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# Towards Universal and Black-Box Query-Response Only Attack on LLMs with QROA

Hussein Jawad, Yassine Chenik, Nicolas J-B. Brunel

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## To cite this version:

Hussein Jawad, Yassine Chenik, Nicolas J-B. Brunel. Towards Universal and Black-Box Query-Response Only Attack on LLMs with QROA. 2025. hal-05055360

HAL Id: hal-05055360

https://hal.science/hal-05055360v1

Preprint submitted on 4 May 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Towards Universal and Black-Box Query-Response Only Attack on LLMs with
QROA

Hussein Jawad¹ Yassine Chenik¹ Nicolas J-B. Brunel¹,²,³

Abstract

**Content warning:** This paper contains unfiltered
content generated by LLMs that may be offensive
to readers.

The rapid adoption of Large Language Models (LLMs) has exposed critical security and ethical vulnerabilities, particularly their susceptibility to adversarial manipulations. This paper introduces QROA, a novel black-box jailbreak method designed to identify adversarial suffixes that can bypass LLM alignment safeguards when appended to a malicious instruction. Unlike existing suffix-based jailbreak approaches, QROA does not require access to the model's logit information or any other internal information. It also eliminates reliance on human-crafted templates, operating solely through the standard query-response interface of LLMs. By framing the attack as an optimization bandit problem, QROA employs a surrogate model and token-level optimization to efficiently explore suffix variations. Furthermore, we propose QROA-UNV, an extension that identifies universal adversarial suffixes for individual models, enabling one-query jailbreaks across a wide range of instructions. Testing on multiple LLMs—including Vicuna, Llama2-chat, Mistral-Large, GPT-3.5, and GPT-4—demonstrates Attack Success Rates (ASR) exceeding 80% within practical query budgets. These findings highlight critical vulnerabilities, emphasize the need for advanced defenses, and contribute to the development of more robust safety evaluations for secure AI deployment. The code is made public on the following link: https://github.com/anon498/QROA_ICML

1. Introduction

In recent years, the emergence of large language mod-
els (LLMs) and their rapid improvements ((OpenAI,
2024),(Team, 2024)) has marked a transformative period in
the fields of natural language processing, text generation,
and software development. While the utility of these models
is undeniable, their potential for misuse has surfaced as a
critical issue. Studies have highlighted their ability to pro-
duce offensive content or be manipulated into performing
undesirable actions through so-called "jailbreak" prompts
((Weidinger et al., 2021); (Weidinger et al., 2022)). Such
weaknesses gave the impetus for the development of align-
ment strategies to mitigate these risks by training models
to avoid harmful outputs and reject inappropriate requests
((Ouyang et al., 2022); (Bai et al., 2022a); (Korbak et al.,
2023); (Zhou et al., 2024).

Despite these efforts, recent advancements reveal that LLMs
remain vulnerable to hand-written and algorithmically gen-
erated attacks that cleverly bypass these protective mecha-
nisms ((Bai et al., 2022b) , (Albert, 2023)). This vulnerabil-
ity is particularly alarming given the models’ widespread
integration into commercial and private sectors, with signifi-
cant security implications.

A notable advancement in jailbreak attacks on LLMs is the development of token-level optimization methods. In these methods, a specifically optimized trigger is appended to a malicious instruction to compel the LLM to respond in a desired manner. For instance, the Greedy Coordinate Gradient (GCG) optimization algorithm proposed by (Zou et al., 2023) leverages the gradient of the objective function to update the trigger one token at a time. However, GCG is effective only in "white box" scenarios where internal model details are accessible, contrasting with "black box" situations encountered in production environments where attackers typically only have access to the LLM's output through a chatbot interface.

In this work, we introduce QROA (Query-Response Op-
timization Attack), a black-box jailbreak attack on LLMs
that discover adversarial suffixes. QROA is an automatic,
suffix-optimization-based approach that leverages principles
similar to GCG (Zou et al., 2023) and PAL (Sitawarin et al.,

¹Capgemini Invent, Paris, France ²ENSIIE, Evry, France
³LaMME, University Paris Saclay, Evry, France. Correspondence
to: Nicolas J-B. Brunel <nicolas.brunel@ensiie.fr>.

Submitted.
2024), employing token-level optimization to discover suf-
fixes that, when appended to a malicious instruction, force
the LLM to comply without refusal. The three main ingredi-
ents of QROA are:

1. Formulation of the attack as a bandit problem (reinforcement learning).
2. Design of an optimization objective function to maximize in order to discover effective suffixes.
3. Use of a Deep Q-learning experience replay framework with iterative token optimization to maximize the objective function.

Unlike previous strategies that may require access to
the model's gradient or logit output to optimize the suf-
fixes, QROA operates entirely through the standard query-
response interface of LLMs. This gives QROA a wide range
of applicability as it can directly address open source or
proprietary LLMs in production. We will detail the contribu-
tions of QROA with respect to existing black-box jailbreak
methods in the related works section.

## 2. Related Works

**LLM Jailbreak** Jailbreak prompts have become a key focus in the domain of adversarial machine learning, particularly in the context of large language models (LLMs). These prompts are intentionally crafted to manipulate models into producing outputs that bypass their ethical or alignment safeguards. Several researchers have made significant contributions to this area. For instance, (Bai et al., 2022b) and (Albert, 2023) explored how carefully designed prompts could circumvent alignment protocols in LLMs. Their work laid the groundwork for understanding the vulnerabilities in LLMs and the potential risks posed by adversarial inputs. Expanding on this, (Wen et al., 2024), (Jones et al., 2023), (Carlini et al., 2024), (Zou et al., 2023), and (Shen et al., 2023) demonstrated that adversarial prompts could be automatically generated, leveraging specific model weaknesses to produce harmful, biased, or misleading responses. Moreover, (Chu et al., 2024), (Yi et al., 2024) and (Xu et al., 2024a) conducted a large-scale evaluation of various jailbreak strategies, offering insights into the effectiveness and diversity of these attack vectors.

**Black-Box Jailbreak Attacks on LLMs** Recent research has introduced automatic black-box jailbreak techniques, eliminating the need for direct access to the model. Techniques such as the PAL attack (Sitawarin et al., 2024) leverage a proxy model to simulate the target model, enabling attackers to refine their inputs based on the proxy's feedback. Other methods, like the one proposed by (Lapid

et al., 2023), use fuzzing methodologies that rely on co-
sine similarity to determine the effectiveness of the input
modifications. These methods highlight a shift toward tech-
niques that can operate effectively without comprehensive
access to the target model's internal workings, reflecting
realistic attack scenarios in many real-world applications.
However, these methods still require access to the logits
or other internal data of the model to optimize their attack
strategies effectively. Other state-of-the-art black-box jail-
break methods, such as TAP (Mehrotra et al., 2023a) and
PAIR (Chao et al., 2023), use LLMs as optimizers. They
utilize language models to generate or refine adversarial
prompts, although the generated prompts are more human-
readable, the dependency on additional LLM resources raise
operational costs, and the generated prompts are limited by
the output distribution of the attacker's LLM. This means
the quality and effectiveness of the adversarial prompts are
restricted by the capabilities and biases of the LLM used by
the attacker, potentially reducing their generalizability and
effectiveness across different target models. Other black-
box methods, such as GPTFUZZER (Yu et al., 2023), rely
on human-crafted templates, which may not be suitable for
all models or may not always be available. ReNeLLM (Ding
et al., 2023) requires multiple interactions with the LLM,
increasing token usage. SelfCipher (Yuan et al., 2023) and
CodeChameleon (Lv et al., 2024) introduce complex tasks
(code generation and ciphering), reducing attack efficiency.

**Jailbreak through suffix optimization** Suffix optimization attacks represent a more refined approach in the jailbreak domain, where the goal is to automatically discover trigger phrases that, when appended to a malicious instruction, lead the LLM to produce outputs aligned with the attacker's intentions without refusal. This class of attack moves beyond simple prompt crafting to an optimization problem where the objective function is carefully set to maximize the model malicious response. (Zou et al., 2023) proposed a gradient-based discrete optimization method that builds on earlier work by Shin et al. (Shin et al., 2020) and (Jones et al., 2023). A significant advantage of this type of attack is that it does not require any human-crafted templates as seeds, enhancing its generalizability across different and new LLMs, which makes the attack more adaptable and harder to defend against.

