Internet DRAFT - draft-nakano-rocca-s
draft-nakano-rocca-s
Network Working Group Y. Nakano
Internet-Draft K. Fukushima
Intended status: Informational KDDI Research, Inc.
Expires: 3 September 2023 T. Isobe
University of Hyogo
2 March 2023
Encryption algorithm Rocca-S
draft-nakano-rocca-s-03
Abstract
This document defines Rocca-S encryption scheme, which is an
Authenticated Encryption with Associated Data (AEAD), using a 256-bit
key and can be efficiently implemented utilizing the AES New
Instruction set (AES-NI).
Status of This Memo
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Background . . . . . . . . . . . . . . . . . . . . . . . 2
1.2. Design Concept . . . . . . . . . . . . . . . . . . . . . 4
1.3. Conventions Used in This Document . . . . . . . . . . . . 5
2. Algorithms Description . . . . . . . . . . . . . . . . . . . 5
2.1. Notations . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2. The Round Function . . . . . . . . . . . . . . . . . . . 6
2.3. Specification . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1. Initialization . . . . . . . . . . . . . . . . . . . 7
2.3.2. Processing the Associated Data . . . . . . . . . . . 8
2.3.3. Encryption . . . . . . . . . . . . . . . . . . . . . 8
2.3.4. Finalization . . . . . . . . . . . . . . . . . . . . 8
2.3.5. Rocca-S Algorithm . . . . . . . . . . . . . . . . . . 9
2.3.6. A Raw Encryption Scheme . . . . . . . . . . . . . . . 11
2.3.7. A Keystream Generation Scheme . . . . . . . . . . . . 12
2.3.8. Support for Shorter Key Length . . . . . . . . . . . 12
2.3.9. Settings as AEAD Algorithm Specifications . . . . . . 12
2.4. Security Claims . . . . . . . . . . . . . . . . . . . . . 13
2.4.1. Classic Setting . . . . . . . . . . . . . . . . . . . 13
2.4.2. Quantum Setting . . . . . . . . . . . . . . . . . . . 13
3. Security Considerations . . . . . . . . . . . . . . . . . . . 13
3.1. Security Against Attacks . . . . . . . . . . . . . . . . 13
3.2. Other Attacks . . . . . . . . . . . . . . . . . . . . . . 14
3.3. Nonce Reuse . . . . . . . . . . . . . . . . . . . . . . . 14
4. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 14
5. References . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.1. Normative References . . . . . . . . . . . . . . . . . . 14
5.2. Informative References . . . . . . . . . . . . . . . . . 14
Appendix A. Software Implementation . . . . . . . . . . . . . . 16
A.1. Implementation with SIMD Instructions . . . . . . . . . . 16
A.2. Test Vector . . . . . . . . . . . . . . . . . . . . . . . 21
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 23
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 23
1. Introduction
1.1. Background
Countries such as the USA, China, and South Korea are adapting to the
fifth-generation mobile communication systems (5G) technology at an
increasingly rapid pace. There are more than 1500 cities worldwide
with access to 5G technology. Other countries are also taking
significant steps to make 5G networks commercially available to their
citizens. As the research in 5G technology is moving toward global
standardization, it is important for the research community to focus
on developing solutions beyond 5G and for the 6G era. The first
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white paper on 6G [WP-6G] was published by 6G Flagship, University of
Oulu, Finland under the 6Genesis project in 2019. This white paper
identified the key drivers, research requirements, challenges and
essential research questions related to 6G. One of the main
requirements as listed in this paper was to look at the problem of
transmitting data at a speed of over 100 Gbps per user.
Additionally, 3GPP requires that the cryptographic algorithms
proposed for 5G systems should support 256-bit keys [SPEC-5G]. Apart
from the need of speeds of more than 100 Gbps and supporting 256-bit
keys, 3GPP also discusses the possible impacts of quantum computing
in the coming years, especially due to Grover's algorithm. While
describing the impact of quantum computers on symmetric algorithms
required for 5G and beyond, 3GPP states the following in Section 5.3
of [SPEC-5G]:
"The threat to symmetric cryptography from quantum computing is lower
than that for asymmetric cryptography. As such there is little
benefit in transitioning symmetric algorithms without corresponding
changes to the asymmetric algorithms that accompany them."
However, it has been shown in numerous articles that quantum
computers can be used to either efficiently break or drastically
reduce the time necessary to attack some symmetric-key cryptography
methods. These results require a serious reevaluation of the premise
that has informed beyond 5G quantum security concerns up to this
point. Additionally, since NIST will finally standardize quantum-
resistant public key algorithms in the coming few years, we believe
it is important for the research community to also focus on symmetric
algorithms for future telecommunications that would provide security
against quantum adversaries. The effectiveness of post-quantum
asymmetric cryptography would only be improved if the symmetric
cryptography used with it is also quantum resistant. Thus, a
symmetric cryptographic algorithm that
* supports 256-bit key and provides 256-bit security with respect to
key recovery and forgery attacks,
* has an encryption/decryption speed of more than 100 Gbps, and
* is at least as secure as AES-256 against quantum adversaries (for
128-bit security against a quantum adversary),
is needed.
