## 2 Related Works  
Cryptography is commonly used as a countermeasure against wiretapping, and authentication is commonly used as a countermeasure against attacks. Cryptography is classified into common key cryptography and public key cryptography [6]. The common key cryptography performs encryption and decryption using the common key in the sender and the receiver. Therefore, it is necessary for the sender and the receiver to share the key which is known to no one else [6]. On the other hand, public key cryptography involves the receiver publishing the public key, the sender encrypts information using the public key, and the receiver decrypts it using the private key paired with the public key. Although public key encryption does not require key sharing, many studies have been conducted to discover public keys securely and efficiently [11; 12; 13]. Authentication includes password authentication, biometric authentication, and one-time password authentication [7]. Password authentication uses passwords that are registered on the authentication server. Only users who know the password can be authenticated. Biometric authentication uses biometric information as the password. It has a lower risk of forgery, theft, and forgetting than a password. One-time password authentication is effective as a countermeasure against forgery and theft because the password is changed every time. These are countermeasures for the upper layer, but countermeasures for the lower layer--that we are targeting--are also being studied. As countermeasures against wiretapping at the lower layer, there are key generation methods using biometric and physical information. Examples of physical information are channel state information, received signal strength indicators, distance, angle of arrival, and so on [14; 15]. Biometric information is specific to each user, and physical information is specific to the location of the user. Using user-specific information, keys can be created securely. For this reason, attempts to use biometric information for authentication have been made for a long time, and it has been used practically for unlocking cellular phones. Distance or location information measured by an ultra-wide band (UWB) is applied for keyless entry authentication to prevent relay attacks for unlocking automobiles [16], and it is expected to be put into practical use soon. These key generation methods can also be used for our proposed shortened information. We select the distance information considering the accuracy and feasibility of cellular phones. [PERSON]'s secret sharing has been applied to multiple communication channels [17]. [PERSON]'s secret sharing is an algorithm in cryptography [18]. Information is divided into multiple parts of distributed information using polynomials and shared. To reconstruct the original information, a certain number of parts are required. [PERSON]'s secret sharing is not efficient in communication, and many studies have been conducted to solve this problem [19; 20; 21]. In [17], when encrypted information is transmitted using multiple channels, the encryption key for the information is encrypted by using [PERSON]'s secret sharing and transmitted through multiple channels, thereby achieving highly reliable communication. We used the concept of secret sharing, but our proposal uses shortened code to transmit more efficiently and to increase attack resistance simultaneously. As countermeasures against attacks at the lower layer, improvements are made to the signal-to-noise ratio (SNR) by a smart antenna composed of multiple antennas [22]. Beamforming is realized by adjusting the phase and amplitude of each antenna. The sender can increase the SNR of the receiver by directing the beam toward the receiver. The sender can decrease the SNR of the cyberterrorist by directing the null to the cyberterrorist. This study differentiates the reception performance of the receiver and the cyberterrorist by the directivity of the antenna, but our proposal differentiates between them by the error correction capability.