This paper presents a deformable spherical robot with a six-strut topological structure capable of achieving multimodal locomotion in complex amphibious environments. The robot realizes isotropic rolling and asymmetric jumping through its innovative geometric-based configuration while integrating an airbag-driven module for underwater buoyancy control. Based on collision dynamics analysis, we develop a prototype of the deformable spherical robot. Experiments conducted on land, in transition zones, and underwater validate the robot’s multimodal locomotion feasibility in multi-medium environments.

The use of normal bases for representing elements in a binary field is attractive in some applications because it is easy to perform squaring operations in hardware. In such cases, the costs of implementing the multiplication operation become a primary concern. We present new algorithms for reducing the space complexity of Gaussian normal basis multipliers over binary fields GF(2m), where m is odd. Compared with previous results, our approach incurs no additional costs in time complexity, and achieves improvements in space complexity over a wide range of finite fields and digit sizes. For the binary fields specified in the NIST FIPS 186-3 elliptic curve digital signature algorithm standards document, our algorithms reduce by 16% (respectively, 27%) the number of XOR gates needed for the implementation of a digit-level parallel-input parallel-output multiplier over a 163-bit (respectively, 409 bit) binary field.