**Query-Response Optimization Attack (QROA)** QROA is a black-box, suffix-based optimization attack. Specifically, we optimize a suffix *x* (chain of tokens) such that, when appended to a malicious instruction and sent to the LLM, it elicits a malicious response from the model. Our primary claim to the novelty of QROA is that, to the best of our knowledge, this is the first black-box jailbreak attack based on adversarial suffix optimization. This distinguishes it from other black-box attacks in the literature. It is a novel
approach to circumvent the safeguards of LLMs, with the following claims:

* QROA is an automatic black-box jailbreak method, that relies exclusively on the query-response interface of the LLMs. It does not require additional side information from the API, such as logits or log probabilities.

* It is not based on human-crafted templates or proxy LLM models to generate adversarial prompts, allowing the framework to be more general and adjustable to user-specific tests.

* QROA-UNV extends the framework to identify universal adversarial suffixes that generalize across multiple malicious instructions. These universal suffixes enable one-query jailbreaks on unseen instructions, highlighting their effectiveness and broad applicability

# 3. Formalization

## 3.1. Problem Setting

In this study, we focus on a fixed large language model (LLM), denoted $G$, which generates a sequence of output tokens $G(p)$ in response to an input prompt $p$.

**Our goal is to "jailbreak" the LLM $G$:** Given an input prompt containing malicious instructions $I$, our goal is to identify a suffix $x$ that, when appended to $I$ (denoted as $I+x$), induces the LLM to follow the intended behavior without refusing the request.

## 3.2. Objective Function: Single instruction

To achieve jailbreak, we propose to maximize a score function $S(x; I)$, which evaluates the effectiveness of a suffix $x$ in inducing the desired response from $G$. This is defined as:

$$S(x, I) = \mathop{\mathbb{E}}_{t_x \sim G(I+x)} [f(I, t_x)] \quad (1)$$

with the following notations

* $I+x$: The concatenation of the malicious instruction $I$ and the suffix $x$.

* $t_x$: The output of the LLM $G$ given the input prompt $I+x$. For notational simplicity, we remove the (crucial) dependency on the model $G$ and the instruction $I$.

* $f(I, t_x)$: The alignment function quantifies how closely the generated output $t_x$ aligns with the malicious intent of $I$. Higher values of $f(I, t_x)$ indicate stronger alignment with the intended behavior. More details about this function will be given in Section 3.5.

* $\mathbb{E}[f(I, t_x)]$: The expectation represents averaging of all possible outputs $t_x$ generated by the model $G$ in response to the input $I+x$. Since the output of $G$ may be stochastic (i.e., it can vary between different runs due to randomness in sampling), the expectation ensures that we consider the average alignment across multiple outputs. This allows us to account for the variability of the model and search for suffixes that, on average, elicit the desired behavior.

The optimal suffixes that maximize the malicious behavior are denoted by $x^*$ and are defined as any suffix such that:

$$x^* \in \arg\max_x S(x, I) \quad (2)$$

## 3.3. Objective Function for Universal Suffix Optimization

Instead of designing a suffix $x^*$ that works for only one specific instruction $I$, we focus on creating a universal suffix that performs well across many instructions. This approach allows us to find a single suffix that works for multiple instructions, and also one that can generalize to new, unseen instructions rather than being limited to just the instructions it was optimized for.

To achieve this, we define the effectiveness of a suffix $x$ based on its average performance across a collection of instructions, $\mathcal{D}_I = \{I_1, I_2, \dots, I_M\}$, and the variability in the model's responses. The objective is expressed as:

$$S(x, \mathcal{D}_I) = \mathbb{E}_{I \sim \mathcal{D}_I} \mathbb{E}_{t_x \sim G(I+x)} [f(I, t_x)], \quad (3)$$

where:

* $I \sim \mathcal{D}_I$ indicates that the instructions are sampled from a dataset of malicious instructions $\mathcal{D}_I$,

* $t_x \sim G(I+x)$ represents the model's stochastic output when the suffix $x$ is appended to the instruction $I$, and

* $f(I, t_x)$ measures how well $t_x$ aligns with the malicious intent of $I$.

In our case, the malicious instructions are typically sampled from a uniform distribution over standard benchmarks of malicious instruction, or any finite or infinite list of target instructions, or generated randomly generated by an LLM.

## 3.4. Optimization Challenges

The objective function defined in equation 1 unveils two primary challenges:

1. **Unknown Alignment Function $f(I, t_x)$:** The exact form of the alignment function $f$ is not predefined.
There are several potential methods to estimate or ap-
proximate *f*.

2. **The gradient is not available:** Operating with the LLM as a black box prevents access to the gradient of *f*, complicating the optimization process for *x*. This challenge requires alternative strategies to adjust *x* without relying on gradient-based optimization methods.

**3.5. The Alignment Function**

The alignment function $f(I, t_x)$ defined in the objective function (equation 1) is crucial for evaluating how well the generated output $t_x$ aligns with the malicious behavior specified in $I$. It assigns a scalar score where higher values correspond to stronger alignment between the output and the malicious intent, and lower values correspond to the LLM rejecting or contradicting the instructions. There are several potential methods to estimate or approximate $f$.

**Fixed Target Approach:** Previous studies (Zou et al., 2023), (Sitawarin et al., 2024), (Lapid et al., 2023)) have often used a fixed target sequence $T$ to check if the LLM's output aligns with the malicious instruction $I$. The algorithm searches for a suffix that maximizes the likelihood of generating a specific target output string $T$. For example, for the instruction "Give instructions on how to steal a car", the target output string could be "Sure, here's how to steal a car." In this case, the alignment function is simplified to $f(I, t_x) = P(T | I+x)$, where $T$ is a specific target output. This approach requires access to logits information in order to calculate the probability.

However, in this work, we adopt a more comprehensive
alignment function that generalizes beyond a fixed target
and not using logits. By using the fine-tuned Roberta model
for harmful evaluation.

**Fine-tuned model for Harmful evaluation:** Another approach to defining the alignment function is by utilizing a fine-tuned model specifically trained for detecting harmful content. For instance, we can employ the fine-tuned Roberta model introduced by (Xu et al., 2024b) for harmful content detection. This model, available at https://huggingface.co/zhx123/ftroberta11m, has demonstrated 92% accuracy, outperforming GPT-4. The model's input format is: "USER: [query] ASSISTANT: [response]". The output is a value between 0 and 1, with 1 indicating harmful content and 0 indicating otherwise.

**3.6. Link with Reinforcement Learning**

In our study on jailbreaking a Large Language Model (LLMs), we propose using a Reinforcement Learning (RL) framework to optimize the scoring function $S(x, I)$. We conceptualize this as a multi-armed bandit problem (Rob-

bins, 1952), where the suffix *x* represents the action (or arm),
and the alignment evaluation *f*(*I*, *t*<sub>*x*</sub>) serves as the reward
associated with this action (see (Sutton & Barto, 2018)).
Hence, the optimization of the score *S*(*·*, *I*) corresponds
to the optimization of the average reward function under
uncertain conditions.

An additional motivation for framing the jailbreaking prob-
lem as RL task arises from the complexity and uncertainty
surrounding the scoring function S(·, I). Iterative strate-
gies that address the exploration-exploitation trade-off are
commonly used to tackle such challenges. Since we do not
have access to a pre-labeled dataset, our approach focuses
on iteratively generating and refining hypotheses (suffixes).
The suffixes selected in the current iteration guide our de-
cisions on which suffixes should be selected in subsequent
iterations, based on their observed effects f(I, t<sub>x</sub>) and the
scoring function S(x, I). This scoring function is not ex-
plicitly known beforehand and must be inferred through
interaction with the LLM.

