anonymous and efficient authentication scheme for privacy-preserving distributed learning

Abstract
This report provides an overview of the anonymous and efficient
authentication scheme for privacy-preserving distributed learning.
This work has helped to alleviate some of the drawbacks of
privacy-preserving in distributed learning or has innovated new
technologies for various applications. I attempted to identify the
paper's problem(s) while also comprehending the methodology
(that is, the working model and algorithms).

Table of Contents
1. Introduction
2. Proposed Methodology
3. Results
4. Problem found in the methodology
5. Conclusions

Chapter 1
Introduction
A tremendous amount of data has been generated and transmitted to cloud servers due to the
integration of machine learning (ML) and cloud computing, which has been developed
rapidly in the past decade. It leads to significant communication and computation overheads.
To resolve this issue, the concept of distributed learning (DL) is used.
In this, the participating devices first train the ML model locally with the raw data, and once
computed, it sends the model parameters to the cloud. The cloud then aggregates into a global
ML model. Since there is no need to upload the user data to the cloud, the risk of privacy
leakage is reduced in distributed learning (DL).
DL is still subject to privacy violations when the cloud server is not fully trusted. In
distributed scenarios, it shows that the cloud is able to recover the input of an ML model with
the knowledge of full or partial model parameters. Once the raw data is recovered, the
personal information of the participants is disclosed. At the cloud server side, achieving
secure parameter aggregation without revealing the raw parameters is a challenge in DL.
To tackle this challenge, deploying encryption techniques or differential privacy (DP) are two
primary approaches.
1) Encryption techniques, such as homomorphic encryption and secure multiparty
computation, are employed to design secure data exchange and aggregation protocols.
Benefiting from the protocols, the cloud is able to calculate the global model without
accessing the model parameters of individual participants.
Cons:
 Encryption techniques is not generalised for all ML algorithms in DL.
 It also consumes a lot of communication and computation resources because it uses a
lot of cryptographic primitives.
2) Differential privacy (DP) is deployed to obfuscate information by introducing
random noise to the raw data or model parameters. DP-based schemes are generalised
for all ML algorithms in DL.
Cons:
 The randomness reduces data utility, bringing undesired accuracy degradation to ML
models.
 Model convergence with longer latency.
 DP is ineffective for accuracy-sensitive situations.

To overcome the existing cons, the anonymous and efficient authentication scheme for
privacy-preserving distributed learning is used, which is generalised for all ML algorithms
without data reduction.
The proposed scheme is based on the fact that if the participants in the DL system are
anonymous, then although the raw data is recovered, the adversary cannot link the data to the
corresponding participant's real identity, thereby achieving privacy preservation.
 In this scheme, it deploys anonymous authentication. It is effective for
all ML algorithms without reducing data utility. It can also be integrated with the
defence schemes to detect poisoning attacks and free-rider attacks.
 The new generalised certificateless signature scheme PCLS,
which is built on pairing-based cryptography, The designed signature scheme has
an anonymous and efficient authentication protocol that supports batch verification
(AAPBV).
 An algorithm of dynamic batch verification (DBV) which can dynamically adjust the
batch size during batch verification. In conventional batch verification, the batch size
is not adjustable. All the messages are discarded if the batch verification fails.
When the failure occurs, DBV is launched to adjust the batch size and redo
verification.
The major problems addressed in this paper are:
 Adversary is able to derive the raw data (user identity) by analysing the obtained
machine learning models.
 Significantly reduces the time consumption in batch verification, achieving high
computational efficiency.
Apart from this, the proposed protocol address:
 Confidentiality
 Anonymity
 Mutal Authentication
 Unlinkability
 Unforgery
 Forward Security
 Backward Security
 Non-repudiation