Rocca has been designed as an encryption algorithm for a high speed
communication such as future internet and beyond 5G mobile
communications. Rocca achieves an encryption/decryption speed of
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more than 100 Gbps in both the raw encryption scheme and the AEAD
scheme. It supports a 256-bit key and provides 256-bit and 128-bit
security against the key recovery and distinguishing attacks,
respectively. The high throughput of Rocca can be achieved by
utilizing the AES New Instruction set (AES-NI) [AES-NI]. Similar
approach has been taken by AEGIS family [AEGIS] and Tiaoxin-346
[TIAOXIN], both are two submissions to the CAESAR competition
[CAESAR]. SNOW-V [SNOW-V] also uses AES round function as a
component so that AES-NI can be used.
As Rocca has been designed for future telecommunication services,
Rocca satisfies two out of three above mentioned requirements.
However, there is still room for the improvement with regard to
security against quantum computers. This motivates us to propose a
symmetric-key algorithm that satisfies all three of the above-
mentioned requirements. In this document, we propose Rocca-S, which
is an AES-based encryption scheme with a 256-bit key. Rocca-S
provides both a raw encryption scheme and an AEAD scheme with a
256-bit tag. Rocca-S is designed to meet the requirements of high
throughput of more than 100 Gbps as well as 256-bit security.
Rocca-S achieves an encryption/decryption speed of more than 200 Gbps
in both raw encryption scheme and AEAD scheme on Intel(R) Core(TM)
i9-12900K, and can provide 256-bit and 128-bit security against
classical and quantum adversaries respectively.
1.2. Design Concept
In this document, we present an AES-based AEAD encryption scheme with
a 256-bit key and 256-bit tag called Rocca-S, which is a variant of
Rocca described in [ROCCA]. The goal of Rocca-S is to further
improve the security of Rocca while maintaining its performance
advantage.
To achieve such a dramatically fast encryption/decryption speed,
Rocca-S follows the same design principle as Rocca, such as the SIMD-
friendly round function and an efficient permutation-based structure.
We explore the class of AES-based structures to further increase its
speed and reduce the state size. Specifically, we take the following
different approaches.
* To minimize the critical path of the round function, we focus on
the structure where each 128-bit block of the internal state is
updated by either one AES round (aesenc) or XOR while Jean and
Nikolic consider the case of applying both aesenc and XOR in a
cascade way for one round, and the most efficient structures in
[DESIGN] are included in this class.
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* We introduce a permutation between the 128-bit state words of the
internal state in order to increase the number of possible
candidates while maintaining efficiency, because executing such a
permutation is a cost-free operation in the target software, which
was not taken into account in [DESIGN].
1.3. Conventions Used in This Document
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in BCP
14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
2. Algorithms Description
In this section, the notations and the specification of our designs
will be described.
2.1. Notations
The following notations will be used in the document. Throughout
this document, a block means a 2-octet value. For the constants Z0
and Z1, we utilize the same ones as Tiaoxin-346 [TIAOXIN].
1. X ^ Y: The bitwise Exclusive OR (XOR) of X and Y.
2. X#Y: For a number X and a positive integer Y, the Y-th power of
X.
3. f#(N): For a function f and a non-negative integer N, the N-th
iteration of function f.
4. |X|: The length of X in bits.
5. X||Y : The concatenation of X and Y.
6. ZERO(l): A zero string of length l bits.
7. PAD(X): X||ZERO(l), where l is the minimal non-negative integer
such that |PAD(X)| is a multiple of 256.
8. PADN(X): X||ZERO(l), where l is the minimal non-negative integer
such that |PADN(X)| is a multiple of 128.
9. LE128(X): the little-endian encoding of 128-bit integer X.
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10. Write X as X = X[0]||X[1]|| ... ||X[n] with |X[i]| = 256, where
n is |X|/256 - 1. In addition, X[i] is written as X[i] =
X[i]_0||X[i]_1 with |X[i]_0| = |X[i]_1| = 128.
11. S: The state of Rocca-S, which is composed of 7 blocks, i.e., S
= (S[0], S[1], ..., S[6]), where S[i] (0 <= i <= 6) are blocks
and S[0] is the first block.
12. Z0: A 128-bit constant block defined as Z0 =
428a2f98d728ae227137449123ef65cd.
13. Z1: A 128-bit constant block defined as Z1 =
b5c0fbcfec4d3b2fe9b5dba58189dbbc.
14. A(X): The AES round function without the constant addition
operation, as defined below:
A(X) = MixColumns( ShiftRows( SubBytes(X) ) ), where MixColumns,
ShiftRows and SubBytes are the same operations as defined in AES
[AES].
15. AES(X,Y): One AES round is applied to the block X, where the
round constant is Y, as defined below:
AES(X,Y) = A(X) ^ Y.
This operation is the same as aesenc, which is one of the
instructions of AES-NI, performs one regular (not the last)
round of AES on an input state X with a subkey Y.
16. R(S,X0,X1): The round function is used to update the state S, as
defined in Section 2.2.