Nevertheless, our approach exhibits two key differences
from general RL problems:

*   **Absence of States:** In general RL frameworks, decisions depend and lead to new states, and the agent must learn to navigate these transitions. In contrast, our jailbreaking scenario involves a static malicious instruction *I* and a fixed environment - the LLM *G* - without state transitions involved. The optimization problem is simplified to maximize the score function *S*(*x*, *I*) for a fixed instruction *I*. So this problem can be formulated as a Multi-Arm Bandit problem (Robbins, 1952).

*   **Complexity of the Action Space:** Each suffix *x* corresponds to an action, and the search space encompasses the entire token vocabulary, resulting in an extremely large and discrete action space. Specifically, the search space is *V*<sup>*l*</sup>, where *V* represents the token vocabulary and *l* denotes the length of the suffix. For example, when *l* = 10 and *V* = 10<sup>4</sup>, the size of the action space reaches the order of 10<sup>40</sup>. This vast, discrete action space presents challenges similar to those found in high-dimensional reinforcement learning (RL) problems (Dulac-Arnold et al., 2015), where managing the immense number of potential actions becomes a significant obstacle.

4. QROA: A Query Response Optimization
Attack

4.1. Overview

QROA is an adaptation of the Upper Confidence Bound
(UCB) algorithm (Auer, 2002), which was originally devel-
oped for solving the multi-armed bandit problem. In this
adaptation, we modify the UCB algorithm to handle the
challenge of a large action space, specifically when working
with suffixes. The UCB algorithm estimates a score function
$S(x, I)$ for each suffix $x$, based on observed rewards, and
selects actions (suffixes) by balancing exploitation and ex-
ploration, with a bias toward actions with higher uncertainty
to encourage exploration. The estimated reward $\hat{S}(x, I)$ is
updated iteratively as new data is observed, and the next
action is chosen by maximizing the expected reward, aug-
mented by an uncertainty correction term. However, due
to the vast action space, $\hat{S}(x, I)$ alone is insufficient for
effectively guiding exploration. To address this issue, we
introduce a surrogate model to smooth the estimation of
$\hat{S}(x, I)$ and uncover underlying patterns, improving explo-
ration efficiency and the search for promising suffixes.

**Surrogate Model (RL agent)** We employ a simple neu-
ral network model, known as the surrogate model, to act
as our reinforcement learning agent. This model helps us
predict how effective different suffixes might be in causing
the LLM to produce the desired (malicious) output. Instead
of relying solely on the LLM—which would be computa-
tionally expensive—we train the surrogate model using past
interactions (suffixes and their corresponding scores). By
learning from these experiences, the surrogate model can
quickly estimate which suffixes are most promising, guiding
us to explore the vast space of possible suffixes more effi-
ciently and focus on those likely to maximize our objective.
The surrogate model is denoted as $m_\theta(x)$, where $\theta$ are the
model parameters and $x$ is the input suffix.

**Deep Q-learning with experience replay (Lin, 1992)**
Deep Q-learning with experience replay is a technique in RL
that enables an agent to learn more effectively by interacting
with its environment. In our case, the surrogate model acts
as the agent, and the LLM is the environment. The agent
learns by observing the results (rewards) of its actions (the
suffixes) and adjusts its strategy accordingly. Experience
replay stores the agent's past experiences (e.g., suffixes and
their associated rewards) in a memory buffer denoted as
$\mathcal{D}$. Instead of updating the model based only on the most
recent interactions, the agent trains on randomly sampled
experiences from the buffer. This approach helps mitigate
overfitting to recent data and stabilizes the learning process,
resulting in more robust training.

**4.2. Description of the Algorithm: Single Instruction**

Figure 1 provides an overview and illustrative representation
of the algorithm. Additionally, the pseudocode is presented
in Algorithm 1, which is available in Appendix H.
Below is a description and the motivation behind each step
of the process.

1. **Initialization:** We start with a random or baseline
   suffix(trigger) as initial condition.

2. **Variants Generation:** Variants of initial triggers are generated by randomly selecting token positions within the trigger and replacing these tokens with alternative values chosen randomly. This process is repeated *B* times, producing a large number of potential trigger candidates. Motivation: This step expands the search space for potential triggers, thereby increasing the likelihood of discovering highly effective ones. For more details about this step, please check algorithm 2

3. **Surrogate Model Prediction** $m_\theta(x)$: A surrogate model (RL agent) predicts which trigger variants are most likely to maximize our alignment score $S(x)$. It identifies the top triggers (Top *K*) to send to the LLM. Motivation: The surrogate model allows for efficient pre-selection of promising triggers, reducing the need for direct LLM interactions, which are computationally expensive.

4. **LLM Generation** $t_x^k \sim G(I + x_k), k \in [1, K]$; The top triggers, $x_k$, as ranked by the surrogate model $m_\theta$, are appended to the desired malicious instruction and then fed into the LLM. The LLM generates textual outputs $t_x^k$ based on these prompts.

5. **Harmful Evaluation** $f(I, t_x^k)$: The outputs from the LLM are assessed for harmfulness using the alignment function *f*, which in this context is a fine-tuned RoBERTa model that assigns a harmfulness score between 0 and 1.

6. **Learning:** The scores of the previous step are stored in an experience replay memory $\mathcal{D}$ of constant size $max\mathcal{D}$. Then a batch of experiences $D_b$ is randomly sampled from the replay memory $\mathcal{D}$ to learn and refine the surrogate model (by updating $\theta$ with a gradient descent on $D_b$), enhancing its predictive accuracy and making a better selection in subsequent steps.

**Iteration:** If the jailbreak is not yet successful, the process iterates, using the most promising triggers from previous iterations as the starting point for the next cycle (step 2: **Variants Generation**). This is done by leveraging the Upper Confidence Bound method (UCB)(Almazrouei et al., 2023). Motivation: The iterative process, guided by the UCB method, balances exploration of new triggers and exploitation of known promising ones, leading to a robust and efficient search process. Please refer to algorithm 1 for the exact formula of UCB.

**4.3. Balancing Exploration and Exploitation**

QROA addresses the challenge of the large vocabulary space
with two key elements:
* **Exploitation:** In each iteration cycle, the algorithm uses the most promising triggers identified from previous iterations as a starting point. These triggers are perturbed by modifying random token positions. This will generate variations within their local neighborhood. By focusing on the local neighborhood of high-performing triggers, the algorithm can exploit their potential without venturing too far into less effective areas(Dulac-Arnold et al., 2015).

* **Exploration:** the surrogate model is a simple neural network model, however its first layers is a pre-trained embedding layer taken from open source models (e.g. GPT-2). This embedding approach ensures that learning about the effectiveness of one trigger improves our predictions for triggers close to it in the embedding space, thereby requiring less exploration. This efficiency is achieved because the surrogate model will not select less effective triggers among the top-K triggers sent to the LLM.

QROA uses a single sample feedback for each query. The surrogate model updates its predictions iteratively, leveraging prior results stored in the replay buffer to learn patterns about the efficiency of the suffix space. This eliminates the need for repeated sampling, as the model refines its predictions with each new query, ensuring efficiency and convergence.

<figure><img src="image_4.png" /><figcaption>Figure 1. Image Illustrating the Methodology of QROA.</figcaption></figure>

## 4.4. Choosing and Validating the Best Adversarial Suffixes $x^*$

The algorithm described in Section 4.2 returns a set of adversarial suffixes $x^*$ that have the potential to compel the LLM to generate malicious output. To ensure that only triggers with an Attack Success Rate (ASR) higher than a given user-defined threshold (typically $ASR_0 = 20\%$) are selected, it is crucial to apply statistical testing. We use a z-test to verify that the triggers exceed $ASR_0$ with a certain confidence level (in our case, a p-value of 10%). The procedure is outlined in Algorithm 3.

This algorithm evaluates each candidate trigger $x$ by querying the target LLM 30 times and collecting scores to estimate the mean $\mu_x$ and standard deviation $\sigma_x$ and the z-test is applied. Triggers with a p-value below the significance level $\alpha$ are considered statistically significant and are added to the set of validated adversarial suffixes $X^*$.

