Truth tables of low Hamming weight 1st-order correlation immune Boolean functions with 12 variables
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Abstract The dataset comprises two components: (1) 52,339 12-variable, 1st-order correlation immune Boolean functions with weight 256 (2⁸), and (2) 141,893 12-variable, 1st-order correlation immune Boolean functions with weights ranging from 222 to 256. Both sets were generated using the OIWR algorithm. Each line represents one Boolean function by its truth table. Instructions: Mesnager and Su's 2021 work (DOI: 10.1109/TIT.2021.3109946 ) presents a low Hamming weight 1st-order correlation immune Boolean function construction method constrained to weights that are powers of 2. We extend these results using the OIWR algorithm (https://eprint.iacr.org/2026/985), achieving two significant advances: (1) generating multiple Boolean functions under identical constraints, and (2) breaking the power-of-two weight limitation. Our dataset provides truth tables for the special case of 12-variable, weight-256, 1st-order correlation immune Boolean functions, comprising: 1. "12_256_1.txt": 52,339 truth tables (one per line), each representing a distinct 12-variable, weight-256 (2⁸), 1st-order correlation-immune Boolean function.2. "12_(222-256)_1.txt": 141,893 truth tables (one per line) representing 12-variable, 1st-order correlation-immune functions with weights spanning 222-256, distributed as shown in Table: Weight Count Weight Count 222 40 232 19,943 226 1,257 236 28,852 230 10,947 228 4,246 234 27,668 224 258 238 22,914 240 14,717 242 6,478 220 5 244 3,352 246 717 248 432 252 43 250 23 256 1
摘要 本数据集包含两个组成部分：(1) 52,339个12变量、1阶相关免疫布尔函数（1st-order correlation immune Boolean functions），其汉明重量为256（2⁸）；(2) 141,893个12变量、1阶相关免疫布尔函数，其汉明重量范围为222至256。两组函数均通过OIWR算法（OIWR algorithm）生成，每行以真值表形式对应一个布尔函数。 数据集说明 Mesnager与Su于2021年发表的研究（DOI: 10.1109/TIT.2021.3109946）提出了一种低汉明重量（low Hamming weight）1阶相关免疫布尔函数的构造方法，该方法将汉明重量约束为2的幂次。本研究通过OIWR算法（OIWR algorithm，https://eprint.iacr.org/2026/985）对上述成果进行拓展，取得两项重要突破：其一，可在相同约束条件下生成多个布尔函数；其二，打破了汉明重量需为2的幂次的限制。本数据集针对12变量、汉明重量为256的1阶相关免疫布尔函数这一特殊场景提供了真值表，具体包含以下两类文件： 1. "12_256_1.txt"：包含52,339条真值表（每行对应一条），每条对应一个独立的12变量、汉明重量为256（2⁸）的1阶相关免疫布尔函数。 2. "12_(222-256)_1.txt"：包含141,893条真值表（每行对应一条），对应汉明重量范围为222至256的12变量1阶相关免疫布尔函数，其分布情况如下表所示： 汉明重量 数量 汉明重量 数量 222 40 232 19,943 226 1,257 236 28,852 230 10,947 228 4,246 234 27,668 224 258 238 22,914 240 14,717 242 6,478 220 5 244 3,352 246 717 248 432 252 43 250 23 256 1
