We will describe the design process and ideas behind the two new hash functions LUX and Cheetah. LUX is a stream based hash function. Cheetah is a block-cipher based one, using MD-HAIFA mode. We will also discuss issues related to the SHA-3 competition: speed vs. security, parallel vs sequential attacks, possible selection scenario for the 1st round. Joint work with Ivica Nikolic and Dmitry Khovratovich. (Update of AES-based stream cipher LEX will appear later.)