case, 128 + 128 = 256 bits of key material need to be
generated and, since encrypting each block yields 64 bits after
discarding half, four blocks need to be encrypted. The counter
values for these blocks are 0, 1, 2 and 3. For AES-256, six blocks
are needed in total, with counter values 0 through 5 (inclusive).
In pseudocode form, where ++ indicates concatenation and x[:8]
indicates taking only the first eight bytes from x:
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if bytelen(key-generating-key) == 16 {
record-authentication-key =
AES128(key = key-generating-key,
input = "00000000" ++ nonce)[:8] ++
AES128(key = key-generating-key,
input = "01000000" ++ nonce)[:8]
record-encryption-key =
AES128(key = key-generating-key,
input = "02000000" ++ nonce)[:8] ++
AES128(key = key-generating-key,
input = "03000000" ++ nonce)[:8]
} else if bytelen(key-generating-key) == 32 {
record-authentication-key =
AES256(key = key-generating-key,
input = "00000000" ++ nonce)[:8] ++
AES256(key = key-generating-key,
input = "01000000" ++ nonce)[:8]
record-encryption-key =
AES256(key = key-generating-key,
input = "02000000" ++ nonce)[:8] ++
AES256(key = key-generating-key,
input = "03000000" ++ nonce)[:8] ++
AES256(key = key-generating-key,
input = "04000000" ++ nonce)[:8] ++
AES256(key = key-generating-key,
input = "05000000" ++ nonce)[:8]
}
Define the _length block_ as a 16-byte value that is the
concatenation of the 64-bit, little-endian encodings of
bytelen(additional_length) * 8 and bytelen(plaintext) * 8. Pad the
plaintext and additional data with zeros until they are each a
multiple of 16 bytes, the AES block size. Then X_1, X_2, ... (the
series of field elements that are inputs to POLYVAL) are the
concatenation of the padded additional data, the padded plaintext and
the length block.
Calculate S_s = POLYVAL(record-authentication-key, X_1, X_2, ...).
XOR the first twelve bytes of S_s with the nonce and clear the most-
significant bit of the last byte. Encrypt the result with AES using
the record-encryption key to produce the tag.
The ciphertext is produced by using AES, with the record-encryption
key, in counter mode on the unpadded plaintext. The initial counter
block is the tag with the most-significant bit of the last byte set
to one. The counter advances by incrementing the first 32 bits
interpreted as an unsigned, little-endian integer. The result of the
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encryption is the resulting ciphertext (truncated to the length of
the plaintext) followed by the tag.
5. Decryption
Decryption takes a 16- or 32-byte key-generating key, a 96-bit nonce,
and arbitrary-length ciphertext & additional data byte-strings. It
either fails, or outputs a plaintext that is 16 bytes shorter than
the ciphertext.
Firstly, the record-encryption and record-authentication keys are
derived in the same manner as when encrypting.
If the ciphertext is less than 16 bytes or more than 2^36 + 16 bytes,
then fail. Otherwise split the input into the encrypted plaintext
and a 16-byte tag. Decrypt the encrypted plaintext with the record-
encryption key in counter mode, where the initial counter block is
the tag with the most-significant bit of the last byte set to one.
The counter advances in the same way as for encryption.
Pad the additional data and plaintext with zeros until they are each
a multiple of 16 bytes, the AES block size. Calculate the length
block and X_1, X_2, ... as above and compute S_s = POLYVAL(record-
authentication-key, X_1, X_2, ...). Compute the expected tag by
XORing S_s and the nonce, clearing the most-significant bit of the
last byte and encrypting with the record-encryption key. Compare the
provided and expected tag values in constant time. If they do not
match, fail. Otherwise return the plaintext.
6. AEADs
We define two AEADs, in the format of RFC 5116, that use AES-GCM-SIV:
AEAD_AES_128_GCM_SIV and AEAD_AES_256_GCM_SIV. They differ only in
the size of the AES key used.
The key input to these AEADs becomes the key-generating key. Thus
AEAD_AES_128_GCM_SIV takes a 16-byte key and AEAD_AES_256_GCM_SIV
takes a 32-byte key.
The parameters for AEAD_AES_128_GCM_SIV are then: K_LEN is 16, P_MAX
is 2^36, A_MAX is 2^61 - 1, N_MIN and N_MAX are 12 and C_MAX is 2^36
+ 16.
The parameters for AEAD_AES_256_GCM_SIV differ only in the key size:
K_LEN is 32, P_MAX is 2^36, A_MAX is 2^61 - 1, N_MIN and N_MAX are 12
and C_MAX is 2^36 + 16.
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7. Field operation examples
Polynomials in this document will be written as 16-byte values. For
example, the sixteen bytes 01000000000000000000000000000492 would
represent the polynomial x^127 + x^124 + x^121 + x^114 + 1, which is
also the value of x^-128 in this field.
