## Advantages

As in the conventional UOV scheme, the data size of signatures is small and the processing time of signature generation and verification is fast. Furthermore, by using a polynomial quotient ring, the data size of the public key is also small. Detailed advantages of QR-UOV are as follows :

### Public key and signature size.

The plain UOV is known as a scheme with a small signature and a large public key. ( Currently proposed parameters in security level I have approximately 50KB public key and 100B signature.)Our proposed parameter sets with q=31 and l=3 reduce the public key size by approximately 50-60% compared with the plain UOV (approximately 20KB in security level I) with a few hundreds bits of signature.

### Efficiency.

The signature generation and verification processes consist of simple linear algebra operations over small finite fields and thus QR-UOV can be implemented very efficiently.

### Security.

The EUF-CMA security of QR-UOV is formally proven in the QROM assuming the difficulty of two problems, the UOV and QR-MQ problems.

### Simplicity.

The design of the plain UOV is extremely simple, and our QR-UOV is a natural extension of UOV utilizing the quotient rings structure.