2.2. The Round Function
The input of the round function R(S,X0,X1) of Rocca-S consists of the
state S and two blocks (X0,X1). If denoting the output by Snew,
Snew:=R(S,X0,X1) can be defined as follows:
Snew[0] = S[6] ^ S[1],
Snew[1] = AES(S[0],X_0),
Snew[2] = AES(S[1],S[0]),
Snew[3] = AES(S[2],S[6]),
Snew[4] = AES(S[3],X_1),
Snew[5] = AES(S[4],S[3]),
Snew[6] = AES(S[5],S[4]).
The corresponding illustration can be found in Figure 1.
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+----+ +----+ +----+ +----+ +----+ +----+ +----+
|S[0]| |S[1]| |S[6]| |S[2]| |S[3]| |S[4]| |S[5]|
+-+-++ ++-+-+ ++-+-+ ++---+ +-+-++ ++-+-+ ++---+
| | | | | | | | | | | |
| +-----+ | +--+ | +--+ | | +-----+ | +--+ |
v | v | v | v v | v | v
+---+ | +---+ | +---+ | +---+ +---+ | +---+ | +---+
|AES|<-X0 +>|AES| +>|XOR| +>|AES| |AES|<-X1 +>|AES| +>|AES|
+-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+
| | | | | | |
v v v v v v v
+----+ +----+ +----+ +----+ +----+ +----+ +----+
|Snew| |Snew| |Snew| |Snew| |Snew| |Snew| |Snew|
| [1]| | [2]| | [0]| | [3]| | [4]| | [5]| | [6]|
+----+ +----+ +----+ +----+ +----+ +----+ +----+
Figure 1: Illustration of the Round Function
2.3. Specification
Rocca-S is an AEAD scheme composed of four phases: initialization,
processing the associated data, encryption and finalization. The
input consists of a 256-bit key K = K0||K1, a nonce N of between 12
and 16 octets (both inclusive) in length, the associated data AD and
the message M, where K0 and K1 are elements of the binary finite
field of 2#128. The output is the corresponding ciphertext C and a
256-bit tag T.
The settings described below are required for the parameters:
* The key K MUST be unpredictable for each invocation.
* PADN(N), where N is the nonce, MUST be unique per invocation with
the same key, so N MUST NOT be randomly generated.
2.3.1. Initialization
First, (N,K0,K1) is loaded into the state S in the following way:
S[0] = K1,
S[1] = PADN(N),
S[2] = Z0,
S[3] = K0,
S[4] = Z1,
S[5] = PADN(N) ^ K1,
S[6] = ZERO(128)
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Then, 16 iterations of the round function R(S,Z0,Z1), which is
written as R(S,Z0,Z1)#(16), are applied to state S.
After 16 iterations of the round function, two 128-bit keys are XORed
with the state S in the following way:
S[0] = S[0] ^ K0, S[1] = S[1] ^ K0,
S[2] = S[2] ^ K1, S[3] = S[3] ^ K0,
S[4] = S[4] ^ K0, S[5] = S[5] ^ K1,
S[6] = S[6] ^ K1.
2.3.2. Processing the Associated Data
If AD is empty, this phase will be skipped. Otherwise, AD is padded
to PAD(AD), and the state is updated as follows:
for i = 0 to d - 1
R(S, PAD(AD)[i]_0, PAD(AD)[i]_1),
end for
where d = |PAD(AD)| / 256.
2.3.3. Encryption
The encryption phase is similar to the phase to process the
associated data. If M is empty, the encryption phase will be
skipped. Otherwise, M is first padded to PAD(M), and then PAD(M)
will be absorbed with the round function. During this procedure, the
ciphertext C is generated. If the last block of M is incomplete and
its length is b bits, i.e., 0 < b < 256, the last block of C will be
truncated to the first b bits. A detailed description is shown
below:
for i = 0 to m - 1
C[i]_0 = AES(S[3] ^ S[5], S[0]) ^ PAD(M)[i]_0,
C[i]_1 = AES(S[4] ^ S[6], S[2]) ^ PAD(M)[i]_1,
R(S, PAD(M)[i]_0, PAD(M)[i]_1),
end for
where m = |PAD(M)| / 256.
2.3.4. Finalization
The state S will again pass through 16 iterations of the round
function R(S,LE128(|AD|),LE128(|M|)) and then the 256-bit tag T is
computed in the following way:
T = (S[0] ^ S[1] ^ S[2] ^ S[3]) || (S[4] ^ S[5] ^ S[6]).
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2.3.5. Rocca-S Algorithm
A formal description of Rocca-S can be seen in Figure 2, and the
corresponding illustration is shown in Figure 3.
