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We present a highly detectable, trustless watermarking scheme for LLMs: the detection algorithm contains no secret information, and it is executable by anyone. We embed a publicly-verifiable cryptographic signature into LLM output using rejection sampling. We prove that our scheme is cryptographically correct, sound, and distortion-free. We make novel uses of error-correction techniques to overcome periods of low entropy, a barrier for all prior watermarking schemes. We implement our scheme and make empirical measurements over open models in the 2. Our experiments suggest that our formal claims are met in practice. These capabilities include in-context learning, code completion, text-to-image generation, and document and code chat. However, GenAI technologies are also being used for nefarious purposes e. To protect against such use cases, a large body of work has focused on detecting AI-generated content Lavergne et al. At present, the main approach when trying to detect AI-generated text is to train yet another AI model to perform the detection Zellers et al. This method makes a critical assumption: that AI-generated text has embedded features that are identifiable by AI. The key problem with this assumption is that generative models are explicitly designed to produce realistic content that is difficult to distinguish from natural content generated by a human or nature. To circumvent this fundamental issue, a recent line of work Aaronson , ; Kirchenbauer et al. The detection process measures the signal: if the signal is sufficiently strong, the content was likely watermarked. In particular, the cryptographic approach of Christ et al. The same key is used to generate and measure the signal. The aforementioned watermarking approaches have one problem in common: the model provider and the detector both need to know a shared secret key. This is acceptable in scenarios where the entity trying to detect the watermark is the same entity generating the content. However, such a setup has limitations:. Lack of privacy: The entity who wants to check the integrity of the content might not be willing to share it with the detector. For example, one looking to identify whether their medical records are AI-generated may not want to share the records themselves. Conflict of interest: The entity providing the detection API might not be trusted in certain cases. For instance, consider a case where the entity is accused of generating a certain inappropriate text and is brought to a court of law. It is not reasonable to ask the same entity to tell whether the text is watermarked. One solution could be sharing the secret with the world so everyone can run the detection. However, this raises another important problem: anyone can now embed the secret to any content, AI-generated or not. This would not be acceptable because the watermarking is subject to denial of service attacks. An attacker can create masses of watermarked content that is not AI-generated to undermine the dependability of the detector. Consider the effect on one of the main applications of watermarking: an entity may want to use the watermark as a signature for their content. Such signatures are useful when a the generated content needs to come with proof of a credible generator, and b the entity needs to refute an accusation about a generated content; i. This application is rendered impossible in a world with availability attacks. In this paper, we aim to solve the aforementioned problems for LLMs that produce text. We ask:. Is it possible to construct a publicly-detectable watermarking scheme? We find that the answer is yes: we construct a publicly-detectable scheme that provably resolves the trust issue—users can cryptographically verify the presence of a watermark. Further, they have a guarantee that the only entity capable of embedding the watermark is the model provider, resolving the privacy and conflict of interest issues above. We state the properties for public detectability below:. Security: To guarantee a user is convinced that a watermark is detected, the watermarking scheme must achieve cryptographic detectability: false positives or negatives must never occur in practice. Weak robustness: It is possible that text obtained from LMs is modified—to some extent—before publication. The watermark detector should be able to detect a watermark so long as the cryptographic signature is still embedded in the text. Prior work in the secret key setting aimed for strong robustness where detection should be possible even if the LLM output has changed substantially but text semantics are preserved. Strong robustness has since been shown to be impossible in the general case Zhang et al. Distortion-freeness: The watermarking scheme should not degrade the quality of the LLM output. No probabilistic polynomial-time PPT adversary should be able to distinguish between watermarked and non-watermarked text. Model agnosticity: The watermarking scheme should use the model as a black box, i. Public verifiablity: Without access to the model weights or secret material of the watermarking scheme, the detector should be able to determine whether a candidate text is watermarked. We give an overview of the key ideas in our construction. Refer to Figure 1 for a visual representation and Section 4 for full details. After this process, a complete message-signature pair is embedded into a contiguous sequence of generated