Local pseudorandom generators are a class of fundamental cryptographic primitives having very broad applications in theoretical cryptography. Following Couteau <i>et al.’s</i> work at ASIACRYPT 2018, this paper further studies the concrete security of one important class of local pseudorandom generators, i.e., Goldreich’s pseudorandom generators. Our first attack is of the guess-and-determine type. Our result significantly improves the state-of-the-art algorithm proposed by Couteau <i>et al.</i>, in terms of both asymptotic and concrete complexity, and breaks all the challenge parameters they proposed. For instance, for a parameter set suggested for 128 bits of security, we could solve the instance faster by a factor of about 2<sup>77</sup>, thereby destroying the claimed security completely. Our second attack further exploits the extremely sparse structure of the predicate <inline-formula> <tex-math notation="LaTeX">$P_{5}$ </tex-math></inline-formula> and combines ideas from iterative decoding. This novel attack, named guess-and-decode, substantially improves the guess-and-determine approaches for cryptographic-relevant parameters. All the challenge parameter sets proposed in Couteau <i>et al.’s</i> work in ASIACRYPT 2018 aiming for 80-bit (128-bit) security levels can be solved in about 2<sup>58</sup> (2<sup>78</sup>) operations. We suggest new parameters for achieving 80-bit (128-bit) security with respect to our attacks. We also extend the attacks to other promising predicates and investigate their resistance.