A trade-off between collision probability and key size in universal hashing using polynomials |
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Authors: | Palash Sarkar |
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Institution: | 1.Applied Statistics Unit,Indian Statistical Institute,Kolkata,India |
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Abstract: | Let
\mathbbF{\mathbb{F}} be a finite field and suppose that a single element of
\mathbbF{\mathbb{F}} is used as an authenticator (or tag). Further, suppose that any message consists of at most L elements of
\mathbbF{\mathbb{F}}. For this setting, usual polynomial based universal hashing achieves a collision bound of
(L-1)/|\mathbbF|{(L-1)/|\mathbb{F}|} using a single element of
\mathbbF{\mathbb{F}} as the key. The well-known multi-linear hashing achieves a collision bound of
1/|\mathbbF|{1/|\mathbb{F}|} using L elements of
\mathbbF{\mathbb{F}} as the key. In this work, we present a new universal hash function which achieves a collision bound of
mélogm Lù/|\mathbbF|, m 3 2{m\lceil\log_m L\rceil/|\mathbb{F}|, m\geq 2}, using 1+élogm Lù{1+\lceil\log_m L\rceil} elements of
\mathbbF{\mathbb{F}} as the key. This provides a new trade-off between key size and collision probability for universal hash functions. |
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Keywords: | |
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