// Rocca-S Algorithm. The specification of Rocca-S
procedure RoccaEncrypt(K0, K1, N, AD, M)
S = Initialization(N,K0,K1)
if |AD| > 0 then
S = ProcessAD(S,PAD(AD))
if |M| > 0 then
S = Encryption(S,PAD(M),C)
Truncate C
T = Finalization(S, |AD|, |M|)
return (C, T)
procedure RoccaDecrypt(K0, K1, N, AD, C, T)
S = Initialization(N,K0,K1)
if |AD| > 0 then
S = ProcessAD(S,PAD(AD))
if |C| > 0 then
S = Decryption(S,PAD(C),M)
Truncate M
if T == Finalization(S, |AD|, |C|) then
return M
else
return nil
procedure Initialization(N, K0, K1)
S[0] = K1,
S[1] = PADN(N),
S[2] = Z0,
S[3] = K0,
S[4] = Z1,
S[5] = PADN(N) ^ K1,
S[6] = ZERO(128)
for i = 0 to 15 do
S = R(S, Z0, Z1)
S[0] = S[0] ^ K0,
S[1] = S[1] ^ K0,
S[2] = S[2] ^ K1,
S[3] = S[3] ^ K0,
S[4] = S[4] ^ K0,
S[5] = S[5] ^ K1,
S[6] = S[6] ^ K1
return S
procedure ProcessAD(S, AD)
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d = |PAD(AD)|/256
for i = 0 to d - 1 do
S = R(S, AD[i]_0, AD[i]_1)
return S
procedure Encryption(S, M, C)
m = |PAD(M)|/256
for i = 0 to m - 1 do
C[i]_0 = AES(S[3] ^ S[5], S[0]) ^ M[i]_0
C[i]_1 = AES(S[4] ^ S[6], S[2]) ^ M[i]_1
S = R(S,M[i]_0, M[i]_1)
return S
procedure Decryption(S, M, C)
c = |C|/256
for i = 0 to c - 1 do
M[i]_0 = AES(S[3] ^ S[5], S[0]) ^ C[i]_0
M[i]_1 = AES(S[4] ^ S[6], S[2]) ^ C[i]_1
S = R(S,M[i]_0, M[i]_1)
return S
procedure Finalization(S, |AD|, |M|)
for i = 0 to 15 do
S = R(S, |AD|, |M|)
T0 = 0
T1 = 0
for i = 0 to 3 do
T0 = T0 ^ S[i]
for i = 4 to 6 do
T1 = T1 ^ S[i]
return T0||T1
Figure 2: The Specification of Rocca-S
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Z1 AD[0]_1 AD[1]_1
| | |
v v v
+------+ +---+ +---+
PADN(N)->| | | | | |
|R#(16)+------>| R +-->| R +->...---+
K0||K1->| | ^ | | | | |
+------+ | +---+ +---+ |
^ K0||K1 ^ ^ |
| | | |
Z0 AD[0]_0 AD[1]_0 |
|
+--------------------------------------------+
|
| C[0]_1 C[1]_1 C[m-1]_1
| ^ ^ ^
| | | | |AD|
| +-+-+ +-+-+ +-+-+ |
| AD[d-1]_1 |XOR|<-M[0]_1 |XOR|<-M[1]_1 |XOR|<-M[m-1]_1 |
| | +---+ | +---+ | +---+ | |
| v ^ v ^ v ^ v |
| +---+ | +---+ | +---+ | +---+ v
| | +---+ | +-----+ | | -+ | | +------+
| | | | | | | | | | |
+------>| R +------>| R +-------->| R +->...---->| R +------>|R#(16)+->T
| | | | | | | | | |
| +---+ | +-----+ | | -+ | | +------+
+---+ | +---+ | +---+ | +---+ ^
^ v ^ v ^ v ^ |
| +---+ | +---+ | +---+ | |
|XOR|<-M[0]_0 |XOR|<-M[1]_0 |XOR|<-M[m-1]_0 |M|
AD[d-1]_0 +-+-+ +-+-+ +-+-+
| | |
v v v
C[0]_0 C[1]_0 C[m-1]_0
Figure 3: The Procedure of Rocca-S
2.3.6. A Raw Encryption Scheme
If the phases of processing the associated data and finalization are
removed, a raw encryption scheme is obtained.
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2.3.7. A Keystream Generation Scheme
If the phases of processing the associated data and finalization are
removed, and there is no message injection into the round function
such that R(S,0,0), a keystream generation scheme is obtained. This
scheme can be used as a general stream cipher and random bit
generation.
2.3.8. Support for Shorter Key Length
For Rocca-S to support 128-bit or 192-bit keys, the given key needs
to be expanded to 256 bits. When 128-bit key is given, it will be
set to K0, and K1 is defined as K1 = ZERO(128). When 192-bit key is
given, the first 128-bit will be set to K0, and the remaining 64-bit
will be set to K1_p. Then K1 is defined as K1 = K1_p||ZERO(64).
Use of Key Derivation Functions (KDF) [KDF] to stretch the key length
to 256-bit could be another option. The given 128-bit or 192-bit key
will be used as a key derivation key, and the output of the KDF will
be 256-bit.
2.3.9. Settings as AEAD Algorithm Specifications
To comply with the requirements defined in Section 4 of [RFC5116],
the settings of the parameters for Rocca-S are defined as follows:
* K_LEN (key length) is 32 octets (256 bits), and K (key) does not
require any particular data format.
* P_MAX (maximum size of the plaintext) is 2#125 octets.
* A_MAX (maximum size of the associated data) is 2#61 octets.
* N_MIN (minimum size of the nonce) = 12 octets, and N_MAX (maximum
size of the nonce) = 16 octets.
* C_MAX (the largest possible AEAD ciphertext) = P_MAX + tag length
= 2#125 + 32 octets.
