Reducing the WSN’s Communication Overhead by the SD-SPDZ Encryption Protocol Alexander K. Alexandrov 1,* 1 Institute of Robotics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., 1113 Sofia, Bulgaria Abstract Wireless Sensor Networks (WSN) have emerged as a pivotal technology in many application areas such as environmental monitoring, IoT, military applications, and healthcare. These networks consist of spatially distributed, autonomous sensors that cooperatively monitor physical or environmental conditions, such as temperature, sound, or pollution levels. The unique characteristics of WSNs, including their resource constraints (e.g., energy, memory, and computational capacity), make them vulnerable to various security threats. Information security in WSNs is crucial to ensure the confidentiality, integrity, and availability of the data they collect and transmit. As these wireless sensors collect and share data, they ensure the security and privacy of transmitted information becomes critical. In recent years, with an increasing emphasis on security, there has been a growing interest in Multi-Party Computation (MPC). MPC allows multiple parties to compute a joint function over their inputs while keeping those inputs private. The SPDZ protocol is among the most prominent and influential secure computation protocols. While the initial SPDZ protocol and its successor, SPDZ-2, have shown promising results, there were still challenges related to performance, scalability, and overall security. This paper presents a newly developed protocol named SD-SPDZ (Sensor Data SPDZ). The proposed protocol is based on MPC SPDZ-2 protocol and proposes changes to increase the performance in the preprocessing phase by implementing a new algorithm for the Beaver triples calculation. This protocol enhances the privacy-preserving attributes and efficiency of its predecessors. SD-SPDZ integrates advanced cryptographic techniques, offering a more robust and scalable solution for secure computations in WSNs. The primary benefits include reduced communication overhead, faster computation times, and improved resistance against various cyberattacks. The integration of SD-SPDZ in WSNs could improve performance sensitively and change the way sensor data is securely processed in sensor networks. It provides a promising pathway to ensure that as technology advances, the integrity and confidentiality of the data in these networks remain uncompromised. In summary, as WSNs play an increasingly critical role in modern-day applications, the need for advanced high- performance security mechanisms such as the SD-SPDZ protocol becomes more evident. This combination of cutting-edge, high-performance, secure computation with wireless sensor networks promise a future where data can be both globally accessible and privately computed, bridging the gap between performance and privacy. Keywords WSN, Information security, sensor data encryption, SPDZ, SD-SPDZ, Fixed Block Ciphers 1. Introduction Constraints and Challenges Wireless Sensor Networks (WSN) [1] are being used in Limited Resources: WSN nodes typically have limited numerous applications ranging from environmental mon- processing capability, memory, and energy. itoring to defense and healthcare. The distributed nature Dynamic Network Topology: Nodes can join or leave, of WSNs and their deployment in potentially hostile en- posing challenges for key management. vironments make data encryption crucial to ensure data Physical Vulnerability: Sensor nodes may be deployed in confidentiality, integrity, and authenticity. Historically, hostile environments, susceptible to physical attacks. traditional encryption algorithms such as Advanced En- cryption Standard (DES) [2] and Data Encryption Stan- Current Encryption Techniques dard (DES) [3] were evaluated for WSNs. However, due Lightweight Block Ciphers: They require less computa- to resource constraints in WSN nodes, some additional tional power and memory [4]. encryption techniques gained popularity. Stream Ciphers: Focus on processing data bit-by-bit, re- quiring minimal memory [5]. Examples are Trivium and Grain. Public Key Cryptography: Though resource-intensive, BISEC’23: 14th International Conference on Business Information they can be optimized for specific tasks like initial key Security, November 24, 2023, Niš, Serbia exchange [6]. * Corresponding author. Multi-Party Computation: Multi-Party Computation $ akalexandrov@ir.bas.bg (A. K. A. ) (MPC) [7] is a subfield of cryptography that enables multi- © 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). ple parties to jointly compute a function over their inputs CEUR Workshop Proceedings http://ceur-ws.org ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org) CEUR ceur-ws.org Workshop ISSN 1613-0073 Proceedings without revealing those inputs to each other. 2. Related works The main benefits of the MPC based encryption proto- cols are: In the area of the existing approaches, protocols, and Privacy: Ensures that individual inputs remain secret algorithms used to reduce the encrypted communica- from other participants. tion overhead in WSNs the following is commonly used Correctness: Guarantees that the output is correct even nowadays: BGW Protocol: The Beimel, Malkin, and Mi- if some participants behave maliciously. cali (BGW) protocol [8] is one of the foundational works This essential in some WSN’s as: in the area of secure multi-party computation. SPDZ can Secure voting systems where voters want to compute be viewed as a descendant of the BGW protocol, where the result without revealing individual votes; both focus on achieving security against a malicious ad- Military applications; versary. Collaborative data analysis in medical research where TinyOT: An efficient protocol [9] for two-party compu- institutions want to compute a joint result without shar- tation, TinyOT inspired many techniques used in SPDZ, ing patient data directly. especially the ones in the preprocessing phase. Over- drive2K: Overdrive refers to optimizations and enhance- ments of the SPDZ protocol, further improving the effi- 1.1. Sensor data encryption techniques ciency of the offline phase [10]. With the rising proliferation of the Internet of Things MASCOT: