Multi-level file digests for electronic files are disclosed. A top level digest represents a single digest for the associated electronic file. Lower level digests represent digests for portions of the associated electronic file. The top level digest is derived from the lower level digests. The top level digest is useful for facilitating rapid comparison to determine whether electronic files are the same. In one embodiment, electronic files are encrypted with a block encryption scheme, and digests are efficiently calculated and stored on a block-by-block basis. Advantageously, when modifications to an encrypted electronic file occurs, only those modified blocks need to be processed to undergo decryption and re-encryption to determine the appropriate digest.

 
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< Public key encryption with digital signature scheme

< Hashing byte streams into elements of the Shafarevich-Tate group of an abelian variety

> Device of applying protection bit codes to encrypt a program for protection

> Method to control and secure setuid/gid executables and processes

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