Abstract: This paper investigates the effect of Spread Transform（ST） on averaging collusion resistance of quantization based digital fingerprinting schemes and compares the performance of quantization based digital fingerprinting schemes with and without ST through theoretical and experimental study of a quantization based orthogonal fingerprinting scheme. Study shows that an ST gain factor defined as the ratio of a spreading parameter to a direction parameter exerts important influence on anti-collusion performance of ST quantization based fingerprinting schemes. In situations with different strength of noise, anti-collusion performance responds differently to the variation of ST gain factor. ST gain factor equaling 1 renders the performance of ST quantization based fingerprinting the same as its non-ST counterpart.

Key words: digital fingerprinting, digital watermarking, quantization, collusion attack, Spread Transform（ST）

摘要： 以一种量化正交指纹为基础，通过理论分析和仿真实验，研究扩展变换对量化数字指纹抵抗平均合谋攻击能力的影响，并对包含和不包含扩展变换的量化数字指纹进行比较。结果表明，定义为扩展参数和方向参数的比值的扩展变换增益因子对含扩展变换的量化数字指纹抵抗平均攻击的性能有重要影响。在不同的噪声强度下，抗合谋攻击能力随扩展变换增益因子变化的变化方式不同。此外，扩展变换增益因子等于1使得扩展变换量化指纹与对应的非扩展变换量化指纹的抗平均合谋攻击能力相当。

关键词: 数字指纹, 数字水印, 量化, 合谋攻击, 扩展变换