If a = 66e94bd4ef8a2c3b884cfa59ca342b2e and b =
ff000000000000000000000000000000 then a + b =
99e94bd4ef8a2c3b884cfa59ca342b2e, a * b =
37856175e9dc9df26ebc6d6171aa0ae9 and dot(a, b) =
ebe563401e7e91ea3ad6426b8140c394.
8. Worked example
Consider the encryption of the plaintext "Hello world" with the
additional data "example" under key ee8e1ed9ff2540ae8f2ba9f50bc2f27c
using AEAD_AES_128_GCM_SIV. The random nonce that we'll use for this
example is 752abad3e0afb5f434dc4310.
In order to generate the record-authentication and record-encryption
keys, a counter is combined with the nonce to form four blocks.
These blocks are encrypted with key given above:
Counter | Nonce Ciphertext
00000000752abad3e0afb5f434dc4310 -> 310728d9911f1f38c40e952ca83d093e
01000000752abad3e0afb5f434dc4310 -> 37b24316c3fab9a046ae90952daa0450
02000000752abad3e0afb5f434dc4310 -> a4c5ae624996327947920b2d2412474b
03000000752abad3e0afb5f434dc4310 -> c100be4d7e2c6edd1efef004305ab1e7
The latter halves of the ciphertext blocks are discarded and the
remaining bytes are concatenated to form the per-record keys. Thus
the record-authentication key is 310728d9911f1f3837b24316c3fab9a0 and
the record-encryption key is a4c5ae6249963279c100be4d7e2c6edd.
The length block contains the encoding of the bit-lengths of the
additional data and plaintext, respectively, which are and 56 and 88.
Thus the length block is 38000000000000005800000000000000.
The input to POLYVAL is the padded additional data, padded plaintext
and then the length block. This is 6578616d706c650000000000000000004
8656c6c6f20776f726c64000000000038000000000000005800000000000000.
Calling POLYVAL with the record-authentication key and the input
above results in S_s = ad7fcf0b5169851662672f3c5f95138f.
Before encrypting, the nonce is XORed in and the most-significant bit
of the last byte is cleared. This gives
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d85575d8b1c630e256bb6c2c5f95130f because that bit happened to be one
previously. Encrypting with the record-encryption key gives the tag,
which is 4fbcdeb7e4793f4a1d7e4faa70100af1.
In order to form the initial counter block, the most-significant bit
of the last byte of the tag is set to one. That doesn't result in a
change in this example. Encrypting this with the record key gives
the first block of the keystream: 1551f2c1787e81deac9a99f139540ab5.
The final ciphertext is the result of XORing the plaintext with the
keystream and appending the tag. That gives
5d349ead175ef6b1def6fd4fbcdeb7e4793f4a1d7e4faa70100af1.
9. Security Considerations
A detailed analysis of these schemes appears in [AES-GCM-SIV] and the
remainder of this section is a summary of that paper.
We recommend a limit of 2^50 plaintexts encrypted with a given key.
Past this point, AES-GCM-SIV may be distinguishable from an ideal
AEAD. (This is based on standard assumptions about AES.)
The AEADs defined in this document calculate fresh AES keys for each
nonce. This allows a larger number of plaintexts to be encrypted
under a given key. Without this step, each SIV encryption would be
like a standard GCM encryption with a random nonce. Since the nonce
size for GCM is only 12 bytes, NIST set a limit [GCM] of 2^32
encryptions before the probability of duplicate nonces becomes too
high.
The authors felt that, while large, 2^32 wasn't so large that this
limit could be safely ignored. For example, consider encrypting the
contents of a hard disk where the AEAD record size is 512 bytes, to
match the traditional size of a disk sector. This process would have
encrypted 2^32 records after processing 2TB, yet hard drives of
multiple terabytes are now common.
Deriving fresh AES keys for each nonce alleviates this problem.
If the nonce is fixed then AES-GCM-SIV acts like AES-GCM with a
random nonce, with the caveat that identical plaintexts will produce
identical ciphertexts. However, we feel that the 2^32 limit for AES-
GCM is too risky in a multi-key setting. Thus with AES-GCM-SIV we
recommend that, for a specific key, a nonce not be repeated more than
2^8 times. (And, ideally, not be repeated at all.) See theorem six
and figure four from the paper for detailed bounds.
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Suzuki et al [multibirthday] show that even if nonces are selected
uniformly at random, the probability that one or more values would be
repeated 256 or more times is negligible until the number of nonces
reaches 2^102. (Specifically the probability is 1/((2^96)^(255)) *
Binomial(q, 256), where q is the number of nonces.) Since 2^102 is
vastly greater than the limit on the number of plaintexts per key
given above, we don't feel that this limit on the number of repeated
nonces will be a problem. This also means that selecting nonces at
random is a safe practice with AES-GCM-SIV.
