Stories with Tag compression algorithm

• A JPEG Image Compression Service Using Part Homomorphic Encryption

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  Posted: 2025-03-03 09:35:29

  Verbose tl;dr

  This project introduces a JPEG image compression service that incorporates partially homomorphic encryption (PHE) to enable compression on encrypted images without decryption. Leveraging the somewhat homomorphic nature of certain encryption schemes, specifically the Paillier cryptosystem, the service allows for operations like Discrete Cosine Transform (DCT) and quantization on encrypted data. While fully homomorphic encryption remains computationally expensive, this approach provides a practical compromise, preserving privacy while still permitting some image processing in the encrypted domain. The resulting compressed image remains encrypted, requiring the appropriate key for decryption and viewing.

  This GitHub repository, titled "ShadowyCompression," introduces a novel approach to JPEG image compression that incorporates partially homomorphic encryption (PHE) to address privacy concerns in cloud-based image processing. The core idea is to enable compression operations on encrypted image data without requiring decryption, thereby safeguarding the image content from unauthorized access by cloud service providers or other potential adversaries.

  The system leverages the Brakerski-Fan-Vercauteren (BFV) scheme, a type of PHE that allows for additions and multiplications on encrypted data within a specific range and depth. This is crucial for supporting the Discrete Cosine Transform (DCT) and quantization steps, which are fundamental components of the JPEG compression algorithm. Specifically, the implementation uses the SEAL library, a well-regarded implementation of the BFV scheme, to perform these homomorphic operations.

  The compression process begins by encrypting the image data using the BFV scheme. Then, the encrypted image blocks undergo a homomorphic DCT, transforming the spatial domain representation into the frequency domain. This transformation is achieved through homomorphic matrix multiplication. Following the DCT, the encrypted frequency coefficients are quantized, also homomorphically, to reduce the data size by discarding less significant information. This involves dividing the coefficients by predetermined quantization tables and rounding the results. These quantized coefficients, still encrypted, then represent the compressed image data.

  The repository provides a proof-of-concept implementation demonstrating the feasibility of this approach. It includes code for encrypting the image, performing the homomorphic DCT and quantization, and subsequently decrypting the compressed data. While fully functional, the project acknowledges performance limitations inherent in current PHE implementations. Homomorphic operations are computationally expensive compared to their unencrypted counterparts, resulting in significantly longer processing times for compression. The project identifies optimization as a key area for future work, aiming to improve the efficiency and practicality of the proposed method. Furthermore, the project focuses solely on the compression pipeline, with the decompression process left for future development. While not implementing a complete JPEG pipeline, it showcases the potential of PHE for privacy-preserving image compression, paving the way for future research and development in this area.

  • JPEG
  • Image Compression
  • Homomorphic Encryption
  • Part Homomorphic Encryption
  • Data Security
  • privacy
  • Cloud Computing
  • image processing
  • Cryptography
  • Security
  • compression algorithm
  • Digital Images
  • Signal Processing

  Summary of Comments ( 13 )
  https://news.ycombinator.com/item?id=43240013

  Verbose tl;dr

  Hacker News users discussed the practicality and novelty of the JPEG compression service using homomorphic encryption. Some questioned the real-world use cases, given the significant performance overhead compared to standard JPEG compression. Others pointed out that the homomorphic encryption only applies to the DCT coefficients and not the entire JPEG pipeline, limiting the actual privacy benefits. The most compelling comments highlighted this limitation, suggesting that true end-to-end encryption would be more valuable but acknowledging the difficulty of achieving that with current homomorphic encryption technology. There was also skepticism about the claimed 10x speed improvement, with requests for more detailed benchmarks and comparisons to existing methods. Some commenters expressed interest in the potential applications, such as privacy-preserving image processing in medical or financial contexts.

  The Hacker News post discussing the JPEG image compression service using part homomorphic encryption generated a moderate amount of discussion, with several commenters exploring different aspects of the project and its implications.

  One commenter questioned the practical application of the service, given the already highly optimized nature of existing JPEG compression algorithms. They wondered if the security benefits offered by homomorphic encryption truly outweighed the potential performance costs and complexities. This sparked a small thread where others discussed the potential niche use cases, such as scenarios requiring computation on encrypted data without decryption, like in secure cloud environments. However, the consensus seemed to lean towards the limited practical applicability for everyday image compression.

  Another commenter expressed interest in the specific homomorphic encryption scheme utilized in the project, inquiring about its implementation details and performance characteristics. This led to a brief discussion about the trade-offs between different homomorphic encryption techniques and the challenges of achieving efficient computation on encrypted data. The original poster did not provide extensive details on the implementation, leaving some questions unanswered.

  Several commenters focused on the novelty of applying homomorphic encryption to image compression, acknowledging its academic interest while remaining skeptical about its real-world impact. They pointed out that the computational overhead associated with homomorphic encryption typically makes it impractical for performance-sensitive applications like image processing.

  One comment highlighted the security considerations of using homomorphic encryption, specifically mentioning the potential vulnerabilities of chosen plaintext attacks. This raised a discussion about the importance of carefully selecting appropriate parameters and security measures when implementing homomorphic encryption schemes.

  Finally, a few comments touched upon the broader implications of homomorphic encryption and its potential future applications in various fields, including secure data analysis and privacy-preserving computation. However, these comments were generally brief and speculative, reflecting the nascent stage of homomorphic encryption technology.

  In summary, the comments on Hacker News reflected a mix of curiosity, skepticism, and cautious optimism regarding the application of homomorphic encryption to image compression. While acknowledging the theoretical appeal and potential security benefits, many commenters questioned the practical viability and performance implications of the approach, particularly given the maturity and efficiency of existing compression methods. The discussion highlighted the ongoing challenges and trade-offs associated with homomorphic encryption technology and its potential future role in secure computation.

