Asymmetric All-or-nothing Transforms
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In this paper, we initiate a study of asymmetric all-or-nothing transforms (or asymmetric AONTs). A (symmetric) t-all-or-nothing transform is a bijective mapping defined on the set of s-tuples over a specified finite alphabet. It is required that knowledge of all but t outputs leaves any t inputs completely undetermined. There have been numerous papers developing the theory of AONTs as well as presenting various applications of AONTs in cryptography and information security. In this paper, we replace the parameter t by two parameters t_o and t_i, where t_i ≤ t_o. The requirement is that knowledge of all but t_o outputs leaves any t_i inputs completely undetermined. When t_i < t_o, we refer to the AONT as asymmetric. We give several constructions and bounds for various classes of asymmetric AONTs, especially those with t_i = 1 or t_i = 2. We pay particular attention to linear transforms, where the alphabet is a finite field 𝔽_q and the mapping is linear.
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