In addition to calculating fresh AES keys for each nonce, these AEADs
also calculate fresh POLYVAL keys. Previous versions of GCM-SIV did
not do this and, instead, used part of the AEAD's key as the POLYVAL
key. Bleichenbacher pointed out that this allowed an attacker who
controlled the AEAD key to force the POLYVAL key to be zero. If a
user of this AEAD authenticated messages with a secret additional-
data value then this would be insecure as the attacker could
calculate a valid authenticator without knowing the input. This does
not violate the standard properties of an AEAD as the additional data
is not assumed to be confidential. However, we want these AEADs to
be robust to plausible misuse and also to be drop-in replacements for
AES-GCM and so derive nonce-specific POLYVAL keys to avoid this
issue.
A security analysis of a similar scheme appears in [GCM-SIV].
10. IANA Considerations
This document has no actions for IANA.
11. Acknowledgements
The authors would like to thank Uri Blumenthal, Ondrej Mosnaček,
Daniel Bleichenbacher, Kenny Paterson, Bart Preneel, John Mattsson
and Deb Cooley's team at NSA Information Assurance for their helpful
suggestions.
12. References
12.1. 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,
<http://www.rfc-editor.org/info/rfc2119>.
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12.2. Informative References
[AES-GCM-SIV]
Gueron, S., Langley, A., and Y. Lindell, "AES-GCM-SIV:
specification and analysis", 2017,
<https://eprint.iacr.org/2017/168>.
[GCM] Dworkin, M., "Recommendation for Block Cipher Modes of
Operation: Galois/Counter Mode (GCM) and GMAC", NIST SP-
800-38D, November 2007,
<http://csrc.nist.gov/publications/nistpubs/800-38D/
SP-800-38D.pdf>.
[GCM-SIV] Gueron, S. and Y. Lindell, "GCM-SIV: Full Nonce Misuse-
Resistant Authenticated Encryption at Under One Cycle Per
Byte", Proceedings of the 22nd ACM SIGSAC Conference on
Computer and Communications Security , 2015,
<http://doi.acm.org/10.1145/2810103.2813613>.
[multibirthday]
Kazuhiro, S., Dongvu, T., Kaoru, K., and T. Koji,
"Birthday Paradox for Multi-collisions", ICISC 2006: 9th
International Conference, Busan, Korea, November 30 -
December 1, 2006. Proceedings , 2006,
<http://dx.doi.org/10.1007/11927587_5>.
[RFC5116] McGrew, D., "An Interface and Algorithms for Authenticated
Encryption", RFC 5116, DOI 10.17487/RFC5116, January 2008,
<http://www.rfc-editor.org/info/rfc5116>.
Appendix A. The relationship between POLYVAL and GHASH
GHASH and POLYVAL both operate in GF(2^128), although with different
irreducible polynomials: POLYVAL works modulo x^128 + x^127 + x^126 +
x^121 + 1 and GHASH works modulo x^128 + x^7 + x^2 + x + 1. Note
that these irreducible polynomials are the "reverse" of each other.
GHASH also has a different mapping between 128-bit strings and field
elements. Where as POLYVAL takes the least-significant to most-
significant bits of the first byte to be the coefficients of x^0 to
x^7, GHASH takes them to be the coefficients of x^7 to x^0. This
continues until, for the last byte, POLYVAL takes the least-
significant to most-significant bits to be the coefficients of x^120
to x^127 while GHASH takes them to be the coefficients of x^127 to
x^120.
The combination of these facts means that it's possible to "convert"
values between the two by reversing the order of the bytes in a
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16-byte string. The differing interpretations of bit order takes
care of reversing the bits within each byte and then reversing the
bytes does the rest. This may have a practical benefit for
implementations that wish to implement both GHASH and POLYVAL.
In order to be clear which field a given operation is performed in,
let mulX_GHASH be a function that takes a 16-byte string, converts it
to an element of GHASH's field using GHASH's convention, multiplies
it by x and converts back to a string. Likewise, let mulX_POLYVAL be
a function that converts a 16-byte string to an element of POLYVAL's
field using POLYVAL's convention, multiplies it by x and converts
back.
Given the 16-byte string 01000000000000000000000000000000, mulX_GHASH
of that string is 00800000000000000000000000000000 and mulX_POLYVAL
of that string is 02000000000000000000000000000000. As a more
general example, given 9c98c04df9387ded828175a92ba652d8, mulX_GHASH
of that string is 4e4c6026fc9c3ef6c140bad495d3296c and mulX_POLYVAL
of it is 3931819bf271fada0503eb52574ca5f2.
Lastly, let ByteReverse be the function that takes a 16-byte string
and returns a copy where the order of the bytes has been reversed.