• Iterated Log Coding

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  Posted: 2025-02-26 07:43:21

  Verbose tl;dr

  Iterated Log Coding (ILC) offers a novel approach to data compression by representing integers as a series of logarithmic operations. Instead of traditional methods like Huffman coding or arithmetic coding, ILC leverages the repeated application of the logarithm to achieve potentially superior compression for certain data distributions. It encodes an integer by counting how many times the logarithm base b needs to be applied before the result falls below a threshold. This "iteration count" becomes the core of the compressed representation, supplemented by a fractional value representing the remainder after the final logarithm application. Decoding reverses this process, effectively "exponentiating" the iteration count and incorporating the fractional remainder. While the blog post acknowledges that ILC's practical usefulness requires further investigation, it highlights the theoretical potential and presents a basic implementation in Python.

  This blog post introduces a novel compression technique called "Iterated Log Coding," or "iterlog," which cleverly exploits the predictable nature of sorted integer sequences. The core idea revolves around representing each integer in a sorted sequence not by its absolute value, but by the difference between it and the preceding integer, a concept similar to delta encoding. However, iterlog takes this further by recursively applying this differencing process. Instead of just storing these differences directly, it stores the base-2 logarithm of each difference, rounded up to the nearest integer. This process of taking the log of the differences is iterated until all remaining values become zero.

  The author argues that this approach is particularly well-suited for compressing sorted sequences containing clusters of similar values, a common characteristic of many real-world datasets. When integers are close together, their differences, and consequently the logarithms of these differences, will be small. Representing these small values requires fewer bits, leading to significant compression. The iterated nature of the algorithm further amplifies this effect. As the differences shrink through successive iterations, the logarithms also decrease, leading to progressively smaller representations.

  The blog post details the encoding and decoding processes with illustrative examples. Encoding involves repeatedly calculating differences between consecutive numbers and then their logarithms, storing the rounded-up logarithm values at each level. A key point is that the first number in the sequence and the number of elements in the sequence need to be stored separately as they are not part of the differencing process. The number of iterations required is also implicitly stored by the presence of all zeros in the final iteration. Decoding reverses this process by repeatedly exponentiating and summing the logged differences, effectively reconstructing the original sequence.

  The author acknowledges that iterlog coding is not a general-purpose compression algorithm and might not be suitable for all types of data. It's particularly effective for sorted sequences with clustered values, where the differences between successive elements are small. In situations where the differences are large and vary significantly, iterlog may not offer significant compression advantages or might even increase the data size compared to uncompressed representation. The post concludes with a Python implementation of the iterlog encoding and decoding algorithms, allowing readers to experiment with the technique and evaluate its performance on different datasets. The author invites further exploration and optimization of the idea, suggesting that varying the logarithm base or utilizing alternative rounding strategies could potentially improve compression ratios in specific scenarios.

  • data compression
  • iterated logarithm
  • logarithm
  • coding theory
  • compression algorithm
  • binary coding
  • Elias coding
  • variable-length coding
  • integer compression
  • succinct data structures

  Summary of Comments ( 23 )
  https://news.ycombinator.com/item?id=43181610

  Verbose tl;dr

  Hacker News users generally praised the clarity and novelty of the Iterated Log Coding approach. Several commenters appreciated the author's clear explanation of a complex topic and the potential benefits of the technique for compression, especially in specialized domains like bioinformatics. Some discussed its similarities to Huffman coding and Elias gamma coding, suggesting it falls within a family of variable-length codes optimized for certain data distributions. A few pointed out limitations or offered alternative implementations, including using a lookup table for smaller values of 'n' for performance improvements. The practicality of the method for general-purpose compression was questioned, with some suggesting it might be too niche, while others found it theoretically interesting and a valuable addition to existing compression methods.

  The Hacker News post "Iterated Log Coding" discussing the blog post about a new compression algorithm has generated a moderate amount of discussion, with several commenters engaging with the core ideas presented.

  One of the most compelling threads revolves around the practicality and novelty of the "iterated log" approach. A user points out that the method is reminiscent of Elias gamma coding, a well-established variable-length coding scheme. This sparked further discussion comparing the two methods, with some suggesting that iterated log coding might offer advantages in certain scenarios, particularly when dealing with very large numbers, while others remain skeptical, highlighting the efficiency and existing implementations of Elias gamma coding.

  Another commenter questions the choice of using base-10 logarithms in the examples, suggesting that base-2 logarithms would be more natural in a computational context. This comment prompts a brief discussion about the rationale behind the base choice, with the possibility that base-10 was selected for easier human readability in the illustrative examples.

  Several commenters express interest in seeing benchmarks and comparisons against existing compression algorithms. They emphasize the importance of real-world performance data to evaluate the effectiveness of the proposed method. One user specifically asks about the performance on typical integer sequences found in practice.

  There's also a short exchange regarding the potential applications of this compression method. One commenter suggests it could be useful for compressing indexes in databases.

  Finally, a few commenters delve into the theoretical underpinnings of the algorithm, discussing its relationship to other coding schemes and exploring its potential limitations. One user mentions the connection to prefix codes and how the unique decodability property is ensured.

  Overall, the comments section reveals a mixture of curiosity, skepticism, and cautious optimism towards the iterated log coding approach. While some see it as a potentially interesting idea with specific niche applications, others remain unconvinced of its practical value compared to established techniques. The prevailing sentiment appears to be a desire for more empirical evidence and comparisons to solidify the claims made in the original blog post.