Chapter 2
Proposed Methodology
2.1 System Overview
 Participants: It refer to individuals that are equipped with intelligent devices, such as
laptop, smart phone, tablet, and so on.
 Cloud Server: It receives the model parameters from participants and aggregates into
a global ML model
 Trusted Authority (TA): TA is a powerful system manager that is responsible for
system initialization, participant registrations, key generation, identity management,
and so on.
2.2 Model Flow
 Step 1: The cloud server initializes a global model and distributes the model to all
participants.
 Step 2: After receiving the global model, each participant continues to train the model
on its local dataset and obtains the updated model parameters Wn. Wn is then
uploaded to the cloud server.
 Step 3: The cloud server aggregates the model parameters. The global ML model is
corrected with Wg and sent to the participants for next-round training.
 Step 4: Repeat Steps 2, 3 until the global model converges.
2.3 Pairing based certificateless signature scheme (PCLS)
PCLS, there are two main modifications compared with the typical certificateless signature
scheme.
 Instead of setting the signer’s real identity as the partial public key, the hash value of
the signer’s real identity is the partial public key, protecting the real identities from
disclosure.
 Modified the signature generation and message verification to support batch
verification, such that the authentication is more efficient.
The PCLS scheme involves the following steps:
 Setup:
Let G1 denote a cyclic additive group of a prime order p.
G2 denotes a cyclic multiplicative group with the same prime order p.
p satisfies p > 2l, where l is the security parameter.
P is a generator of G1 and e: G1 × G1 → G2 is a bilinear pairing operator.

TA randomly selects XTA ∈ Z*
p as its private key and computes YTA = XTA P as its
public key.
TA picks two hash functions H1 and H2, where
H1: {0, 1}*
→ G1
H2: {0, 1}*
× G1 → Z*
p
TA publishes (l, p, P, e, G1, G2, H1, H2, YT A) as the system parameters.
Private key XTA is kept by TA and remains as a secret.
 Key-Extract:
The signer randomly selects X’
∈ Z*
p as its partial private key and calculates
Y’
= X’
P as its partial public key.
The signer computes Y’’
= H1(I D) as the other partial public key and sends Y’’
to TA,
where ID is its true identity.
Given Y’’
, TA then sets X’’
= XTA Y’’
and sends to the signer through a secure
channel. The signer uses (X’
, X’’
) as its full private key and (Y, Y’’
) as its full public
key.
 Sign:
Before sending a message m, the signer randomly chooses r ∈ Z*
p and signs the
message as follows:
k = H2(m||Y’
||Y’’
||YTA, r P)
U = X’
YTA − X’’
k
The signature is σ = (k, U) on message m.
 Verify:
After receiving the message m with signature σ, the verifier checks
e(Y’ , YTA) = e(U, P)e(Y’’
, YTA)k
Proof –
e(U, P)e(Y’’, YTA)k
= e(U, P)e(Y’’
, XTA P)k
= e(U, P)e(X’’
, P)k
= e(U + k X’’
, P)
= e(X’ YTA, P)
= e(YTA, Y’
)
= e(Y’ , YTA)
The message is accepted if the checking holds.

2.4 Anonymous authentication protocol AAPBV
The proposed AAPBV involves four stages, including initialization, registration,
authentication, and batch verification.
In the initialization stage, the TA initializes the system parameters and publishes to the
participants and the cloud.
In the registration stage, a participant registers to TA with its real identity and generates full
public key and private key assisted by TA.
In the authentication stage, a participant generates a valid signature, signs the message, and
uploads to the cloud. The cloud then authenticates the participant and decrypts the message.
To improve the computational efficiency in large-scale DL, the cloud can authenticate a batch
of messages at the same time.
In the batch verification stage, the batch verification may fail if there are illegal participants
who upload messages signed by invalid signatures. In this case, the cloud launches the DBV
algorithm to dynamically shrink the batch size and redo verification. Thus, the illegitimate
messages may be filtered. In this way, the number of discarded messages is reduced and more
legal messages are saved for machine learning.
 Initialization stage –
TA initializes the system and generates the system parameters given the security
parameter l.
Let G1 denote a cyclic additive group of a prime order p > 2l.
G2 denotes a cyclic multiplicative group with the same prime order p.
P is a generator of G1 and e: G1 × G1 → G2 is a bilinear pairing operator.
TA picks three secure hash functions H1, H2, and H3,
where H1: {0, 1}* → G1,
H2: {0, 1}*×G1 → Z* p,
H3 : {0, 1}* → Z* p.
TA randomly selects XTA ∈ Z* p as its private key and computes YTA = XTA P as its
public key.
The private key XTA is kept by TA and remains a secret. (l, p, P, e, G1, G2, H1, H2,
H3, YTA) is published as the system parameters.
 Registration stage-
Cloud and participants both need to register to the TA.
Cloud
1. It randomly selects X’c ∈ Z*p as its partial private key.
2. Calculates Y’c = X’ as its partial public key.
3. It sends its identity IDc to the TA via a secure channel.
TA then computes Y’’c = H1(I D), X’’c = XTAY’’c and returns key pair (X’’c , Y’’c) to
the cloud. (IDc, X’’c , Y’’c ) is stored in the record of TA.
The cloud publishes (Y’c, Y’’c ) as its full public key and keeps (X’c, X’’c ) as its full private
key.

