Access control encryption (ACE) enforces, through a sanitizer as the mediator, that only legitimate sender-receiver pairs can communicate, without the sanitizer knowing the communication metadata, including its sender and recipient identity, the policy over them, and the underlying plaintext. Any illegitimate transmission is indistinguishable from pure noise. Existing works focused on computational security and require trapdoor functions and possibly other heavyweight primitives. We present the first ACE scheme with information-theoretic security (unconditionally against unbounded adversaries). Our novel randomization techniques over matrices realize sanitization (traditionally via homomorphism over a fixed randomness space) such that the secret message in the hidden message subspace remains intact if and only if there is no illegitimate transmission.