Now GHASH and POLYVAL can be defined in terms of one another:
POLYVAL(H, X_1, ..., X_n) =
ByteReverse(GHASH(mulX_GHASH(ByteReverse(H)), ByteReverse(X_1), ...,
ByteReverse(X_n)))
GHASH(H, X_1, ..., X_n) =
ByteReverse(POLYVAL(mulX_POLYVAL(ByteReverse(H)), ByteReverse(X_1),
..., ByteReverse(X_n)))
As a worked example, let H = 25629347589242761d31f826ba4b757b, X_1 =
4f4f95668c83dfb6401762bb2d01a262 and X_2 =
d1a24ddd2721d006bbe45f20d3c9f362. POLYVAL(H, X_1, X_2) =
f7a3b47b846119fae5b7866cf5e5b77e. If we wished to calculate this
given only an implementation of GHASH then the key for GHASH would be
mulX_GHASH(ByteReverse(H)) = dcbaa5dd137c188ebb21492c23c9b112. Then
ByteReverse(GHASH(dcba..., ByteReverse(X_1), ByteReverse(X_2))) =
f7a3b47b846119fae5b7866cf5e5b77e, as required.
In the other direction, GHASH(H, X_1, X_2) =
bd9b3997046731fb96251b91f9c99d7a. If we wished to calculate this
given only an implementation of POLYVAL then we would first calculate
the key for POLYVAL, mulX_POLYVAL(ByteReverse(H)), which is
f6ea96744df0633aec8424b18e26c54a. Then ByteReverse(POLYVAL(f6ea...,
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ByteReverse(X_1), ByteReverse(X_2))) =
bd9b3997046731fb96251b91f9c99d7a.
Appendix B. Additional comparisons with AES-GCM
Some, non-security, properties also differ between AES-GCM and AES-
GCM-SIV that are worth noting:
AES-GCM allows plaintexts to be encrypted in a streaming fashion,
i.e. the beginning of the plaintext can be encrypted and transmitted
before the entire message has been processed. AES-GCM-SIV requires
two passes for encryption and so cannot do this.
AES-GCM allows a constant additional-data input to be precomputed in
order to save per-record computation. AES-GCM-SIV varies the
authenticator key based on the nonce and so does not permit this.
The performance for AES-GCM vs AES-GCM-SIV on small machines can be
roughly characterised by the number of AES operations and the number
of GF(2^128) multiplications needed to process a message. Let a =
(bytelen(additional-data) + 15) / 16 and p = (bytelen(plaintext) +
15) / 16. Then AES-GCM requires p + 1 AES operations and p + a + 1
field multiplications.
Defined similarly, AES-GCM-SIV with AES-128 requires p + 5 AES
operations and p + a + 1 field multiplications. With AES-256 that
becomes p + 7 AES operations.
With large machines, the available parallelism becomes far more
important and such simple performance analysis is no longer
representative. For such machines, we find that decryption of AES-
GCM-SIV is only about 5% slower then AES-GCM, as long as the message
is at least a couple of kilobytes. Encryption tends to be about
2/3's the speed because of the additional pass required.
Appendix C. Test vectors
C.1. AEAD_AES_128_GCM_SIV
AEAD_AES_128_GCM_SIV:
AAD_len = 0 bytes
MSG_len = 0 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
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K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG =
PADDED_AAD =
PADDED_MSG =
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 00000000000000000000000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = dc20e2d83f25705bb49e439eca56de25
CTRBLK = dc20e2d83f25705bb49e439eca56dea5
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = dc20e2d83f25705bb49e439eca56de25
AAD =
CIPHERTEXT =
Decrypted MSG =
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 0 bytes
MSG_len = 8 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
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AAD =
MSG = 0100000000000000
PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 00000000000000004000000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = 578782fff6013b815b287c22493a364c
CTRBLK = 578782fff6013b815b287c22493a36cc
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = 578782fff6013b815b287c22493a364c
AAD =
CIPHERTEXT = b5d839330ac7b786
Decrypted MSG = 0100000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 0 bytes
MSG_len = 12 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG = 010000000000000000000000
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PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 00000000000000006000000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = a4978db357391a0bc4fdec8b0d106639
CTRBLK = a4978db357391a0bc4fdec8b0d1066b9
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = a4978db357391a0bc4fdec8b0d106639
AAD =
CIPHERTEXT = 7323ea61d05932260047d942
Decrypted MSG = 010000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 0 bytes
MSG_len = 16 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG = 01000000000000000000000000000000
PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
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Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 00000000000000008000000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = 303aaf90f6fe21199c6068577437a0c4
CTRBLK = 303aaf90f6fe21199c6068577437a0c4
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = 303aaf90f6fe21199c6068577437a0c4
AAD =
CIPHERTEXT = 743f7c8077ab25f8624e2e948579cf77
Decrypted MSG = 01000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 0 bytes
MSG_len = 32 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG = 01000000000000000000000000000000
02000000000000000000000000000000
PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
02000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
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Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 00000000000000000001000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = 1a8e45dcd4578c667cd86847bf6155ff
CTRBLK = 1a8e45dcd4578c667cd86847bf6155ff
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = 1a8e45dcd4578c667cd86847bf6155ff
AAD =
CIPHERTEXT = 84e07e62ba83a6585417245d7ec413a9
fe427d6315c09b57ce45f2e3936a9445
Decrypted MSG = 01000000000000000000000000000000
02000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 0 bytes
MSG_len = 48 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
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Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 00000000000000008001000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = 5e6e311dbf395d35b0fe39c2714388f8
CTRBLK = 5e6e311dbf395d35b0fe39c2714388f8
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = 5e6e311dbf395d35b0fe39c2714388f8
AAD =
CIPHERTEXT = 3fd24ce1f5a67b75bf2351f181a475c7
b800a5b4d3dcf70106b1eea82fa1d64d
f42bf7226122fa92e17a40eeaac1201b
Decrypted MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 0 bytes
MSG_len = 64 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
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PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 00000000000000000002000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = 8a263dd317aa88d56bdf3936dba75bb8
CTRBLK = 8a263dd317aa88d56bdf3936dba75bb8
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = 8a263dd317aa88d56bdf3936dba75bb8
AAD =
CIPHERTEXT = 2433668f1058190f6d43e360f4f35cd8
e475127cfca7028ea8ab5c20f7ab2af0
2516a2bdcbc08d521be37ff28c152bba
36697f25b4cd169c6590d1dd39566d3f
Decrypted MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 8 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
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NONCE = 03000000000000000000000000000000
AAD = 01
MSG = 0200000000000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 08000000000000004000000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = 3b0a1a2560969cdf790d99759abd1508
CTRBLK = 3b0a1a2560969cdf790d99759abd1588
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = 3b0a1a2560969cdf790d99759abd1508
AAD = 01
CIPHERTEXT = 1e6daba35669f427
Decrypted MSG = 0200000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 12 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01
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MSG = 020000000000000000000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 08000000000000006000000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = 08299c5102745aaa3a0c469fad9e075a
CTRBLK = 08299c5102745aaa3a0c469fad9e07da
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = 08299c5102745aaa3a0c469fad9e075a
AAD = 01
CIPHERTEXT = 296c7889fd99f41917f44620
Decrypted MSG = 020000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 16 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01
MSG = 02000000000000000000000000000000
PADDED_AAD = 01000000000000000000000000000000
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PADDED_MSG = 02000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 08000000000000008000000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = 8f8936ec039e4e4bb97ebd8c4457441f
CTRBLK = 8f8936ec039e4e4bb97ebd8c4457449f
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = 8f8936ec039e4e4bb97ebd8c4457441f
AAD = 01
CIPHERTEXT = e2b0c5da79a901c1745f700525cb335b
Decrypted MSG = 02000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 32 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01
MSG = 02000000000000000000000000000000
03000000000000000000000000000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
03000000000000000000000000000000
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Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 08000000000000000001000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = e6af6a7f87287da059a71684ed3498e1
CTRBLK = e6af6a7f87287da059a71684ed3498e1
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = e6af6a7f87287da059a71684ed3498e1
AAD = 01
CIPHERTEXT = 620048ef3c1e73e57e02bb8562c416a3
19e73e4caac8e96a1ecb2933145a1d71
Decrypted MSG = 02000000000000000000000000000000
03000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 48 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01
MSG = 02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
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03000000000000000000000000000000
04000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 08000000000000008001000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = 6a8cc3865f76897c2e4b245cf31c51f2
CTRBLK = 6a8cc3865f76897c2e4b245cf31c51f2
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = 6a8cc3865f76897c2e4b245cf31c51f2
AAD = 01
CIPHERTEXT = 50c8303ea93925d64090d07bd109dfd9
515a5a33431019c17d93465999a8b005
3201d723120a8562b838cdff25bf9d1e
Decrypted MSG = 02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 64 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01
MSG = 02000000000000000000000000000000
03000000000000000000000000000000
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04000000000000000000000000000000