Similarly the participant Un(n ∈ [1, N]), computes its full public and private key.
The participant Un publishes (Y’n, Y’’n ) as its full public key and secretly keeps (X’n, X’’n )
as its full private key.
 Authentication stage-
Participant Un, before uploading the updated model parameters Wn to the cloud, it
generates the signature on and signs Wn as follows.
1. Randomly pick r, v ∈ Z*p.
2. Calculate Dn = H2(Wn || Y’n || Y’’n || Y’c).
3. Calculate kn = H2(Wn || Y’n || Y’’n || Y’c , r P).
4. Calculate Un = X’n YTA – X’’n kn .
5. σn = (kn, Un).
6. Calculate Zn = vP, Z’n = vY’c.
7. Calculate W*n = Encs(Wn || Y’n || Y’’n || Y’c , Zn)
8. Send the update request message reqn = (W*n , σn , kn , Un , Dn , Z’n) to the
cloud.
After receiving the request reqn, the cloud authenticate the message as follows
1. Recover Zn = X’c
-1
Z’n.
2. Calculate Wn || Y’n || Y’’n || Y’c = Decs(W*n , Zn ).
3. Check Dn = H2(Wn || Y’n || Y’’n || Y’c ). If the equation holds, continue to the
next step or authentication failed and stop it.
4. Check the validity of σn following the Verify step in the proposed PCLS. It
rejects the request if σn is invalid. Otherwise, continue to the next step.
5. The cloud establishes a session key S1
n = H3 ( Dn || Wn || Zn ) for the next first
session. For the subsequent sessions, the session key is calculated as
S j+1
n = H3 ( Sj
n || Zn ), ∀ j ≥ 1.
It is noted that, with the content of Wn , the cloud can detect the data poisoning attacks and
free-rider attacks by integrating with the existing detection schemes
 Batch verification stage –
The cloud can verify the validity of all received signatures via batch verification.
Given a list of requests R = {reqn = (W*n , σn, kn , Un , Dn , Z’n )}N
n = 1, the batch
verification follows
. e(∑ n=1
N
Y’n , Y’TA) = e(∑ n=1
N
Un , P) e(∑ n=1
N
knY’’n , YTA )
If holds, all the signatures in the list are valid. Otherwise, the cloud launches the
DBV algorithm to find an appropriate batch size and redo batch verification.
If there is a failure in batch verification, the cloud picks a verification rate €, where €
∈ (0, 1) is a percentage value, and randomly selects M = € N requests from

the list R. The M requests are batch verified following above equation. If equation
holds, the cloud then uses the M message to aggregate and update the global
ML model. Otherwise, the cloud repeats the above steps at most η iterations.
If the verification fails in the all η iterations, the cloud continues to lower the batch
size with M = €M. It will continue until the batch size M is less than λN,
where λ ∈ (0, 1) and λN defines the threshold of batch size.