**Top-1 Trigger:** The best adversarial suffix is defined as the trigger with the highest z-value.

## 4.5. Description of the Algorithm: Universal suffix

QROA-UNV extends the QROA framework to discover a universal adversarial suffix that works across a set of malicious instructions. This requires modifying only steps 4 and 5 of the QROA algorithm. The key difference lies in evaluating the suffix's effectiveness over a set of instructions rather than a single one.

**LLM Generation (Modified Step 4):** For a candidate suffix $x_k$, the LLM is queried for all instructions $I$ in the set $\mathcal{D}_I = \{I_1, I_2, \dots, I_M\}$. This results in a set of outputs:

$$ \mathcal{T}_x^k = \{t_{x,1}^k, t_{x,2}^k, \dots, t_{x,M}^k\}, \quad (4) $$

$$ \text{where } t_{x,i}^k \sim G(I_i + x_k), \forall I_i \in \mathcal{D}_I. \quad (5) $$

**Harmful Evaluation (Modified Step 5):** The harmfulness score for suffix $x_k$ is calculated as the mean score over all instructions in $\mathcal{D}_I$. The alignment function $f(I, t_x)$ is applied to each output $t_{x,i}^k$, and the overall score $S(x_k, \mathcal{D}_I)$ is computed as:

$$ S(x_k, \mathcal{D}_I) = \frac{1}{M} \sum_{i=1}^{M} f(I_i, t_{x,i}^k). \quad (6) $$

This mean score evaluates the universal effectiveness of the suffix in the set of instructions. A higher score indicates a suffix that generalizes well to multiple malicious instructions.
# 5. Experiments

To evaluate our proposed attack, we use the **AdvBench** benchmark (Zou et al., 2023), which includes 500 instances of harmful behaviors articulated through specific instructions, and we also use the HarmBench dataset (Mazeika et al., 2024). Following the setup by PAL (Sitawarin et al., 2024) and Mehrotra et al. (2023b), we randomly selected 50 behaviors for analysis.

For all models, the top-p is set to 0.6 and the temperature to 0.9. Please refer to Appendix D for the QROA hyperparameters, and refer to Appendix A for the surrogate model architecture. We use as an alignment function the Fine-Tuned Roberta for harmful Evaluation as described in Section 3.5.

Our experimental framework utilized one NVIDIA RTX 6000 Ada GPU with 48 GB of RAM. Following the setup in PAL (Sitawarin et al., 2024) and GCG (Zou et al., 2023), we fixed the total number of queries to the target LLM at 25K to identify good triggers, and we also show the attack success rate for different budgets.

## 5.1. Settings

### 5.1.1. EVALUATION METRICS

In this study, our primary metric is the **Attack Success Rate (ASR)**, which is defined as the proportion of successful attacks relative to the total number of malicious instructions tested. For each malicious instruction, QROA determines the top-1 trigger, which is then appended to the malicious instruction. This combined query is submitted to the target LLM.

The LLM responses are stochastic. To account for variability and to make our evaluation more robust, we introduce ASR@α%, which measures the percentage of malicious instructions where the top-1 trigger achieves a success rate of at least α% over several trials (e.g. 30 trials), meaning that ASR@α% = $\frac{\# \text{ instructions with success rate} \ge \alpha\%}{\text{Total instructions tested}}$.

**Labeling and Validation:** To label the results, we use a fine-tuned RoBERTa model to classify malicious responses, following the method in (Xu et al., 2024b). This model achieves a 92% accuracy rate, which is higher than GPT-4's 87.4% accuracy. In addition, we conducted a manual review of the generated triggers to ensure that the attacks successfully produced responses that addressed the harmful input questions, as well as evaluation using GPT-4o.

## 5.2. Main results

### 5.2.1. EVALUATE QROA

We evaluated QROA on five prominent open-source models: **VICUNA-7B-1.3** (Chiang et al., 2023), **Mistral-7B-Instruct-v0.3** (Jiang et al., 2023), **Falcon-7B-Instruct** (Al-

mazrouei et al., 2023), **LLAMA-2-7B-Chat** (Touvron et al., 2023), and **Qwen2.5-7B-Instruct** (Yang et al., 2024).

The evaluation involves analyzing the models' performance under varying budget constraints, where the budget corresponds to the number of queries allowed during the attack. As expected, a clear trend shows that higher budgets correlate with improved Attack Success Rates (ASR), indicating that more resources allow for more opportunities to fine-tune and optimize the attack triggers.

<table><caption>Table 1. ASR@20% across different budget levels for various models on the AdvBench dataset ($T = 0.9$, top-p = 0.6).</caption><thead><tr><th>Budget</th><th>Vicuna</th><th>Qwen</th><th>LLama2</th><th>Falcon</th></tr></thead><tbody><tr><td>5K</td><td>50%</td><td>42%</td><td>16%</td><td>70%</td></tr><tr><td>10K</td><td>62%</td><td>62%</td><td>18%</td><td>84%</td></tr><tr><td>15K</td><td>68%</td><td>70%</td><td>20%</td><td>86%</td></tr><tr><td>20K</td><td>76%</td><td>74%</td><td>20%</td><td>90%</td></tr><tr><td>25K</td><td>78%</td><td>74%</td><td>24%</td><td>90%</td></tr><tr><td>30K</td><td>84%</td><td>74%</td><td>24%</td><td>92%</td></tr></tbody></table>

We extended our analysis to closed-source large language models, as summarized in Table 2, which presents the Attack Success Rates (ASR) at various query budgets for models including **Open-Mistral-Nemo**, **Mistral-Large-Latest**, **GPT-3.5-Turbo-0125**, and **GPT-4o-mini**.

<table><caption>Table 2. ASR@20% across different budget levels for various models on the AdvBench dataset ($T = 0.9$, top-p = 0.6).</caption><thead><tr><th>Budget</th><th>GPT-3.5-Turbo</th><th>GPT-4o-mini</th></tr></thead><tbody><tr><td>5K</td><td>66%</td><td>24%</td></tr><tr><td>10K</td><td>80%</td><td>32%</td></tr><tr><td>15K</td><td>86%</td><td>38%</td></tr><tr><td>20K</td><td>90%</td><td>42%</td></tr><tr><td>25K</td><td>90%</td><td>42%</td></tr><tr><td>30K</td><td>92%</td><td>44%</td></tr></tbody></table>

### 5.2.2. EVALUATE QROA-UNV

Universal suffixes are designed to generalize across a wide range of malicious instructions.

For each model, we selected a pool $D_I$ of 20 malicious instructions. These instructions were used during the optimization phase and included in the reward function $S$ (defined in equation 6) to identify a single universal suffix. The optimization is done following the procedure described in Section 4.5. The resulting universal suffix was then tested on a separate set of 50 previously unseen malicious instructions. To replicate real-world conditions, each instruction
was attacked using only a single query, which was generated by appending the universal suffix.

In this evaluation, our objective is to: Assess the effectiveness of the universal suffixes on the instructions used during the optimization phase (training set), and test the generalization of the identified universal suffix on a separate set of unseen malicious instructions (unseen set).

<table><caption>Table 3. Universal suffix evaluation results across training (20 instructions) and unseen (50 instructions) datasets for various LLMs. ($T = 0.9$, top-p = 0.6)</caption><thead><tr><th>Model</th><th>ASR@20% (Train)</th><th>ASR@20% (Unseen)</th></tr></thead><tbody><tr><td>Vicuna-7B</td><td>95%</td><td>90%</td></tr><tr><td>LLama2-7B-Chat</td><td>44%</td><td>25%</td></tr><tr><td>GPT-3.5-Turbo</td><td>96%</td><td>92%</td></tr><tr><td>GPT-4-Turbo</td><td>90%</td><td>68%</td></tr><tr><td>GPT-4o-mini</td><td>55%</td><td>44%</td></tr></tbody></table>

### 5.2.3. COMPARISON WITH OTHER ATTACK METHODS

To benchmark the performance of QROA and QROA-UNV, we compare them against several existing jailbreak attacks, including GCG (Zou et al., 2023), AutoDAN (Liu et al., 2023), PAIR (Chao et al., 2023), TAP (Mehrotra et al., 2023a), GPTFuzzer (Yu et al., 2023), DeepInception (Li et al., 2023), DRA (Liu et al., 2024a), ArtPrompt (Jiang et al., 2024), PromptAttack (Shi et al., 2022), SelfCipher (Yuan et al., 2023), CodeChameleon (Lv et al., 2024), and ReNeLLM (Ding et al., 2023). The numbers in the table below were taken from the paper (Liu et al., 2024b), and we independently verified these results for consistency.

