What you are describing is basically a blind index (search for it, there are lots of good resources online). Blind indexes can be quite useful, but they have a number of limitations - the partial match issue as you point out, but also you cannot do range queries or sorting, and they leak some information (e.g. duplicates have the same index value). Blind indexes are most definitely not fully homomorphic encryption.
> Vaultree's proprietary encryption breakthroughs are in various encryption technologies traditionally limited to niche use cases. We finally enable users to process entirely encrypted data with Fully Homomorphic and Searchable Encryption (FHSE) and other technologies in the field. Explaining what they are would take all day, but here's a one-liner: FHSE enables data processing to be run directly on encrypted data in the same way as on plain text data.
