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Ball, Marshall ; Dachman-Soled, Dana ; Loss, Julian ( , Lecture notes in computer science)
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Ball, Marshall ; Chattopadhyay, Eshan ; Liao, Jyun-Jie ; Malkin, Tal ; Tan, Li-Yang. ( , CRYPTO)Micciancio, Daniele ; Ristenpart, Thomas. (Ed.)We present the first explicit construction of a non-malleable code that can handle tampering functions that are bounded-degree polynomials. Prior to our work, this was only known for degree-1 polynomials (affine tampering functions), due to Chattopad- hyay and Li (STOC 2017). As a direct corollary, we obtain an explicit non-malleable code that is secure against tampering by bounded-size arithmetic circuits. We show applications of our non-malleable code in constructing non-malleable se- cret sharing schemes that are robust against bounded-degree polynomial tampering. In fact our result is stronger: we can handle adversaries that can adaptively choose the polynomial tampering function based on initial leakage of a bounded number of shares. Our results are derived from explicit constructions of seedless non-malleable ex- tractors that can handle bounded-degree polynomial tampering functions. Prior to our work, no such result was known even for degree-2 (quadratic) polynomials.more » « less
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Ball, Marshall ; Dachman-Soled, Dana ; Kulkarni, Mukul ( , Crypto)