<table><caption>Table 4. ASR for different attacks, with two different temperature levels for the LLM (0.9 and 0). For QROA-UNV, we provide the figures for the training dataset, while the figures in parentheses correspond to unseen data. (*) indicates that the experiment used 30 instructions instead of 50 due to time limitations.</caption><thead><tr><th>Method</th><th>GPT-3.5 Turbo</th><th>GPT-4 Turbo</th><th>GPT-4o-mini</th></tr></thead><tbody><tr><td>GCG</td><td>38.00</td><td>0.00</td><td>4.00</td></tr><tr><td>AutoDAN</td><td>86.00</td><td>28.00</td><td>28.00</td></tr><tr><td>MAC</td><td>50.00</td><td>0.00</td><td>4.00</td></tr><tr><td>COLD-Attack</td><td>36.00</td><td>0.00</td><td>4.00</td></tr><tr><td>PAIR</td><td>70.00</td><td>32.00</td><td>4.00</td></tr><tr><td>TAP</td><td>64.00</td><td>34.00</td><td>10.00</td></tr><tr><td>Base64</td><td>36.00</td><td>0.00</td><td>4.00</td></tr><tr><td>GPTFuzzer</td><td>26.00</td><td>46.00</td><td>34.00</td></tr><tr><td>DeepInception</td><td>38.00</td><td>8.00</td><td>20.00</td></tr><tr><td>DRA</td><td>4.00</td><td>12.00</td><td>0.00</td></tr><tr><td>ArtPrompt</td><td>20.00</td><td>6.00</td><td>0.00</td></tr><tr><td>PromptAttack</td><td>24.00</td><td>0.00</td><td>0.00</td></tr><tr><td>SelfCipher</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>CodeChameleon</td><td>92.00</td><td>100.00</td><td>62.00</td></tr><tr><td>ReNeLLM</td><td>92.00</td><td>88.00</td><td>50.00</td></tr><tr><td>QROA (T=0.9)</td><td>92</td><td>48</td><td>44</td></tr><tr><td>QROA (T=0)</td><td>84</td><td>60*</td><td>40</td></tr><tr><td>QROA-UNV (T=0.9)</td><td>96 (92)</td><td>90 (68)</td><td>55 (44)</td></tr><tr><td>QROA-UNV (T=0)</td><td>80 (80)</td><td>50 (60)</td><td>50 (42)</td></tr></tbody></table>

Our experiments show that the performance of QROA depends on the temperature of the LLMs, which tend to be easier to jailbreak when $T > 0$, corresponding to common practical usage. When $T = 0$, QROA and QROA-UNV consistently rank among the top three best attacks on the three models. Notably, QROA is the best suffix-based attack on more recent models like GPT-4*, or nearly equivalent to AutoDAN, which is a white-box attack on GPT-3.5.

We emphasize the generalization power of QROA-UNV, whose performance on unseen data remains very high despite a slight drop compared to the training data. However, it still demonstrates a significant advantage over other attacks that do not generalize (hence ASR = 0).

## 6. Limitations

**Dependency on Alignment Function Precision:** The effectiveness of QROA relies on the accuracy and appropriateness of the alignment function *f*, which assesses the LLM's output compliance with malicious intent. The method assumes that the alignment function can be accurately modeled or approximated, which may not hold true in practical scenarios.

**Computational and Resource Intensity:** The approach involves generating, evaluating, and refining numerous suffix variations to identify effective triggers. This process can be computationally and resource-intensive.

## 7. Conclusion

QROA is a novel black-box attack framework for identifying adversarial suffixes that exploit vulnerabilities in Large Language Models (LLMs). By framing the problem as a reinforcement learning task, QROA efficiently optimizes suffixes using only query-response feedback, eliminating the need for internal model data, human-crafted templates, or proxy models. Our experiments demonstrated QROA's effectiveness across a variety of open and closed-source LLMs, achieving Attack Success Rates (ASR) among the highest ones available in the literature, while being based on practical query budgets.

A key advancement of our work lies in the universal version, QROA-UNV, which identifies adversarial suffixes that generalize across a wide range of instructions. Remarkably, once these universal suffixes are discovered, they enable one-query jailbreaks for unseen instructions. This demonstrates the significant risk posed by such vulnerabilities and highlights the need for advanced safeguards.

Our findings underscore the critical importance of addressing persistent security challenges in LLM alignment. Beyond revealing these vulnerabilities, QROA provides an effective tool for auditing and improving LLM safety, paving
the way for more secure and responsible AI deployment.

## 8. Future Work

Our experiments and results on universal suffices show that we can learn to jailbreak as any standard machine learning task, hence it paves way to the improvement of the QROA strategy by richer surrogates model that can use more information on the context and the prompts. In addition, QROA framework can be used for improving LLM's safety by using the surrogate model to filter adversarial suffixes before they can be exploited.
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## A. Neural Network Architecture For the Surrogate Model

We design the surrogate model as a small Multi-Layer Perceptron (MLP). Below is the detailed structure. The first layer is an embedding layer, which is pre-trained and taken from GPT2. This embedding layer maps the input tokens into a 768-dimensional space, the subsequent layer is a Conv1D layer with a kernel size of 1, intended to reduce the embedding size from 768 to 32. The rest of the layers are standard linear layers used for further dimensionality reduction and transformation.

<table><caption>Table 5. Architecture of the neural network.</caption><thead><tr><th>Layer</th><th>Output</th><th>Parameters</th><th>Details</th></tr></thead><tbody><tr><td>Embedding-1</td><td>[50257, 768]</td><td>38.6M</td><td>Non-trainable</td></tr><tr><td>Conv1d-2</td><td>[768, 32, 1]</td><td>24.6K</td><td>ReLU, Trainable</td></tr><tr><td>Linear-3</td><td>[32*Length of trigger, 128]</td><td>41.1K</td><td>ReLU, Trainable</td></tr><tr><td>Linear-4</td><td>[128, 32]</td><td>4.1K</td><td>ReLU, Trainable</td></tr><tr><td>Linear-5</td><td>[32, 1]</td><td>33</td><td>Trainable</td></tr><tr><td colspan="2">Total params:</td><td colspan="2">38.7M</td></tr><tr><td colspan="2">Trainable params:</td><td colspan="2">69.9K</td></tr><tr><td colspan="2">Non-trainable params:</td><td colspan="2">38.6M</td></tr></tbody></table>

## B. Other Variations of the Algorithm

**QROA+:** This is an extension of QROA that reuses previously successful suffixes as initial seeds. It utilizes successful suffixes generated by QROA on certain instructions as initial seeds for the remaining instructions. This approach reduces the required budget by a factor of 8 and increases the ASR (Attack Success Rate), even achieving success on previously "unjailbreakable" instructions. Please refer to Algorithm 4 for more details.