05000000000000000000000000000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
05000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 08000000000000000002000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = cdc46ae475563de037001ef84ae21744
CTRBLK = cdc46ae475563de037001ef84ae217c4
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = cdc46ae475563de037001ef84ae21744
AAD = 01
CIPHERTEXT = 2f5c64059db55ee0fb847ed513003746
aca4e61c711b5de2e7a77ffd02da42fe
ec601910d3467bb8b36ebbaebce5fba3
0d36c95f48a3e7980f0e7ac299332a80
Decrypted MSG = 02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
05000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 12 bytes
MSG_len = 4 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
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--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 010000000000000000000000
MSG = 02000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 60000000000000002000000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = 07eb1f84fb28f8cb73de8e99e2f48a14
CTRBLK = 07eb1f84fb28f8cb73de8e99e2f48a94
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = 07eb1f84fb28f8cb73de8e99e2f48a14
AAD = 010000000000000000000000
CIPHERTEXT = a8fe3e87
Decrypted MSG = 02000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 18 bytes
MSG_len = 20 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
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NONCE = 03000000000000000000000000000000
AAD = 01000000000000000000000000000000
0200
MSG = 03000000000000000000000000000000
04000000
PADDED_AAD = 01000000000000000000000000000000
02000000000000000000000000000000
PADDED_MSG = 03000000000000000000000000000000
04000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = 9000000000000000a000000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = 24afc9805e976f451e6d87f6fe106514
CTRBLK = 24afc9805e976f451e6d87f6fe106594
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = 24afc9805e976f451e6d87f6fe106514
AAD = 01000000000000000000000000000000
0200
CIPHERTEXT = 6bb0fecf5ded9b77f902c7d5da236a43
91dd0297
Decrypted MSG = 03000000000000000000000000000000
04000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 20 bytes
MSG_len = 18 bytes
BYTES ORDER
LSB--------------------------MSB
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00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01000000000000000000000000000000
02000000
MSG = 03000000000000000000000000000000
0400
PADDED_AAD = 01000000000000000000000000000000
02000000000000000000000000000000
PADDED_MSG = 03000000000000000000000000000000
04000000000000000000000000000000
Record_Hash_Key = d9b360279694941ac5dbc6987ada7377
Record_Enc_Key = 4004a0dcd862f2a57360219d2d44ef6c
LENBLK = a0000000000000009000000000000000
POLYVAL xor N = d9b360279694941a2010be790ff81954
TAG = bff9b2ef00fb47920cc72a0c0f13b9fd
CTRBLK = bff9b2ef00fb47920cc72a0c0f13b9fd
Encryption_Key = 4004a0dcd862f2a57360219d2d44ef6c
TAG' = bff9b2ef00fb47920cc72a0c0f13b9fd
AAD = 01000000000000000000000000000000
02000000
CIPHERTEXT = 44d0aaf6fb2f1f34add5e8064e83e12a
2ada
Decrypted MSG = 03000000000000000000000000000000
0400
SIV_GCM_2_KEYS Passed
AEAD_AES_256_GCM_SIV:
Gueron, et al. Expires August 27, 2017 [Page 28]
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AAD_len = 0 bytes
MSG_len = 0 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG =
PADDED_AAD =
PADDED_MSG =
LENBLK = 00000000000000000000000000000000
POLYVAL xor N = 03000000000000000000000000000000
with_MSbit_cleared = 03000000000000000000000000000000
TAG = 07f5f4169bbf55a8400cd47ea6fd400f
CTRBLK = 07f5f4169bbf55a8400cd47ea6fd408f
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = 07f5f4169bbf55a8400cd47ea6fd400f
AAD =
CIPHERTEXT =
Decrypted MSG =
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
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AAD_len = 0 bytes
MSG_len = 8 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG = 0100000000000000
PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
LENBLK = 00000000000000004000000000000000
POLYVAL xor N = 06230f62f0eac8aa14fe4d646b59cd41
with_MSbit_cleared = 06230f62f0eac8aa14fe4d646b59cd41
TAG = 843122130f7364b761e0b97427e3df28
CTRBLK = 843122130f7364b761e0b97427e3dfa8
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = 843122130f7364b761e0b97427e3df28
AAD =
CIPHERTEXT = c2ef328e5c71c83b
Decrypted MSG = 0100000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
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AAD_len = 0 bytes
MSG_len = 12 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG = 010000000000000000000000
PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
LENBLK = 00000000000000006000000000000000
POLYVAL xor N = 6e81a24732fd6d03ae5af544720a1c13
with_MSbit_cleared = 6e81a24732fd6d03ae5af544720a1c13
TAG = 8ca50da9ae6559e48fd10f6e5c9ca17e
CTRBLK = 8ca50da9ae6559e48fd10f6e5c9ca1fe
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = 8ca50da9ae6559e48fd10f6e5c9ca17e
AAD =
CIPHERTEXT = 9aab2aeb3faa0a34aea8e2b1
Decrypted MSG = 010000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
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AAD_len = 0 bytes
MSG_len = 16 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG = 01000000000000000000000000000000
PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
LENBLK = 00000000000000008000000000000000
POLYVAL xor N = 77eee2bf7c9a165f8b25dea73db32a6d
with_MSbit_cleared = 77eee2bf7c9a165f8b25dea73db32a6d
TAG = c9eac6fa700942702e90862383c6c366
CTRBLK = c9eac6fa700942702e90862383c6c3e6
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = c9eac6fa700942702e90862383c6c366
AAD =
CIPHERTEXT = 85a01b63025ba19b7fd3ddfc033b3e76
Decrypted MSG = 01000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
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AAD_len = 0 bytes
MSG_len = 32 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG = 01000000000000000000000000000000
02000000000000000000000000000000
PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
02000000000000000000000000000000
LENBLK = 00000000000000000001000000000000
POLYVAL xor N = 8a9b6381b3d46f0def7aa0517ba188f5
with_MSbit_cleared = 8a9b6381b3d46f0def7aa0517ba18875
TAG = e819e63abcd020b006a976397632eb5d
CTRBLK = e819e63abcd020b006a976397632ebdd
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = e819e63abcd020b006a976397632eb5d
AAD =
CIPHERTEXT = 4a6a9db4c8c6549201b9edb53006cba8
21ec9cf850948a7c86c68ac7539d027f
Decrypted MSG = 01000000000000000000000000000000
02000000000000000000000000000000
SIV_GCM_2_KEYS Passed
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*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 0 bytes
MSG_len = 48 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
LENBLK = 00000000000000008001000000000000
POLYVAL xor N = c2f8593d8fc29b0c290cae1992f71f51
with_MSbit_cleared = c2f8593d8fc29b0c290cae1992f71f51
TAG = 790bc96880a99ba804bd12c0e6a22cc4
CTRBLK = 790bc96880a99ba804bd12c0e6a22cc4
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = 790bc96880a99ba804bd12c0e6a22cc4
AAD =
CIPHERTEXT = c00d121893a9fa603f48ccc1ca3c57ce
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7499245ea0046db16c53c7c66fe717e3
9cf6c748837b61f6ee3adcee17534ed5
Decrypted MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 0 bytes
MSG_len = 64 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD =
MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
PADDED_AAD =
PADDED_MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
LENBLK = 00000000000000000002000000000000
POLYVAL xor N = 6df38b06046c7c0e225efaef8e2ec4c4
with_MSbit_cleared = 6df38b06046c7c0e225efaef8e2ec444
TAG = 112864c269fc0d9d88c61fa47e39aa08
CTRBLK = 112864c269fc0d9d88c61fa47e39aa88
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
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Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = 112864c269fc0d9d88c61fa47e39aa08
AAD =
CIPHERTEXT = c2d5160a1f8683834910acdafc41fbb1
632d4a353e8b905ec9a5499ac34f96c7
e1049eb080883891a4db8caaa1f99dd0
04d80487540735234e3744512c6f90ce
Decrypted MSG = 01000000000000000000000000000000
02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 8 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01
MSG = 0200000000000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
LENBLK = 08000000000000004000000000000000
POLYVAL xor N = 37e57bafe011b9b36fc6821b7ffb3354
with_MSbit_cleared = 37e57bafe011b9b36fc6821b7ffb3354
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TAG = 91213f267e3b452f02d01ae33e4ec854
CTRBLK = 91213f267e3b452f02d01ae33e4ec8d4
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = 91213f267e3b452f02d01ae33e4ec854
AAD = 01
CIPHERTEXT = 1de22967237a8132
Decrypted MSG = 0200000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 12 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01
MSG = 020000000000000000000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
LENBLK = 08000000000000006000000000000000
POLYVAL xor N = 5f47d68a22061c1ad5623a3b66a8e206
with_MSbit_cleared = 5f47d68a22061c1ad5623a3b66a8e206
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TAG = c1a4a19ae800941ccdc57cc8413c277f
CTRBLK = c1a4a19ae800941ccdc57cc8413c27ff
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = c1a4a19ae800941ccdc57cc8413c277f
AAD = 01
CIPHERTEXT = 163d6f9cc1b346cd453a2e4c
Decrypted MSG = 020000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 16 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01
MSG = 02000000000000000000000000000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
LENBLK = 08000000000000008000000000000000
POLYVAL xor N = 462896726c616746f01d11d82911d478
with_MSbit_cleared = 462896726c616746f01d11d82911d478
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TAG = b292d28ff61189e8e49f3875ef91aff7
CTRBLK = b292d28ff61189e8e49f3875ef91aff7
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = b292d28ff61189e8e49f3875ef91aff7
AAD = 01
CIPHERTEXT = c91545823cc24f17dbb0e9e807d5ec17
Decrypted MSG = 02000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 32 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01
MSG = 02000000000000000000000000000000
03000000000000000000000000000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
03000000000000000000000000000000
LENBLK = 08000000000000000001000000000000
POLYVAL xor N = 4d58c1e341c9bb0ae34eda9509dfc90c
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with_MSbit_cleared = 4d58c1e341c9bb0ae34eda9509dfc90c
TAG = aea1bad12702e1965604374aab96dbbc
CTRBLK = aea1bad12702e1965604374aab96dbbc