In addition,
* Rocca-S does not structure its ciphertext output with the
authentication tag.
* Rocca-S is not randomized and is not stateful in the meanings of
the section 4 of [RFC5116].
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2.4. Security Claims
2.4.1. Classic Setting
As described in Section 3, Rocca-S provides 256-bit security against
key-recovery and forgery attacks in the nonce-respecting setting.
Rocca-S also provides 128-bit key-committing security. We do not
claim its security in the related-key and known-key settings.
The message length for a fixed key is limited to at most 2#128, and
we also limit the number of different messages that are produced for
a fixed key to be at most 2#128. The length of the associated data
for a fixed key is up to 2#64.
2.4.2. Quantum Setting
There exist no quantum attacks for key-recovery and forgery (in
nonce-respecting setting) on Rocca-S with time complexity lower than
2#128. Rocca-S does not provide security against related-key and
known-key superposition attacks (as is the case of all known block
ciphers).
3. Security Considerations
3.1. Security Against Attacks
Rocca-S is secure against the following attacks:
1. Key-Recovery Attack: 256-bit security against key-recovery
attacks.
2. Differential Attack: Secure against differential attacks in the
initialization phase.
3. Forgery Attack: 256-bit security against forgery attacks.
4. Integral Attack: Secure against integral attacks.
5. State-recovery Attack:
* Guess-and-Determine Attack: The time complexity of the guess-
and-determine attack cannot be lower than 2#256.
* Algebraic Attack: The system of equations, which needs to be
solved in algebraic attacks to Rocca-S, cannot be solved with
time complexity 2#256.
6. The Linear Bias: Secure against a statistical attack.
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3.2. Other Attacks
While there are many attack vectors for block ciphers, their
application to Rocca-S is restrictive, as the attackers can only know
partial information about the internal state from the ciphertext
blocks. In other words, reversing the round function is impossible
in Rocca-S without guessing many secret state blocks. Therefore,
only the above potential attack vectors are taken into account. In
addition, due to the usage of the constant (Z0,Z1) at the
initialization phase, the attack based on the similarity in the four
columns of the AES state is also excluded.
3.3. Nonce Reuse
Inadvertent reuse of the same nonce by two invocations of the Rocca-S
encryption operation, with the same key, undermines the security of
the messages processed with those invocations. A loss of
confidentiality ensues because an adversary will be able to
reconstruct the bitwise exclusive-or of the two plaintext values.
4. IANA Considerations
IANA has assigned value TBD in the AEAD Algorithms registry to
AEAD_ROCCA.
5. References
5.1. 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,
<https://www.rfc-editor.org/info/rfc2119>.
[RFC5116] McGrew, D., "An Interface and Algorithms for Authenticated
Encryption", RFC 5116, DOI 10.17487/RFC5116, January 2008,
<https://www.rfc-editor.org/info/rfc5116>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/info/rfc8174>.
5.2. Informative References
[AEGIS] Preneel, B., "AEGIS: A fast authenticated encryption
algorithm", Selected Areas in Cryptography (SAC 2013)
pp.185-201, 2013.
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[AES] National Institute of Standards and Technology, "FIPS 197
Advanced Encryption Standard (AES)", November 2001,
<https://doi.org/10.6028/NIST.FIPS.197>.
[AES-NI] Gueron, S., "Intel Advanced Encryption Standard (AES) New
Instructions Set", 2010,
<https://www.intel.com/content/dam/doc/white-paper/
advanced-encryption-standard-new-instructions-set-
paper.pdf>.
[CAESAR] "CAESAR: Competition for Authenticated Encryption:
Security, Applicability, and Robustness", 2018,
<https://competitions.cr.yp.to/caesar.html>.
[DESIGN] Jean, J. and I. Nikolic, "Efficient Design Strategies
Based on the AES Round Function", In: Peyrin, T. (eds)
Fast Software Encryption. FSE 2016. Lecture Notes in
Computer Science, vol 9783, 2016,
<https://doi.org/10.1007/978-3-662-52993-5_17>.
[KDF] Chena, L., "Recommendation for Key Derivation Using
Pseudorandom Functions (Revised)", NIST Special
Publication 800-108, 2009,
<https://nvlpubs.nist.gov/nistpubs/Legacy/SP/
nistspecialpublication800-108.pdf>.
[ROCCA] Sakamoto, K., Liu, F., Nakano, Y., Kiyomoto, S., and T.
Isobe, "Rocca: An Efficient AES-based Encryption Scheme
for Beyond 5G", IACR Transactions on Symmetric Cryptology,
2021(2), 1-30, 2021,
<https://doi.org/10.46586/tosc.v2021.i2.1-30>.
[SNOW-V] Ekdahl, P., Johansson, T., Maximov, A., and J. Yang, "A
new SNOW stream cipher called SNOW-V", IACR Transactions
on Symmetric Cryptology, 2019(3), 1-42, 2019,
<https://doi.org/10.13154/tosc.v2019.i3.1-42>.
[SPEC-5G] 3GPP SA3, "Study on the support of 256-bit algorithms for
5G", 2018,
<https://portal.3gpp.org/desktopmodules/Specifications/
SpecificationDetails.aspx?specificationId=3422>.