tokens. We remark that our watermarked output is computationally indistinguishable from the original output: as long as there is sufficient entropy at generation time, no PPT algorithm can tell if a text completion came from the watermarking algorithm or the plain algorithm. To detect the presence of a watermark, the detector needs to recover the message-signature pair. As in the private key setting, our protocol needs to handle sequences with limited entropy. Kaptchuk et al. We overcome this problem by leveraging standard error correction. This section defines what it means for a publicly-detectable watermarking scheme to be secure. We will eventually prove that our construction satisfies these definitions. This assumption allows us to capture security properties and present our protocol concisely. If this assumption is met, distortion-freeness is guaranteed. The maximum number of low-entropy periods our scheme can tolerate is exactly the maximum number of errors that the underlying ECC scheme can correct. We refer to two distinct entities in our security model:. An honest model provider will run the watermarking protocol at text generation time. This entity has white-box access to the model weights in addition to any secret material specific to the watermarking protocol, e. Users generate prompts which are sent to the model provider in exchange for the model output. The user should be convinced that the watermark is present or not, i. In this section, we formally define a publicly detectable watermarking scheme, which should satisfy a completeness, b soundness, c distortion-freeness, and d robustness. We prove our scheme meets these definitions. This definition is an asymmetric-key analogue of the symmetric-key completeness definition in Christ et al. We define soundness as. Intuitively, our soundness definition says the following. This implies that any attempted forgery of a watermarked message must contain an overwhelming portion of tokens from genuine watermarked text. This means distortion-freeness ensures that the watermarking algorithm does not noticeably change the quality of the model output, i. This definition is the same as Christ et al. Our scheme uses a public-key signature scheme with the following properties. As a signature scheme, we require this property to guarantee it is hard to forge a watermark. We present our watermarking scheme in Algorithm 2. The core idea is to embed a message and a corresponding publicly-verifiable signature in the generated text. The message-signature pair should be extractable during detection. Once extracted, it can be verified using the public key. To explain our scheme, we describe how to embed one message-signature pair in LLM output—the construction can be applied repeatedly to generate arbitrarily long LLM output i. Refer to Figure 1 for a visual presentation of the construction. The first step is to sample a fixed number of tokens such that the entropy used at generation time to produce those tokens is sufficient for watermarking. This is captured in Line 2 of Algorithm 3. Now, any error-correcting codeword is not a pseudorandom string; therefore, directly embedding a codeword distorts the distribution of the output. However, we can regain pseudorandomness by using the message hash as a one-time pad to mask the codeword. The key idea is to embed bits into a block of tokens such that the block of tokens hashes to the target bit. Note that the hash depends on all previous inputs to hashes for the current signature codeword. This process can be repeated to embed multiple pairs for added resilience. If one such pair is found, the input text is flagged as watermarked. To detect if a watermark is present in candidate text, it suffices to extract one message-signature pair and verify it using the public key. Notably, since we employ error-correcting code to handle the cases where the entropy is low to embed bits, we must invoke the error-correction algorithm to correctly decode the signature embedded in the potentially erroneous codeword. This is exactly what Line 9 does. If the signature verifies, we know with overwhelming probability the text was watermarked See Theorem 4. Otherwise, move on to the next candidate block and try again. If no message-signature pair is verified, we conclude that the text was not watermarked See Theorem 4. A random oracle is a random function drawn uniformly randomly from the set of all possible functions over specific input and output domains. Random oracle models are commonly used in cryptographic construction Bellare and Rogaway , Our proof relies on the following claim. It holds that. By the Hoeffiding inequality Theorem A. This completes the proof. Now we proceed to prove our theorem. The only difference between our sampling algorithm and the original sampling algorithm is the following: The original sampling algorithm i. We just need to prove that these two sampling processes are computationally indistinguishable. The only possibility that the watermarking fails is if the rejection sampling algorithm fails to find the next batch of tokens whose hash is consistent with the target bit. Namely, our embedding algorithm will stop trying to embed the given bit at those locations and simply embed an arbitrary bit. The soundness of our watermarking scheme is based on the unforgeability of the signature scheme by a simple reduction. Then, one may extract this pair, which constitutes a forgery attack against the underlying signature