A Note on Obfuscation-Based Attacks on Private-Coin Evasive LWE

The evasive learning with errors (evasive LWE) assumption is a new assumption recently introduced by Wee [Wee22] and Tsabary [Tsa22] independently, as a significant strengthening of the standard LWE assumption. While the assumption is known to imply various strong primitives including witness encryption [Tsa22, VWW22], the assumption in the most general case (i.e., the private coin variant) is considered quite implausible due to the obfuscation based attack mentioned in [Wee22]. This obfuscation based attack is then later formalized by Vaikuntanathan, Wee, and Wichs [VWW22]. In this note, we revisit their attack and show that the attack actually does not work by showing a concrete counterexample. While various attacks against private-coin evasive LWE are now known, the attack of [VWW22] is the only one that applies in the setting where the sampler is oblivious to the LWE secret, which we call the S-oblivious regime. Therefore, our refutation closes the only known avenue for attacking the assumption in the S-oblivious regime. To complement the above refutation of this attack, we also present a variant of the counterexample assuming the existence of instance-hiding witness encryption. However, our sampler is not S-oblivious, and thus we do not fully recover the attack considered in [VWW22]. Taken together, these results indicate that the security of private-coin evasive LWE in the S-oblivious regime remains open.