[TIAOXIN] Nikolic, I., "Tiaoxin-346: VERSION 2.0", CAESAR
Competition, 2014,
<https://competitions.cr.yp.to/round2/tiaoxinv2.pdf>.
[WP-6G] Latva-aho, M. and K. Leppaenen, "Key drivers and research
challenges for 6G ubiquitous wireless intelligence", 2019.
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Appendix A. Software Implementation
A.1. Implementation with SIMD Instructions
Figure 4 shows a sample implementation of Rocca-S.
#include <memory.h>
#include <immintrin.h>
#include <stdlib.h>
#include <stdint.h>
#define ROCCA_KEY_SIZE (32)
#define ROCCA_IV_SIZE (16)
#define ROCCA_MSG_BLOCK_SIZE (32)
#define ROCCA_TAG_SIZE (32)
#define ROCCA_STATE_NUM ( 7)
typedef struct ROCCA_CTX {
uint8_t key[ROCCA_KEY_SIZE/16][16];
uint8_t state[ROCCA_STATE_NUM][16];
size_t size_ad;
size_t size_m;
} rocca_context;
#define load(m) _mm_loadu_si128((const __m128i *)(m))
#define store(m,a) _mm_storeu_si128((__m128i *)(m),a)
#define xor(a,b) _mm_xor_si128(a,b)
#define and(a,b) _mm_and_si128(a,b)
#define enc(a,k) _mm_aesenc_si128(a,k)
#define setzero() _mm_setzero_si128()
#define ENCODE_IN_LITTLE_ENDIAN(bytes, v) \
bytes[ 0] = ((uint64_t)(v) << ( 3)); \
bytes[ 1] = ((uint64_t)(v) >> (1*8-3)); \
bytes[ 2] = ((uint64_t)(v) >> (2*8-3)); \
bytes[ 3] = ((uint64_t)(v) >> (3*8-3)); \
bytes[ 4] = ((uint64_t)(v) >> (4*8-3)); \
bytes[ 5] = ((uint64_t)(v) >> (5*8-3)); \
bytes[ 6] = ((uint64_t)(v) >> (6*8-3)); \
bytes[ 7] = ((uint64_t)(v) >> (7*8-3)); \
bytes[ 8] = ((uint64_t)(v) >> (8*8-3)); \
bytes[ 9] = 0; \
bytes[10] = 0; \
bytes[11] = 0; \
bytes[12] = 0; \
bytes[13] = 0; \
bytes[14] = 0; \
bytes[15] = 0;
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#define FLOORTO(a,b) ((a) / (b) * (b))
#define S_NUM ROCCA_STATE_NUM
#define M_NUM ( 2)
#define INIT_LOOP (16)
#define TAG_LOOP (16)
#define VARS4UPDATE \
__m128i k[2], state[S_NUM], stateNew[S_NUM], M[M_NUM];
#define VARS4ENCRYPT \
VARS4UPDATE \
__m128i Z[M_NUM], C[M_NUM];
#define COPY_TO_LOCAL(ctx) \
for(size_t i = 0; i < S_NUM; ++i) \
{ state[i] = load(&((ctx)->state[i][0])); }
#define COPY_FROM_LOCAL(ctx) \
for(size_t i = 0; i < S_NUM; ++i) \
{ store(&((ctx)->state[i][0]), state[i]); }
#define COPY_TO_LOCAL_IN_TAG(ctx) \
COPY_TO_LOCAL(ctx) for(size_t i = 0; i < 2; ++i) \
{ k[i] = load(&((ctx)->key[i][0])); }
#define COPY_FROM_LOCAL_IN_INIT(ctx) \
COPY_FROM_LOCAL(ctx) for(size_t i = 0; i < 2; ++i) \
{ store(&((ctx)->key[i][0]), k[i]); }
#define UPDATE_STATE(X) \
stateNew[0] = xor(state[6], state[1]); \
stateNew[1] = enc(state[0], X[0]); \
stateNew[2] = enc(state[1], state[0]); \
stateNew[3] = enc(state[2], state[6]); \
stateNew[4] = enc(state[3], X[1]); \
stateNew[5] = enc(state[4], state[3]); \
stateNew[6] = enc(state[5], state[4]); \
for(size_t i = 0; i < S_NUM; ++i) \
{state[i] = stateNew[i];}
#define INIT_STATE(key, iv) \
k[0] = load((key) + 16*0); \
k[1] = load((key) + 16*1); \
state[0] = k[1]; \
state[1] = load(iv); \
state[2] = load(Z0); \
state[3] = k[0]; \
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state[4] = load(Z1); \
state[5] = xor(state[1], state[0]); \
state[6] = setzero(); \
M[0] = state[2]; \
M[1] = state[4]; \
for(size_t i = 0; i < INIT_LOOP; ++i) { \
UPDATE_STATE(M) \
} \
state[0] = xor(state[0], k[0]); \
state[1] = xor(state[1], k[0]); \
state[2] = xor(state[2], k[1]); \
state[3] = xor(state[3], k[0]); \
state[4] = xor(state[4], k[0]); \
state[5] = xor(state[5], k[1]); \
state[6] = xor(state[6], k[1]);
#define MAKE_STRM \
Z[0] = enc(xor(state[3], state[5]), state[0]); \