Chapter 3
Result
3.1 Computational Efficiency
We evaluate the computational efficiency only based on the three operations,
 Exponentiation
 Multiplication
 Pairing dominate
Operations Time(ms)
Exponentiation in G2 Te : 1.5
Multiplication in G1 Tm : 15.175
Pairing Tp : 18.06
TABLE I (Operating Time)
Table I lists the running time of the three operations over the constructed experimental
platform, where te denotes the time consumption of one exponentiation operation in G2, tm
denotes the time consumption of one multiplication operation in G1, and tp denotes the time
consumption of one pairing operation.
Protocols Sign Verify
Liu et al. [11] 5Tm Te + 4Tm + Tp
Zhang at al. [12] 9Tm 6Tm
Yang et al. [14] Te+Tm Te + 5Tp
Shen et al. [15] Te + Tm + Tp Te + Tm + 2Tp
Proposed 4Tm Te + 2Tm + 3Tp
Protocols Sign Value Verify Value
Liu et al. 75.875 80.26
Zhang at al. 136.575 91.05
Yang et al. 16.675 91.8
Shen et al. 34.735 52.795
Proposed 60.7 86.03
TABLE II( COMPARISON OF THE COMPUTATIONAL TIME WITHOUT BATCH VERIFICATION)
It is noted in table II that, proposed AAPBV outperforms Zhang at al. while consuming more
time than Liu et al., Yang et al., Shen et al. in different stages. Thus, the advantage of the
proposed protocol is not significant comparing with Liu et al., Yang et al., Shen et al. in a
single verification. The reason is that to support batch verification and more security features
(e.g., forward security and non-repudiation), the proposed protocol consumes more
operations of pairing and multiplication.

Protocols Time
Yang et al. 5(n+1) Tm + 5Tp
Shen et al. nTe + nTm + 2nTp
Proposed nTm + 3Tp
TABLE III (COMPUTATIONAL TIME OF BATCH VERIFICATION)
Table III show the comparison of the computational overhead with batch verification from
the theoretical results. Let the batch size be n. For Shen et al., the computational time for
batch verification is nTe + nTm + 2nTp, which is the n times of its verification time without
batch verification in Table II.
Thus, although Shen et al. supports batch verification, the time efficiency is not improved
comparing with the case without batch verification. For the proposed AAPBV and Yang et
al., the time cost is linearly dependent on the batch size and Tm.
Compared with the time consumption listed in Table II, AAPBV and Yang et al. not only
support batch verification, but also improve the computational efficiency. Shen et al. costs
the most computational time, while the proposed AAPBV reduces the time consumption
significantly. Particularly, in proposed protocol, the time consumption is reduced by
approximately 71% compared with Shen et al. and is reduced by approximately 80%
compared with Yang et al. It is also noted that the batch verification in our proposed protocol
reduces the time cost approximately by 82% compared with the case that without batch
verification.
AAPBV has the best time efficiency in batch verification. To support the batch verification, it
employs more operations of pairing and multiplication in single verification. Computational
time with batch verification (BV). Slightly sacrificing the time efficiency in the case of
without batch verification. Since the final authentication is conducted with batch verification,
the sacrifice is acceptable.
Features Liu et al. Zhang et al. Yang et al. Shen et al. Proposed
Confidentiality Yes Yes Yes Yes Yes
Anonymity Yes Yes No Yes Yes
Mutual
Authentication
Yes Yes No No Yes
Unlinkability Yes Yes No No Yes
Unforgery Yes No Yes No Yes
Forward
Security
No Yes No No Yes
Backward
Security
No No No No Yes
Batch
Verification
No No Yes Yes Yes
TABLE IV (Feature Comparison)

Chapter 4
Problem found in the methodology
 The proposed protocol itself can’t detect the internal attacks (e.g., data poisoning
attack and free-rider attack) in DL.
Data poisoning is a type of adversarial attack on machine learning systems in which
an adversary injects a few correctly-labeled, minimally-perturbed samples into the
training data, causing a model to misclassify a particular test sample during inference.
So it needs to integrate with the defence scheme.

Chapter 5
Conclusions
The proposed protocol achieves efficient batch verification with a slight sacrifice of
computational efficiency in single verification. In addition, benefiting from the designed
DBV algorithm, the global model converges quickly under the proposed AAPBV protocol,
further improving the computational efficiency in DL.
The proposed protocol guarantees various security properties while supporting batch
verification. The protocol provides high efficiency and enhanced security with a small
sacrifice in computational costs in single authentication, making it more practical for large-
scale DL systems.

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