## 2 A One-Time Pad with True Randomness
In our modified procedure, \(P_{1}\) and \(P_{2}\) calculate both the sum \(K=s_{1}+s_{2}+s_{3}\), while \(P_{3}\) learns nothing. Therefore, \(K\) will be known only for \(P_{1}\) and \(P_{2}\), while all private inputs remain private and cannot be deduced from the output. Figure 1 graphically shows our proposal, highlighting communication between parties. Observe that, for \(P_{3}\), the role of randomness guarantees that \(x_{3}\) is never disclosed during communication between parties. In fact, for the first part, only \(r_{3,1}\) and \(r_{3,2}\) travel to \(P_{1}\) and \(P_{2}\), respectively. The third component, \(r_{3,3}\), travels masked in the sum \(s_{3}\) when transmitted. Therefore, even in the case where a malicious eavesdropper is following the interchange between \(P_{1}\) and \(P_{2}\) towards \(P_{3}\), it is improbable that the output \(s_{3}\) can be correlated with the secure multiparty sum protocol, or with the random component \(x_{3}\). Therefore, since the final computation of the key \(K\) takes place privately for \(P_{1}\) and \(P_{2}\), the conclusion is that \(P_{1}\) and \(P_{2}\) have effectively shared a common key \(K\), which can be used to mask communication between them. In a usual SMPC summation for three parties, as in [14], the transmission of the shares is different (10 rounds compared to 12) and allows cross-checking of the partial sums to detect a potential dishonest one out of two parties. In addition, the key is shared between the three intervening parties. In our procedure, instead, communication can be sequentially arranged so that the total number of rounds can be reduced to eight, which is a reduction of the order of 30% from the standard multiparty summation protocol; see the Section 3. Now it should be clear that, at this point, the space in which the sums are taken can be a \(\mathbb{Z}_{2}^{N}\) for a suitable \(N\), which means that there is no restriction a priori about whether the sums are binary sums or not. This means that the procedure between parties can be performed bit by bit or by blocks of bits of size \(N\). The summation can be executed using the well-known XOR operator as a classical implementation of the one-time pad protocol. It is worth noting that it is not necessary to limit the quality of the random shares; they can be pseudo but also true random bits. These true random bits can be obtained from any source, such as physical true random numbers commonly found in IoT devices (by capturing states from sensors, accelerometers, channel noise, etc.). True random number generators (TRNGs) produce numbers based on physical processes, such as thermal noise, radioactive decay, or quantum phenomena, making these numbers inherently unpredictable. This unpredictability is theoretically ideal for cryptographic applications where randomness is crucial for security. However, it has been pointed out that using TRNGs in practical cryptographic systems presents several challenges, some of which we detail below (see [15]):  
* In cryptographic protocols, particularly those involving multiple parties, it is essential that all parties agree on the cryptographic keys to be used. If every participant uses their TRNG, reaching a consensus on a common key is challenging since each participant will produce distinct, autonomous values. Coordinating these values among varied systems and across different regions increases complexity and may lead to security risks;
* TRNGs may exhibit slow performance, and their output rates might not meet the demands of high-throughput environments. Furthermore, the dependability of TRNGs can be compromised due to environmental factors and the deterioration of hardware;
* Ensuring the randomness and lack of bias in numbers generated by TRNGs is non-trivial. Continuous testing and monitoring are required to ensure the integrity of randomness, which can be resource intensive.