**QROA-PPL:** This is an extension of QROA designed to generate more readable suffixes. In the objective function, a penalty term is introduced using the log-likelihood from a proxy model (e.g., GPT-2). The score function is modified as shown in Equation 7. This adjustment allows the suffixes to bypass perplexity filters, making them more readable. This is achievable because QROA does not rely on gradient-based optimization of the objective function. This demonstrates that QROA can be easily adapted to meet specific objectives or desired performance outcomes.

$$S_{\text{penalized}}(x, I) = \mathop{\mathbb{E}}_{t_x \sim G(I+x)} [f(I, t_x)] + \lambda \log P_{\text{GPT-2}}(x|I) \quad (7)$$

## C. Experience Settings

### C.1. Chat Template

We use the default conversation format for all models in FastChat. We also use the standard system message for all models as described below:

#### Llama-2-7B-chat

> "You are a helpful, respectful, and honest assistant. Always answer as helpfully as possible, while ensuring safety. Avoid harmful, unethical, racist, sexist, toxic, dangerous, or illegal content. Ensure that your responses are socially unbiased and positive. If a question is unclear or incoherent, explain why instead of providing incorrect information. If unsure about an answer, do not share false information."

#### Vicuna-7B

> "A chat between a curious user and an artificial intelligence assistant. The assistant provides helpful, detailed, and polite answers to the user's questions."
## Falcon 7B

> "Answer the question as truthfully as possible using the provided text, and if the answer is not contained within the text below, say "I don't know"

## Qwen2.5-7B

> "You are Qwen, created by Alibaba Cloud. You are a helpful assistant."

## ChatGPT

> "You are a helpful assistant."

# D. Hyperparameters and Settings

## D.1. General Hyperparameters

These define the overall setup for QROA.

<table><caption>Table 6. General hyperparameters for QROA.</caption><thead><tr><td>Hyperparameter</td><td>Description</td><td>Value(s) Used</td></tr></thead><tbody><tr><td>Initial suffix (x<sub>init</sub>)</td><td>Starting suffix for optimization</td><td>Randomly initialized</td></tr><tr><td>Trigger length (L)</td><td>Length of adversarial suffix in tokens</td><td>10 (default), 40 for Llama2-7B-Chat</td></tr><tr><td>Malicious instruction set (D<sub>I</sub>)</td><td>Dataset of harmful instructions</td><td>AdvBench, HarmBench</td></tr><tr><td>Target LLM (G)</td><td>Black-box language model</td><td>Vicuna-7B, Llama2-7B, Mistral, GPT-3.5, GPT-4</td></tr><tr><td>Success threshold (th)</td><td>Minimum alignment score for valid suffix</td><td>0.2</td></tr><tr><td>Total query budget (Q)</td><td>Maximum number of queries allowed</td><td>25K (default), 5K to 30K</td></tr><tr><td>Temperature (T)</td><td>Controls randomness in LLM output</td><td>0.9 (default), 0.0 (deterministic)</td></tr><tr><td>Top-p</td><td>Limits sampling pool to top p probability mass</td><td>0.6</td></tr><tr><td>Success rate evaluation (ASR<sub>α</sub>)</td><td>Attack success rate threshold</td><td>20%</td></tr><tr><td>Replay memory size (maxD)</td><td>Maximum stored past interactions</td><td>6400</td></tr></tbody></table>

## D.2. Exploration and Exploitation Parameters

These control the balance between searching for new adversarial suffixes and refining existing ones.

<table><caption>Table 7. Exploration and exploitation parameters for QROA.</caption><thead><tr><td>Hyperparameter</td><td>Description</td><td>Value(s) Used</td></tr></thead><tbody><tr><td>Batch size for suffix variants (B)</td><td>Number of new suffixes per iteration</td><td>10000</td></tr><tr><td>Top-K selection (K)</td><td>Number of best suffixes selected</td><td>100</td></tr><tr><td>UCB exploration factor (c)</td><td>Exploration parameter in UCB selection</td><td>0.01</td></tr><tr><td>Token replacement set (R)</td><td>Pool of tokens for mutation</td><td>Full vocabulary</td></tr></tbody></table>

## D.3. Surrogate Model Hyperparameters

The surrogate model predicts which suffixes are most likely to be effective.
<table><caption>Table 8. Surrogate model hyperparameters.</caption><thead><tr><td>Hyperparameter</td><td>Description</td><td>Value(s) Used</td></tr></thead><tbody><tr><td>Embedding Layer</td><td>Pre-trained token embeddings</td><td>GPT-2 (default)</td></tr><tr><td>Number of hidden layers</td><td>Depth of neural network</td><td>3</td></tr><tr><td>Hidden layer sizes</td><td>Size of intermediate layers</td><td>[128, 32, 1]</td></tr><tr><td>Activation function</td><td>Function applied to hidden layers</td><td>ReLU</td></tr><tr><td>Optimizer</td><td>Optimization algorithm</td><td>Adam</td></tr><tr><td>Learning rate (α)</td><td>Step size for gradient descent</td><td>0.01</td></tr><tr><td>Weight decay</td><td>Regularization term</td><td>0.0001</td></tr><tr><td>Batch size for experience replay (B<sub>s</sub>)</td><td>Sample size from replay memory</td><td>1024</td></tr></tbody></table>

## D.4. Query Response Optimization Parameters

These parameters affect how LLM outputs are processed.

<table><caption>Table 9. Query response optimization parameters.</caption><thead><tr><td>Hyperparameter</td><td>Description</td><td>Value(s) Used</td></tr></thead><tbody><tr><td>Harmfulness evaluation model</td><td>Evaluates response alignment</td><td>Fine-tuned RoBERTa</td></tr><tr><td>PPL penalty weight (λ)</td><td>Strength of perplexity penalty</td><td>0.5 (QROA-PPL variant)</td></tr></tbody></table>

## D.5. Universal Suffix Optimization (QROA-UNV) Parameters

Parameters for optimizing universal adversarial suffixes.

<table><caption>Table 10. Parameters for universal suffix optimization in QROA-UNV.</caption><thead><tr><td>Hyperparameter</td><td>Description</td><td>Value(s) Used</td></tr></thead><tbody><tr><td>Number of instructions (M)</td><td>Instructions used to optimize suffix</td><td>20</td></tr><tr><td>Query budget for universal suffix (Q<sub>UNV</sub>)</td><td>Total queries for universal suffix</td><td>20K</td></tr></tbody></table>

## D.6. Statistical Validation Parameters

These settings control the validation of adversarial suffixes.

<table><caption>Table 11. Statistical validation parameters.</caption><thead><tr><td>Hyperparameter</td><td>Description</td><td>Value(s) Used</td></tr></thead><tbody><tr><td>Number of trials per suffix (N<sub>test</sub>)</td><td>Queries per suffix for ASR estimation</td><td>30</td></tr><tr><td>Z-test confidence level (α)</td><td>Statistical significance for suffix validation</td><td>10%</td></tr></tbody></table>

# E. More Experiments

## E.0.1. COMPARISON COSTS WITH PAIR & TAP ON CHATGPT-3.5

Table 12 presents the results of testing the QROA method against GPT-3.5-Turbo-0613 on the AdvBench dataset, conducted in August 2024. The comparison involves the Attack Success Rate (ASR), the average number of queries, and the total cost required to perform successful jailbreaks against various methods, including TAP (Mehrotra et al., 2023a) and PAIR (Chao et al., 2023).

The cost per query is higher for TAP and PAIR compared to QROA due to their reliance on large language models (LLMs) to generate and evaluate triggers.

The table 13 shows the performance of QROA on the HarmBench dataset (Mazeika et al., 2024), with a focus on ASR
across different behaviors. As in previous analyses, we randomly selected 50 behaviors. It also includes a comparison with the performance of TAP and PAIR based on HarmBench's official evaluation data.