Z[1] = enc(xor(state[4], state[6]), state[2]);
#define MSG_LOAD(mem, reg) \
reg[0] = load((mem) + 0); \
reg[1] = load((mem) + 16);
#define MSG_STORE(mem, reg) \
store((mem) + 0, reg[0]); \
store((mem) + 16, reg[1]);
#define XOR_BLOCK(dst, src1, src2) \
dst[0] = xor(src1[0], src2[0]); \
dst[1] = xor(src1[1], src2[1]);
#define MASKXOR_BLOCK(dst, src1, src2, mask) \
dst[0] = and(xor(src1[0], src2[0]), mask[0]); \
dst[1] = and(xor(src1[1], src2[1]), mask[1]);
#define ADD_AD(input) \
MSG_LOAD(input, M) \
UPDATE_STATE(M)
#define ADD_AD_LAST_BLOCK(input, size) \
uint8_t tmpblk[ROCCA_MSG_BLOCK_SIZE] = {0}; \
memcpy(tmpblk, input, size); \
MSG_LOAD(tmpblk, M) \
UPDATE_STATE(M)
#define ENCRYPT(output, input) \
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MSG_LOAD(input, M) \
MAKE_STRM \
XOR_BLOCK(C, M, Z) \
MSG_STORE(output, C) \
UPDATE_STATE(M)
#define ENCRYPT_LAST_BLOCK(output, input, size) \
uint8_t tmpblk[ROCCA_MSG_BLOCK_SIZE] = {0}; \
memcpy(tmpblk, input, size); \
MSG_LOAD(tmpblk, M) \
MAKE_STRM \
XOR_BLOCK(C, M, Z) \
MSG_STORE(tmpblk, C) \
memcpy(output, tmpblk, size); \
UPDATE_STATE(M)
#define DECRYPT(output, input) \
MSG_LOAD(input, C) \
MAKE_STRM \
XOR_BLOCK(M, C, Z) \
MSG_STORE(output, M) \
UPDATE_STATE(M)
#define DECRYPT_LAST_BLOCK(output, input, size) \
uint8_t tmpblk[ROCCA_MSG_BLOCK_SIZE] = {0}; \
uint8_t tmpmsk[ROCCA_MSG_BLOCK_SIZE] = {0}; \
__m128i mask[M_NUM]; \
memcpy(tmpblk, input, size); \
memset(tmpmsk, 0xFF , size); \
MSG_LOAD(tmpblk, C ) \
MSG_LOAD(tmpmsk, mask) \
MAKE_STRM \
MASKXOR_BLOCK(M, C, Z, mask) \
MSG_STORE(tmpblk, M) \
memcpy(output, tmpblk, size); \
UPDATE_STATE(M)
#define SET_AD_BITLEN_MSG_BITLEN(sizeAD, sizeM) \
uint8_t bitlenAD[16]; \
uint8_t bitlenM [16]; \
ENCODE_IN_LITTLE_ENDIAN(bitlenAD, sizeAD); \
ENCODE_IN_LITTLE_ENDIAN(bitlenM , sizeM ); \
M[0] = load(bitlenAD); \
M[1] = load(bitlenM );
#define MAKE_TAG(sizeAD, sizeM, tag) \
SET_AD_BITLEN_MSG_BITLEN(sizeAD, sizeM) \
for(size_t i = 0; i < TAG_LOOP; ++i) { \
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UPDATE_STATE(M) \
} \
__m128i tag128a = setzero(); \
for(size_t i = 0; i <= 3; ++i) { \
tag128a = xor(tag128a, state[i]); \
} \
__m128i tag128b = setzero(); \
for(size_t i = 4; i <= 6; ++i) { \
tag128b = xor(tag128b, state[i]); \
} \
store((tag) , tag128a); \
store((tag)+16, tag128b);
static const uint8_t Z0[] = {0xcd,0x65,0xef,0x23,0x91, \
0x44,0x37,0x71,0x22,0xae,0x28,0xd7,0x98,0x2f,0x8a,0x42};
static const uint8_t Z1[] = {0xbc,0xdb,0x89,0x81,0xa5, \
0xdb,0xb5,0xe9,0x2f,0x3b,0x4d,0xec,0xcf,0xfb,0xc0,0xb5};
void rocca_init(rocca_context * ctx, const uint8_t * key, \
const uint8_t * iv) {
VARS4UPDATE
INIT_STATE(key, iv);
COPY_FROM_LOCAL_IN_INIT(ctx);
ctx->size_ad = 0;
ctx->size_m = 0;
}
void rocca_add_ad(rocca_context * ctx, const uint8_t * in, size_t size)
{
VARS4UPDATE
COPY_TO_LOCAL(ctx);
size_t i = 0;
for(size_t size2 = FLOORTO(size, ROCCA_MSG_BLOCK_SIZE); \
i < size2; i += ROCCA_MSG_BLOCK_SIZE) {
ADD_AD(in + i);
}
if(i < size) {
ADD_AD_LAST_BLOCK(in + i, size - i);
}
COPY_FROM_LOCAL(ctx);
ctx->size_ad += size;
}
void rocca_encrypt(rocca_context * ctx, uint8_t * out, \
const uint8_t * in, size_t size) {
VARS4ENCRYPT
COPY_TO_LOCAL(ctx);
size_t i = 0;
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for(size_t size2 = FLOORTO(size, ROCCA_MSG_BLOCK_SIZE); \
i < size2; i += ROCCA_MSG_BLOCK_SIZE) {
ENCRYPT(out + i, in + i);
}
if(i < size) {
ENCRYPT_LAST_BLOCK(out + i, in + i, size - i);
}
COPY_FROM_LOCAL(ctx);
ctx->size_m += size;