scheme. The robustness of our scheme is rather easy to see. The detection algorithm will recover this consecutive sequence by an exhaustive search, resulting in a successful detection output. We implement both our publicly-detectable protocol and Christ et al. We focus our evaluation on assessing whether distortion-freeness is met in practice. In particular, we need to verify that our 3. Note that our other formal properties, detectability and weak robustness, are immediate from our construction: detectability is inherited from the underlying signature scheme BLS signatures Boneh et al. We additionally evaluate real-world performance under varying conditions. Concretely, we a present a range of generation examples for varying parameters in our protocol alongside examples from the other protocols, b quantify the distortion-freeness of the text completions using GPT-4 Turbo as a judge, c measure generation times against baseline plain generation without any watermarking and detection times for Christ et al. Hereafter, we will refer to the four generation algorithms using the following aliases:. Standard text decoding. Standard text decoding but with the arbitrary-to-binary vocabulary reduction of Christ et al. The base non-substring complete version of the Christ et al. Our public key watermarking protocol. Following prior watermarking evaluations, we use samples from the news-like subset of the C4 dateset Raffel et al. We implement our publicly detectable protocol and the base non-substring-complete version of the Christ et al. Our implementation is written in Python 3 with PyTorch Paszke et al. We focus on the openly available Mistral 7B model Jiang et al. We additionally provide examples from the semi-open Llama 2 Touvron et al. We use the 2. Refer to Appendix C for extensive completion examples. Benchmarking procedure. The benchmarking script selects a fixed number of prompts at random from the C4 dataset, skipping prompts that mention specific products. This ensures that all algorithms produce the same number of tokens. We force generation length to be as long as needed to encode the signature, i. Embedding in characters instead of tokens. Note that throughout the paper we have discussed embedding the signature in tokens for simplicity and alignment with prior work. However, in our implementation, we plant the watermark directly on plain text rather than tokens to avoid inconsistencies in encoding then decoding or vice versa using any given tokenizer: tokenizers do not guarantee that encoding the same string twice will output the same tokens. We show how text completions vary over six benchmarking runs with different generation parameters. We primarily use the Mistral 7B model due to its high quality output for its size class. We display a couple text completions for each algorithm in Table 1. See Table 4 through Table 9 in Appendix C for the full collection of text completions—each table shows one text completion per generation algorithm for 5 distinct prompts. We additionally include a few completion examples from larger models Llama 2 70B and 13B in Table 2 and Table 3. In the next section, we discuss the quality of these examples. Following many works in the NLP literature e. We do not use model perplexity as it is known to assign arbitrary scores in some cases—for example, it can favor repetitive text Holtzman et al. For each batch of four generations one from each algorithm , our prompt template asks the model to: a rate the text completion by giving it a score from 0 worst to best , and b give reasoning for the assigned score in list form. In theory, all the algorithms should be computationally distortion-free if their underlying assumptions are satisfied. Recall distorion-free means no PPT algorithm can distinguish between watermarked and non-watermarked text. We see in Figure 2 that GPT-4 Turbo-assigned scores have similar means and high variance—there is no statistically-significant signal that any particular generation algorithm outperforms the others. This provides evidence toward real-world distortion-freeness. On embedding compactness. In this section, we discuss the generation and detection runtimes shown in Figure 3. Text generation. Watermark detection. This aligns with performance expectations. Detecting an asymmetric watermark takes constant time in our implementation because we know the starting index of the signature. Abstract We present a highly detectable, trustless watermarking scheme for LLMs: the detection algorithm contains no secret information, and it is executable by anyone. However, such a setup has limitations: 1. We ask: Is it possible to construct a publicly-detectable watermarking scheme? We state the properties for public detectability below: 1. Assumption 3. Definition 3. Definition 4. Theorem 4. Claim 1 Balanced Partition. Proof of Claim 1. Hereafter, we will refer to the four generation algorithms using the following aliases: 1. Prompt Plain tokens Plain bits Christ et al. This work 1 Windthorst pulled off a sweep of Collinsville Tuesday, while Archer City and Holliday were unable to advance. Windthorst defeated Collinsville , and Windthorst pulled off a sweep of Collinsville Tuesday, while Archer City and Holliday were unable to advance. Eight Sussex skiers will take to the slopes to battle it out for the honour of being crowned National Champion at the English Alpine Ski Championships which start this weekend.

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