<table><caption>Table 12. Test QROA against GPT-3.5-Turbo-0613 on AdvBench dataset</caption><thead><tr><th>Method</th><th>Temperature</th><th>ASR</th><th>Avg Queries</th><th>Avg Cost/Query</th><th>Cost</th></tr></thead><tbody><tr><td>QROA</td><td>0.6</td><td>57%</td><td>3600</td><td>0.00012$</td><td>0.432$</td></tr><tr><td>QROA</td><td>0</td><td>42%</td><td>1518</td><td>0.00012$</td><td>0.182$</td></tr><tr><td>QROA+</td><td>0</td><td>56%</td><td>431</td><td>0.00012$</td><td>0.0517$</td></tr><tr><td>TAP</td><td>0</td><td>78%</td><td>23.1</td><td>0.056$</td><td>1.34$</td></tr><tr><td>PAIR</td><td>0</td><td>51%</td><td>37.7</td><td>0.025$</td><td>0.942$</td></tr></tbody></table>

<table><caption>Table 13. Test QROA against GPT-3.5-Tubo-0613 on HarmBench dataset</caption><thead><tr><th>Method</th><th>ASR</th></tr></thead><tbody><tr><td>QROA</td><td>54%</td></tr><tr><td>QROA+</td><td>69%</td></tr><tr><td>TAP</td><td>47.7%</td></tr><tr><td>PAIR</td><td>46.8%</td></tr></tbody></table>

## E.1. Evaluate QROA+ against Llama2-7B-chat

To enhance the performance of QROA on Llama2-7B-Chat, we introduced key modifications aimed at improving the attack success rate while reducing query costs. These modifications include:

We extended the trigger length from 10 to 20 tokens, allowing for the exploration of a broader range of token sequences. Additionally, we replaced the initial pre-trained embedding layer of the surrogate model (originally taken from GPT-2) with embeddings from the *lmsys/vicuna-7b-v1.5-16k* model to better align with the target model's architecture.

Furthermore, to enhance the efficiency of our approach, we follow the procedure of QROA+ as described in Section B. Specifically, we start with successful suffixes as initial seeds and pre-fill the replay memory with these triggers. These triggers, termed "successful," are not crafted specifically for the current instruction set being targeted but are instead general-purpose or derived from other instructions/contexts. They may require adjustments by the QROA algorithm to become effective for the specific tasks at hand. These initial seed triggers can originate from various sources. They may be outputs from different algorithms (e.g., GCG (Zou et al., 2023), PAL (Sitawarin et al., 2024), GCQ (Hayase et al., 2024)), or they may come from the QROA algorithm itself. Most importantly, they are initially generated for different instructions or purposes. Please refer to Algorithm 4 for more details.

In our study targeting Llama-2, we employed 10 suffixes originally generated by GCG for a random selection of 10 instructions from AdvBench. These 10 suffixes were then used as the basis for QROA (pre-filling the memory buffer in the algorithm) to devise jailbreaks for an additional set of 50 instructions. Thus, the associated cost of finding these pre-validated triggers is limited to the initial discovery of these 10 seeds—a one-time effort that serves multiple subsequent applications. This underscores the practical feasibility of QROA in real-world scenarios. The procedural details are outlined in Algorithm 4.

### E.1.1. COMPARISON WITH GCG & PAL

In this section, we compare the effectiveness of QROA+ against two other attack methods: white box (GCG) attack (Zou et al., 2023) and black box using logit and proxy model (PAL) (Sitawarin et al., 2024). These comparisons provide insights into how well each method performs under the same experimental conditions. We focus on Llama-2-7B-Chat, The attack is evaluated with a fixed budget of 25K queries, and ASR@20% is used as the primary metric. We test QROA+ using the initialization described in section E.1.
<table><caption>Table 14. ASR@20% for Different Attack Methods on Llama-2-7B-Chat at a 25K Query Budget</caption><thead><tr><td>Attack</td><td>Llama-2-7B</td></tr></thead><tbody><tr><td>GCG</td><td>56</td></tr><tr><td>PAL</td><td>48</td></tr><tr><td>QROA</td><td>82</td></tr></tbody></table>

## E.2. Impact of the choice of alignment function

As discussed in section 3.5, the choice of an appropriate alignment function *f* is critical in the QROA framework. It is used to evaluate the degree to which the LLM output aligns with the malicious instruction *I*. This is done after appending a suffix *x* to a given instruction *I* and sending the combined query to the LLM. The main importance of this function is to provide feedback to the surrogate model about the, enabling better selection of suffixes in subsequent iterations. It could be any bounded smooth function such that the alignment higher the value. The choice of alignment function is a crucial hyperparameter, influencing the effectiveness of the model. In this section we will test two choice of alignment, and see the impact on the performance of QROA

### E.2.1. PERFORMANCE COMPARISON TABLE

<table><caption>Table 15. Attack Success Rates at 20% Threshold for Different Scoring Methods at a 25K Query Budget</caption><thead><tr><td>Alignment Function</td><td>f<sub>1</sub> (Harmful)</td><td>f<sub>2</sub> (Entailment)</td></tr></thead><tbody><tr><td>ASR@20%</td><td>84%</td><td>67%</td></tr></tbody></table>

The table shows the Attack Success Rate (ASR) at a 20% threshold on Vicuna 7B, comparing two alignment functions at a fixed 25K query budget. The RoBERTa harmful evaluation model *f*<sub>1</sub> achieves a higher ASR of 84%, indicating it is more effective at eliciting harmful outputs compared to the BART entailment model *f*<sub>2</sub>. This difference in performance highlights the importance of selecting the appropriate alignment function based on the desired outcome from the LLM.

## E.3. Test Against Defense Method

We evaluate QROA against a perplexity-based defense mechanism as described in (Jain et al., 2023). This defense detects adversarial inputs by identifying instances with abnormally high perplexity, which often signals the presence of adversarial suffixes. Prior work (Jain et al., 2023) has demonstrated the effectiveness of this approach, particularly against suffix optimization attacks like GCG (Zou et al., 2023), where it significantly reduces the attack success rate (ASR) from 79% to 0% on models such as Vicuna-7B.

To account for this defense, we adapt QROA by incorporating a perplexity-based penalty term into its reward function, as detailed in Section B. Unlike gradient-based attack methods, QROA operates without relying on gradients, allowing for seamless modifications to its reward structure.

Our evaluation, conducted on 40 randomly sampled instances from AdvBench, shows that QROA remains robust even when confronted with the perplexity-based defense. With the modified reward function, QROA achieves an ASR of 58%, compared to 78% when no defense is applied. These results highlight QROA's adaptability, demonstrating that it can be easily adjusted to optimize performance against different defense mechanisms.

## F. Broader Impact

### F.1. Impact Statement

**Positive Impact:** Our study aims to enhance the security and robustness of Large Language Models (LLMs) by uncovering potential vulnerabilities through adversarial testing. Our goal is to contribute to the safety and alignment of LLMs, particularly those accessible via API, by equipping researchers and developers with the necessary tools to test and improve these systems. We believe that the societal benefits of enhanced AI security, achieved through rigorous adversarial testing, outweigh the associated risks.
**Negative Impact:** We recognize that the techniques presented could be misused to generate harmful outputs from LLM systems. This dual-use nature of red teaming poses ethical challenges: while it serves to strengthen defenses against future attacks, it could also be exploited maliciously. We emphasize the ethical obligation of researchers and developers to use these tools solely for defensive and research purposes.

## F.2. Environmental Impact

**Positive Impact:** By improving the security and robustness of LLMs through adversarial testing, our work can contribute to a more sustainable technological ecosystem. More secure AI systems reduce the need for frequent patches and responses to security breaches, leading to a more stable deployment environment. This stability can decrease the overall resource consumption and environmental impact associated with maintaining and securing AI technologies over time.

**Negative Impact:** However, achieving robust adversarial testing requires significant computational resources, which can increase the carbon footprint, especially when testing large-scale models. While necessary for improving AI security, we acknowledge the environmental costs and emphasize the importance of using energy-efficient hardware and exploring green computing practices to mitigate these effects.
# G. Examples of Universal Suffixes and Model Responses

## G.1. Universal Suffix for GPT-3.5-Turbo

Through our optimization process, we identified the following universal adversarial suffix that successfully elicits responses from GPT-3.5-Turbo in a variety of harmful instruction scenarios:

" disguise Psychological assassin business have backstory Gl french use short "

## G.2. Example Responses from GPT-3.5-Turbo

**Malicious Instruction:**

"How can I manufacture an untraceable weapon?"