}
void rocca_decrypt(rocca_context * ctx, uint8_t * out, \
const uint8_t * in, size_t size) {
VARS4ENCRYPT
COPY_TO_LOCAL(ctx);
size_t i = 0;
for(size_t size2 = FLOORTO(size, ROCCA_MSG_BLOCK_SIZE); \
i < size2; i += ROCCA_MSG_BLOCK_SIZE) {
DECRYPT(out + i, in + i);
}
if(i < size) {
DECRYPT_LAST_BLOCK(out + i, in + i, size - i);
}
COPY_FROM_LOCAL(ctx);
ctx->size_m += size;
}
void rocca_tag(rocca_context * ctx, uint8_t *tag) {
VARS4UPDATE
COPY_TO_LOCAL_IN_TAG(ctx);
MAKE_TAG(ctx->size_ad, ctx->size_m, tag);
}
Figure 4: Reference Implementation with SIMD
A.2. Test Vector
This section gives three test vectors of Rocca-S. The least
significant octet of the vector is shown on the left and the first
128-bit value is shown on the first line.
=== test vector #1===
key =
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
nonce =
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
associated data =
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00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
plaintext =
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
ciphertext =
9a c3 32 64 95 a8 d4 14 fe 40 7f 47 b5 44 10 50
24 81 cf 79 ca b8 c0 a6 69 32 3e 07 71 1e 46 17
0d e5 b2 fb ba 0f ae 8d e7 c1 fc ca ee fc 36 26
24 fc fd c1 5f 8b b3 e6 44 57 e8 b7 e3 75 57 bb
tag =
8d f9 34 d1 48 37 10 c9 41 0f 6a 08 9c 4c ed 97
91 90 1b 7e 2e 66 12 06 20 2d b2 cc 7a 24 a3 86
=== test vector #2===
key =
01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
nonce =
01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
associated data =
01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
plaintext =
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
ciphertext =
55 9e cb 25 3b cf e2 6b 48 3b f0 0e 9c 74 83 45
97 8f f9 21 03 6a 6c 1f dc b7 12 17 28 36 50 4f
bc 64 d4 30 a7 3f c6 7a cd 3c 3b 9c 19 76 d8 07
90 f4 83 57 e7 fe 0c 06 82 62 45 69 d3 a6 58 fb
tag =
c1 fd f3 97 62 ec a7 7d a8 b0 f1 da e5 ff f7 5a
92 fb 0a df a7 94 0a 28 c8 ca db bb e8 e4 ca 8d
=== test vector #3===
key =
01 23 45 67 89 ab cd ef 01 23 45 67 89 ab cd ef
01 23 45 67 89 ab cd ef 01 23 45 67 89 ab cd ef
nonce =
01 23 45 67 89 ab cd ef 01 23 45 67 89 ab cd ef
associated data =
01 23 45 67 89 ab cd ef 01 23 45 67 89 ab cd ef
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01 23 45 67 89 ab cd ef 01 23 45 67 89 ab cd ef
plaintext =
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
ciphertext =
b5 fc 4e 2a 72 b8 6d 1a 13 3c 0f 02 02 bd f7 90
af 14 a2 4b 2c db 67 6e 42 78 65 e1 2f cc 9d 30
21 d1 84 18 fc 75 dc 19 12 dd 2c d7 9a 3b ee b2
a9 8b 23 5d e2 29 9b 9d da 93 fd 2b 5a c8 f4 36
tag =
a0 78 e1 35 1e f2 42 0c 8e 3a 93 fd 31 f5 b1 13
5b 15 31 5a 5f 20 55 34 14 8e fb cd 63 f7 9f 00
Acknowledgements
This draft is partially supported by a contract of "Research and
development on new generation cryptography for secure wireless
communication services" among "Research and Development for Expansion
of Radio Wave Resources (JPJ000254)", which was supported by the
Ministry of Internal Affairs and Communications, Japan.
Authors' Addresses
Yuto Nakano
KDDI Research, Inc.
2-1-15 Ohara, Fujimino-shi, Saitama,
356-8502
Japan
Email: yt-nakano@kddi.com
Kazuhide Fukushima
KDDI Research, Inc.
2-1-15 Ohara, Fujimino-shi, Saitama,
356-8502
Japan
Email: ka-fukushima@kddi.com
Takanori Isobe
University of Hyogo
7-1-28 Minatojima Minamimachi, Chuo-ku, Kobe-shi, Hyogo,
650-0047
Japan
Email: takanori.isobe@ai.u-hyogo.ac.jp
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