Abstract: Cryptographic methods and systems are described. Certain examples relate to performing cryptographic operations by updating a cryptographic state. The methods and systems may be used to provide cryptographic functions such as hashing, encryption, decryption and random number generation. In one example, a non-linear feedback shift register or expander sequence is defined. The non-linear feedback shift register or expander sequence has a plurality of stages to receive the cryptographic state, wherein at least one of the plurality of stages is updated as a non-linear function of one or more other stages. In certain examples, a cryptographic state is updated over a plurality of rounds. Examples adapted for authenticated encryption and decryption, hashing, and number generation are described.

Abstract: Certain examples described herein relate to secure update propagation. The examples present systems and methods to transmit data in the form of updates over a network and to ensure the authenticity of the updates. The examples use a set-homomorphic digital signature scheme to sign updates such that a combined digital signature may be used to verify a batch of updates in place of a set of individual digital signatures. The combined digital signature may be generated by aggregating individual digital signatures.