Ralph Merkle (Berkeley, California, 1952), a cryptographer at the University of California and Xerox PARC, publishes in 1979 his doctoral thesis and the article "A Certified Digital Signature" describing Merkle trees: hierarchical data structures in which each parent node contains the cryptographic hash of its child nodes, and the root (Merkle root) cryptographically summarizes the entire tree's content. They allow verification of the integrity of any element in the set with a logarithmic number of operations, without examining the whole tree. Bitcoin uses Merkle trees to summarize all transactions in each block into a single 32-byte hash included in the block header, making simplified payment verification (SPV) possible without downloading the entire blockchain. Merkle is co-author of the Merkle-Hellman protocol (with Hellman) and contributed to the theoretical foundations of public-key cryptography.