## IACR News item: 23 January 2023

We give a number of results. We first show that, perhaps surprisingly, $t$ players (rather than $t+1$) with access to a random source are sufficient for the information-theoretic $t$-private computation of any deterministic functionality over $n$ players for any $t We then turn to the question of the possible interplay between the number of random sources and the necessary number of random bits. Since for only very few settings in private computation meaningful bounds on the number of necessary random bits are known, we consider the AND function, for which some such bounds are known. We give a new protocol to$1$-privately compute the$n$-player AND function, which uses a single random source and$6$random bits tossed by that source. This improves, upon the currently best known results (Kushilevitz et al., TCC'19), at the same time the number of sources and the number of random bits (KOPRT19 gives a$2$-source,$8$-bits protocol). This result gives maybe some evidence that for$1\$-privacy, using the minimum necessary number of sources one can also achieve the necessary minimum number of random bits. We believe however that our protocol is of independent interest for the study of randomness in private computation.