Geometric Algebra is known to be intrinsically homomorphic. In X-Logos encryption, the plaintext and key(s) are converted to multivectors thus allowing the use of a broad range of operations and identities available in Geometric Algebra. The key innovations include encryption primitives and types of data representation within the multivector coefficients that retain homomorphism throughout the various multivector operations.
Compute On Encrypted Data
X-Logos homomorphic encryption is a novel application of Geometric Algebra and unlike prevailing approaches, it is near instantaneous. Also, beyond mathematical operations (add, multiply), X-Logos enables search, sort and compare operations. Encrypted data can be updated with new keys without remote decryption. The suite includes identity-based encryption and hierarchical access control among other functions that are carried along in the multivector coefficients of the Geometric Algebra. X-Logos is deterministic and noiseless. The cryptographic strength meets AES.
Real Time Encrypted HD Video
X-Logos encrypts and decrypts HD video with near-zero latency due to the Geometric Algebra foundation. Unlike partial encryption (regions of interest or motion vectors only), X-Logos encrypts the entire feed, whether naïve or frame-by-frame, using only limited compute resources. The encrypted video stream is the same size as the unencrypted stream.
Manipulate encrypted video
Faces or objects identified in unencrypted streams are encrypted with one key and the scene is encrypted with another. According to the keys held by the receiver, the scene may be viewed in whole or in part (such as the entire scene but with faces encrypted). Objects can be tracked, subtracted or added to the scene even when encrypted. Information can be shared by multiple parties/agencies while preserving privacy in surveillance applications.
Smart contracts are updated with new entries or with computations on existing entries without decryption and then appended to the blockchain. Thus, the public versus private disclosure within the blockchain is configurable.
X-Logos is extremely lightweight (no exponentiation or multiple rounds) and may be adapted to the security requirement and the end-point resources of the application. This is done by optimizing the multivector dimension and the size of the coefficients. The primitive remains the same, allowing interoperability with other X-Logos instances.
Founded in 2016 to develop and commercialize its encryption suite, X-Logos LLC is partnering with entities engaged in cloud computing, IoT, smart cities, encrypted controllers, video streaming and secure multiparty computation.