We present a Anonymous Mutual Authentication (AMA) protocol for authentication and key agreement between cryptographic devices. It is an alternative for Terminal Authentication (TA) plus Chip Authentication (ChA) developed for electronic travel documents. Unlike conventional TA, executing AMA does not provide any digital record that could be used as a proof against third parties that an interaction really took place. AMA is symmetric: the code executed by both participants is the same (apart from the sequence of operations). It eases implementation on resource limited devices such as smart cards. AMA does not require prior disclosure of identities: the protocol participants learn them in a way hidden to eavesdroppers.