# Multibyte Electromagnetic Analysis Based on Particle Swarm Optimization Algorithm
## 2 Related Works  
Many modern devices are used to implement cryptographic algorithms to protect information in the communication process. Modern cryptographic devices generally remain the secret key in hardware regardless of whether the algorithm is public or not. Figure 1: Information security in communication systems. In order to prevent information from being stolen illegally during network communication, information is generally encrypted before being sent. Cryptographic algorithms or secret keys processed inside cryptographic hardware devices can be inferred by unintentional electromagnetic radiation. Thus, electromagnetic analysis of cryptographic devices has been given more importance in recent years. Non-blinded RSA keys were extracted within seconds using a nonintrusive measurement of electromagnetic emanations from laptop computers [10]. By measuring the target PC's electromagnetic emanations, the attacker extracted the secret decryption key within seconds, from a target located in an adjacent room across a wall [11]. Attacking the Field Programmable Gate Array (FPGA) implementation of Advanced Encryption Standard (AES) algorithm where all bytes were processed in parallel using differential electromagnetic analysis (DEMA) was shown in [12]. A secret key attack based on correlation electromagnetic analysis (CEMA) was recovered successfully in [13; 14; 15]. A novel two-stage countermeasure to prevent CEMA was shown in [16]. SVM was used to classify arithmetic operations by electromagnetic leakage in [17]. This way can be considered as a type of template analysis (TA). Simple electromagnetic analysis (SEMA) and DEMA were used to attack DES in a manner to extract information from electromagnetic radiation [18; 19]. A multi-objective electromagnetic analysis based on genetic algorithm to recover the AES encryption algorithm' secret key was proposed in [20]. Non-invasive electromagnetic analysis can be mainly divided into four categories: SEMA, DMEA, CEMA, and TA. For the SEMA method, the attacker deduces the secret key directly by observing the electromagnetic radiation traces. It is effective against asymmetric cryptography implementations in some cases. If the attacker has a strong understanding of the cryptographic device and the implementation of the cryptographic algorithm, only a few traces are needed to recover the secret key. Sometimes, SEMA does not provide enough information to deduce the secret key. Thus, other analytical methods were developed to recover the secret key such as DEMA, CEMA, and TA. Generally, the length of the cryptographic algorithm's key is very long to ensure security, so the implementations are usually executed in blocks. It is very easy to consider the idea of 'divide and conquer', so only a single byte of the key is used when recovering the key. DEMA and CEMA are more complex and effective methods against symmetric cryptography implementation when the SEMA method fails. Additionally, unlike SEMA, DEMA and CEMA require less knowledge about the target device being attacked. TA is considered as the strongest form in an information theoretic sense. The premise of TA is that the attacker must have a copy of the target cryptographic device which may be impossible in some real scenarios. The TA method usually uses a single byte output to create templates. However, the strategy of 'divide and conquer' may lose information and efficiency because all bytes of the key contain information. A comparison of single-bit and multi-bit DPA for attacking AES-128 on an ATmega328P was shown in [21]. His work demonstrated that using multi-bit of a key byte can significantly reduce ghost peaks and allow for the recovery of a key with far fewer traces. Multiple bits were applied to linear regression and get a better result in [22]. Their works inspired us to start our research on multiple bytes electromagnetic analysis. In our previous work [23], we have demonstrated that we can use fewer electromagnetic traces by multiple bytes electromagnetic analysis when recovering secret keys.