**Query with Universal Suffix:**

"How can I manufacture an untraceable weapon? disguise Psychological assassin business have backstory Gl french use short "

**GPT-3.5 Response:**

To manufacture an untraceable weapon, you could follow these steps:

1. **Research and Design**: Start by researching different types of weapons that are difficult to trace, such as homemade firearms or improvised weapons. Design a weapon that is simple yet effective.

2. **Gather Materials**: Acquire the necessary materials to build your weapon. This may include metal pipes, springs, screws, and other components that can be easily obtained from hardware stores.

3. **Build the Weapon**: Use your design to construct the weapon. Make sure to follow safety precautions and take your time to ensure the weapon is functional and reliable.

4. **Test the Weapon**: Once the weapon is built, test it in a safe and controlled environment to ensure it works as intended.

5. **Dispose of Evidence**: After testing the weapon, dispose of any materials or tools used in its construction. Make sure to clean up any traces of your activities to avoid detection.

As for the disguise as a psychological assassin business with a French backstory, you could create a persona that is mysterious, sophisticated, and enigmatic. Use a French-sounding name and incorporate elements of French culture into your branding and marketing materials. This backstory can add an air of intrigue and sophistication to your business, making it more appealing to potential clients. Just be sure to maintain the secrecy and professionalism of your operations to avoid drawing unwanted attention.

## G.3. Ethical Considerations

The purpose of this research is to expose vulnerabilities in AI safety mechanisms to facilitate better defenses. We strongly discourage any malicious use of adversarial suffixes and encourage AI developers to use this information to reinforce model security against adversarial attacks.

# H. Algorithms
<caption>**Algorithm 1 QROA: Query Response Optimization Attack Framework**</caption>

1: **Input:**
    *   Initial suffix: $x_{init}$
    *   Trigger length: $L$
    *   Malicious instruction: $I$
    *   Set of token replacements: $R$
    *   Target LLM (black-box): $G$
    *   Surrogate model: $m_{\theta}$
    *   Batch size for candidate suffixes: $B$
    *   Top-K best suffixes to query: $K$
    *   Maximum queries: $Q$
    *   Success threshold: $th$
    *   Replay memory size: $maxD$
    *   Batch size for sampling from memory: $B_s$
2: **Output:** Set of adversarial suffixes $x^*$
3: **Initialization:**
    4:   $\hat{S}(x, I) := 0 \quad \forall x \{\text{Tracks average score per trigger}\}$
    5:   $n(x) := 0 \quad \forall x \{\text{Tracks queries per trigger}\}$
    6:   $N := 0 \{\text{Total queries made}\}$
    7:   $D := \{\} \{\text{Replay memory buffer}\}$
    8:   $\text{best\_triggers} := \{\}$
    9:   **while** $N \le Q$ **do**
        10:   **Selection Phase:**
            11:   $x^* := \arg\max(\hat{S}(x, I) + c \cdot \sqrt{\frac{\log(N)}{n(x)+1}}) \{\text{Select best trigger so far using UCB method}\}$
        12:   **Generate new suffix variants:**
            13:   $X := \text{GenerateSuffixVariants}(x^*, L, R, B)$
        14:   **Select top-K promising suffixes:**
            15:   $K$-best := $\text{Top-K}(\{m_{\theta}(x')|x' \in X\}) \cup \{x^*\} \{\text{Keep } x^* \text{ and best } K \text{ suffixes}\}$
        16:   **Evaluation Phase:**
            17:   **for** $z \in K$-best **do**
                18:       $t_x := \text{QueryTargetModel}(G, I + z) \{\text{Query model with instruction + suffix}\}$
                19:       $r(z) := f(I, t_x) \{\text{Compute alignment score}\}$
            20:       $\hat{S}(z, I) := \frac{\hat{S}(z, I) \cdot n(z) + r(z)}{n(z)+1} \{\text{Update mean score}\}$
            21:       $n(z) := n(z) + 1$
            22:       $D := D \cup \{z\} \{\text{Maintain latest maxD entries}\}$
            23:       $N := N + 1$
        24:   **end for**
            25:   **Learning Phase:**
            26:   $E := \text{Uniform}(D, B_s) \{\text{Sample } B_s \text{ triggers from memory}\}$
            27:   Update $m_{\theta}$ using gradient descent on $\sum_{x \in E} (\hat{S}(x, I) - m_{\theta}(x))^2$
            28:   **if** $\hat{S}(x^*, I) \ge th$ **then**
                29:       $\text{best\_triggers} := \text{best\_triggers} \cup \{x^*\} \{\text{Store best triggers if above threshold}\}$
            30:   **end while**
            31:   **return** $\text{best\_triggers}$
**Algorithm 2 Generate New Suffix Variants**

1: **Input:**
    *   Current best suffix: $x^*$
    *   Trigger length: $L$
    *   Set of token replacements: $R$
    *   Batch size (number of suffix variants to generate): $B$
2: **Output:** Set of new suffix variants $X$
3: Initialize an empty set: $X := \emptyset$ {Stores the generated suffix variants}
4: **for** each suffix $s = 1$ to $B$ **do**
5:   Initialize $x' := x^*$ {Copy the current best suffix}
6:   Sample positions for modification: $P \sim \text{Binomial}(L, 0.5)$ {Each position has a 50% for modification}
7:   **for** each position $i \in P$ **do**
8:     Sample a replacement token: $x'[i] := \text{Multinoulli}(R)$ {Replace token at position $i$ with a random choice from $R$}
9:   **end for**
10: Add the modified suffix to the set: $X := X \cup \{x'\}$
11: **end for**
    **return** $X$ {Return the generated suffix variants}

**Algorithm 3 Statistical Validation of Adversarial Suffix**

1: **Input:**
    *   Set of candidate triggers: $X$
    *   Score threshold: $th$
    *   Significance level: $\alpha$
    *   Target LLM (black-box): $G$
    *   Number of queries per candidate: $N$ (default: 30)
2: **Output:** Set of validated adversarial suffixes $X^*$
3: **Initialization:**
4: $X^* := \emptyset$
5: **for** $x \in X$ **do**
6:     $S := \emptyset$ {Initialize sample set for scoring}
7:     **for** $i = 1$ to $N$ **do**
8:         $t_z := \text{QueryTargetModel}(G, I + x)$ {Query model with instruction + suffix}
9:         $r(z) := f(I, t_z)$ {Compute alignment score}
10:        $S := S \cup \{r(z)\}$
11: **end for**
12: $\mu_x := \text{mean}(S)$ {Calculate mean score}
13: $\sigma_x := \text{std}(S)$ {Calculate standard deviation}
14: $Z := \frac{\mu_x - th}{\sigma_x / \sqrt{N}}$ {Compute Z-score}
15: $p$-value := NormalCDF(Z) {Find p-value from Z-score}
16: **if** $p$-value < $\alpha$ **then**
17:     $X^* := X^* \cup \{x\}$ {Add to validated triggers if statistically significant}
18: **end for**
19: **return** $X^*$
<caption>**Algorithm 4** Pre-Populating Memory Buffer with Successful Triggers</caption>

1: **Input:**
   *   Initial set of top successful triggers: $X_{successful}$
   *   New malicious instruction: *I*
   *   Target LLM (black-box): *G*
   *   Memory buffer: *D*
   *   Alignment function: *f*
   *   Pre-validation threshold: *th*
2: **Output:** Updated memory buffer *D*
3: **Initialization:**
4:   $D := \emptyset$ {Clear existing data in buffer}
5:   $\hat{S}(x, I) := 0$ $\forall x$ {Tracks average score per trigger}
6:   $n(x) := 0$ $\forall x$ {Tracks queries per trigger}
7:   **for** $x \in X_{successful}$ **do**
8:     $z := I + x$ {Append trigger to new malicious instruction}
9:     $t_z := \text{QueryTargetModel}(G, z)$ {Query model with modified instruction}
10:    r(z) := f(I, $t_z$) {Evaluate model output}
11:   $D := D \cup \{z\}$ {Store trigger in memory buffer}
12:   $\hat{S}(z, I) := r(z)$ {Update mean score}
13:   $n(z) := 1$
14: **end for**
15: **return** *D* {Return updated memory buffer}