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = aea1bad12702e1965604374aab96dbbc
AAD = 01
CIPHERTEXT = 07dad364bfc2b9da89116d7bef6daaaf
6f255510aa654f920ac81b94e8bad365
Decrypted MSG = 02000000000000000000000000000000
03000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 48 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01
MSG = 02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
03000000000000000000000000000000
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04000000000000000000000000000000
LENBLK = 08000000000000008001000000000000
POLYVAL xor N = 2666a4aff9a525df9772c16d4eaf8d2a
with_MSbit_cleared = 2666a4aff9a525df9772c16d4eaf8d2a
TAG = 03332742b228c647173616cfd44c54eb
CTRBLK = 03332742b228c647173616cfd44c54eb
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = 03332742b228c647173616cfd44c54eb
AAD = 01
CIPHERTEXT = c67a1f0f567a5198aa1fcc8e3f213143
36f7f51ca8b1af61feac35a86416fa47
fbca3b5f749cdf564527f2314f42fe25
Decrypted MSG = 02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 1 bytes
MSG_len = 64 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01
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MSG = 02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
05000000000000000000000000000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
05000000000000000000000000000000
LENBLK = 08000000000000000002000000000000
POLYVAL xor N = d958d2f61b0a9d343b2f37fb0c519733
with_MSbit_cleared = d958d2f61b0a9d343b2f37fb0c519733
TAG = 5bde0285037c5de81e5b570a049b62a0
CTRBLK = 5bde0285037c5de81e5b570a049b62a0
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = 5bde0285037c5de81e5b570a049b62a0
AAD = 01
CIPHERTEXT = 67fd45e126bfb9a79930c43aad2d3696
7d3f0e4d217c1e551f59727870beefc9
8cb933a8fce9de887b1e40799988db1f
c3f91880ed405b2dd298318858467c89
Decrypted MSG = 02000000000000000000000000000000
03000000000000000000000000000000
04000000000000000000000000000000
05000000000000000000000000000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 12 bytes
Gueron, et al. Expires August 27, 2017 [Page 42]
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MSG_len = 4 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 010000000000000000000000
MSG = 02000000
PADDED_AAD = 01000000000000000000000000000000
PADDED_MSG = 02000000000000000000000000000000
LENBLK = 60000000000000002000000000000000
POLYVAL xor N = 6ec76ae84b88916e073a303aafde05cf
with_MSbit_cleared = 6ec76ae84b88916e073a303aafde054f
TAG = 1835e517741dfddccfa07fa4661b74cf
CTRBLK = 1835e517741dfddccfa07fa4661b74cf
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = 1835e517741dfddccfa07fa4661b74cf
AAD = 010000000000000000000000
CIPHERTEXT = 22b3f4cd
Decrypted MSG = 02000000
SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 18 bytes
Gueron, et al. Expires August 27, 2017 [Page 43]
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MSG_len = 20 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01000000000000000000000000000000
0200
MSG = 03000000000000000000000000000000
04000000
PADDED_AAD = 01000000000000000000000000000000
02000000000000000000000000000000
PADDED_MSG = 03000000000000000000000000000000
04000000000000000000000000000000
LENBLK = 9000000000000000a000000000000000
POLYVAL xor N = 943ef4fd04bd31d193816ab26f8655ca
with_MSbit_cleared = 943ef4fd04bd31d193816ab26f86554a
TAG = b879ad976d8242acc188ab59cabfe307
CTRBLK = b879ad976d8242acc188ab59cabfe387
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = b879ad976d8242acc188ab59cabfe307
AAD = 01000000000000000000000000000000
0200
CIPHERTEXT = 43dd0163cdb48f9fe3212bf61b201976
067f342b
Decrypted MSG = 03000000000000000000000000000000
04000000
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SIV_GCM_2_KEYS Passed
*****************************
Performing SIV_GCM - Two Keys:
*****************************
AAD_len = 20 bytes
MSG_len = 18 bytes
BYTES ORDER
LSB--------------------------MSB
00010203040506070809101112131415
--------------------------------
K = 01000000000000000000000000000000
00000000000000000000000000000000
NONCE = 03000000000000000000000000000000
AAD = 01000000000000000000000000000000
02000000
MSG = 03000000000000000000000000000000
0400
PADDED_AAD = 01000000000000000000000000000000
02000000000000000000000000000000
PADDED_MSG = 03000000000000000000000000000000
04000000000000000000000000000000
LENBLK = a0000000000000009000000000000000
POLYVAL xor N = 2fbb6b7ab2dbffefb797f825f826870c
with_MSbit_cleared = 2fbb6b7ab2dbffefb797f825f826870c
TAG = cfcdf5042112aa29685c912fc2056543
CTRBLK = cfcdf5042112aa29685c912fc20565c3
Record_Hash_Key = b5d3c529dfafac43136d2d11be284d7f
Encryption_Key = b914f4742be9e1d7a2f84addbf96dec3
456e3c6c05ecc157cdbf0700fedad222
TAG' = cfcdf5042112aa29685c912fc2056543
AAD = 01000000000000000000000000000000
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02000000
CIPHERTEXT = 462401724b5ce6588d5a54aae5375513
a075
Decrypted MSG = 03000000000000000000000000000000
0400
SIV_GCM_2_KEYS Passed
Authors' Addresses
Shay Gueron
University of Haifa and Intel Corporation
Abba Khoushy Ave 199
Haifa 3498838
Israel
Email: shay@math.haifa.ac.il
Adam Langley
Google
345 Spear St
San Francisco, CA 94105
US
Email: agl@google.com
Yehuda Lindell
Bar Ilan University
Bar Ilan University
Ramat Gan 5290002
Israel
Email: Yehuda.Lindell@biu.ac.il
Gueron, et al. Expires August 27, 2017 [Page 46]
