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We present randomized algorithms that solve Subset Sum and Knapsack instances with n items in O * (2 0.86n ) time, where the O * (·) notation suppresses factors polynomial in the input size, and polynomial space, assuming random read-only access to exponentially many random bits. These results can be extended to solve Binary Linear Programming on n variables with few constraints in a similar running time. We also show that for any constant k ≥ 2, random instances of k-Sum can be solved usingdoi:10.1137/17m1158203 fatcat:3qkxhuryorccboktcsuxh5lxsa