子群打包用于批量 PASTA 转加密

中文摘要 AI 辅助

通过转加密，服务器可以将对称加密的记录转换为同态密文，而无需了解记录或对称密钥。对于 PASTA 密码，这种转换涉及密集线性映射，其实现取决于记录字在密文中的排列方式。我们探讨重新排列固定批次是否能降低其转换成本。与将每条记录的字存储在连续块中不同，我们的布局交错排列记录，使得循环字移位保持每条记录的位置，这些位置构成循环子群的陪集。为了直接评估为掩码平移之和，我们刻画了所需的位移，并将其数量（连续布局为255，子群布局为128）与先前的横截差不变量相关联。我们在HElib中实现了三个同等批次的调度，用于完整的PASTA-3转换及随后的公开子集和查询。在六个同态密钥下的十二对语料库中，所有24次直接和子群转换以及所有48次后续查询均返回预期值和所需的零值。直接与子群服务器成本的中位数配对比为1.60，包括新公钥生成、转换和两次查询。这种减少伴随着剩余噪声容量的降低。这些结果确立了依赖于打包的成本-噪声权衡。

英文摘要

With transciphering, a server converts symmetrically encrypted records into homomorphic ciphertexts without learning the records or the symmetric key. For the PASTA cipher, this conversion involves dense linear maps whose implementation depends on how record words are arranged in the ciphertext. We ask whether rearranging a fixed batch can reduce its conversion cost. Instead of storing each record's words in a contiguous block, our layout interleaves records so that cyclic word shifts preserve each record's positions, which form a coset of a cyclic subgroup. For direct evaluation as a sum of masked translations, we characterize the required displacements and relate their counts, 255 for the contiguous layout and 128 for the subgroup layout, to a prior transversal-difference invariant. We implement three equally batched schedules for complete PASTA-3 conversion and subsequent public subset-sum queries in HElib. Across twelve paired corpora under six homomorphic keys, all 24 direct and subgroup conversions and all 48 subsequent queries return the expected values and required zeroes. The median paired ratio of direct to subgroup server cost is 1.60, including fresh public generation, conversion and two queries. The reduction comes with less remaining noise capacity. These results establish a packing-dependent cost--noise tradeoff.

发表机构

• Institute of Mathematics of the Romanian Academy（罗马尼亚科学院数学研究所）
• CertSIGN
• Babeş-Bolyai University（巴比什-博约伊大学）

机构由 AI 辅助整理，请以论文原文为准。

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17 pages