A follow-up to SPDZ, MASCOT introduces (IoT) and the widespread deployment of sensor networks a more efficient method [11] for the preprocessing phase across various industries, ensuring the confidentiality, by using oblivious transfer instead of somewhat homo- authenticity, and integrity of sensor data has become morphic encryption, reducing computational overhead. paramount. This study delves deep into the techniques SPDZ2k: The SPDZ2k protocol [12] has been adjusted and strategies employed for sensor data encryption, fo- to operate with calculations based on powers of two. cusing on the unique challenges and requirements pre- The significant difficulty with this is that in Z2k, not sented by these environments. every component has an inverse, an essential factor for ensuring the security of both MASCOT and SPDZ. To Objectives address this, SPDZ2k shifts to Z2k’, where k’ is a greater value, to offset the presence of zero divisors. To understand the peculiarities and constraints of sen- MP-SPDZ: provides a complete implementation of sor data. To evaluate existing encryption methodologies SPDZ2k [13] and features its distinct Z2k version, which suitable for sensor data. To propose efficient techniques is optimized for compile-time k.SPDZ-2: An optimized or improvements tailored for sensor data encryption. version of the original SPDZ, it enhances the online phase for better efficiency. Characteristics of Sensor Data BMR. Beaver and colleagues introduced a method [14] to create garbled circuits from any multi-party compu- Sensor data can be distinguished by: tation framework while maintaining security attributes. • High volume: Many sensors generate data con- This method was later enhanced by Lindell and team by tinuously. employing SPDZ as the foundational protocol. MP-SPDZ • Temporal relevance: Some data may be time- integrates BMR with the SPDZ/MASCOT protocol and sensitive. other security model protocols. Even though this feature • Varying importance: Not all sensor data is equally wasn’t included in SPDZ-2, it was unveiled partially prior critical. to MP-SPDZ’s first edition, as it was utilized by Keller and Yanai in their oblivious RAM development. Yao’s Garbled Circuits. Bellare and co-authors show- Challenges in Sensor Data Encryption cased a version of Yao’s garbled circuits optimized for • Resource Limitations: Sensors often have con- DES-NI, which is the standard DES execution on contem- strained processing capabilities, energy, and mem- porary processors [15]. After the final release of SPDZ-2, ory. this version was incorporated and recently updated to • Transmission Overheads: Encryption might in- encompass the half-gate method. troduce additional latency or payload. • Diverse Deployment: Sensors can be found in 2.1. SPDZ and SPDZ-2 Encryption hostile environments, making them susceptible Protocols Overview to physical attacks. The SPDZ protocol is a foundational Multi-Party Com- putation (MPC) scheme known for its robust security guarantees and practical efficiency. SPDZ facilitates se- Basics of the SPDZ-2 Protocol cure computation among multiple parties as connected The SPDZ-2 protocol [16] is an improvement over the sensor modules, ensuring that individual inputs remain original SPDZ protocol for secure multi-party computa- private. tion (MPC). It builds upon the foundations of the original protocol while addressing certain performance and secu- Protocol Basics rity issues. The SPDZ-2 protocol also employs two main At a high level, the SPDZ protocol encompasses two phases like its predecessor: main phases: Preprocessing Phase: Offline phase where Preprocessing Phase: Where correlated randomness is correlated randomness (like Beaver Triples) is generated generated. without knowing the inputs. Online Phase: Where the actual computation using Online Phase: Actual computation is performed us- the preprocessed data takes place. ing the preprocessed data. SPDZ-2 introduces a more efficient zero-knowledge proof system to ensure that: Secret Sharing in SPDZ • The shares of each party are consistent. • The Beaver’s triples are valid. Given a secret 𝑠, it is split into additive shares 𝑠1 , 𝑠2 , 𝑠3 , 𝑠4 . . . , 𝑠𝑛 such that: Instead of employing full-fledged zero-knowledge ∑︁𝑛 proofs, SPDZ-2 uses MACs (Message Authentication 𝑠= 𝑠𝑖 . (1) Codes) and correlated randomness to ensure honesty 𝑖=1 and correctness without much communication overhead. In the preprocessing phase, a Beaver’s triples (𝑎, 𝑏, 𝑐) are generated where 𝑐 = 𝑎 × 𝑏. During the online phase, Improvements over the original SPDZ given shares of values 𝑥 and 𝑦 that need to be multiplied, the protocol proceeds as: Reduced Communication Overhead: By leveraging MACs Compute and efficient consistency checks, SPDZ-2 reduces the 𝛿𝑥 = 𝑥 − 𝑎 (2) number of rounds of communication, which is especially beneficial in settings with many parties. To ensure consis- and tency of shares and validity of the triples, MACs (Message 𝛿𝑦 = 𝑦 − 𝑏. (3) Authentication Codes) are utilized. Each sensor module locally computes The preprocessing phase is made more efficient, lead- ing to faster overall computation times. At the same time, 𝑥 × 𝑦 = 𝑥 + 𝛿𝑥 × 𝑏 + 𝛿𝑦 × 𝑎 + 𝛿𝑥 × 𝛿𝑦 (4) when applied to wireless sensor networks, the SPDZ-2 protocol can still exhibit considerable communication In the online phase both values 𝑥 and 𝑦 where overhead. Sensor networks have bandwidth constraints, ∑︁𝑛 limited battery life, and operate in high-latency environ- 𝑥= 𝑥𝑖 , (5) ments, making communication efficiency crucial. 𝑖=1 ∑︁𝑛 𝑦= 𝑦𝑖 (6) 𝑖=1 SPDZ-2 Protocol implementation in Wireless are computed as: Sensor Networks (WSN) ∑︁𝑛 Wireless Sensor Networks (WSN) typically consist of spa- 𝑥+𝑦 = (𝑥𝑖 + 𝑦𝑖 ) (7) tially distributed autonomous devices that cooperatively 𝑖=1 monitor physical or environmental conditions. Each sensor module locally adds its shares. Using Applying the SPDZ-2 protocol in WSN enables secure Beaver’s triple, multiplication can be securely performed collaborative data processing without revealing individ- as outlined above. ual sensor readings. The SPDZ protocol also integrates zero-knowledge For a WSN with n sensor nodes, let each node i have proofs to ensure correctness without revealing individual a private value 𝑣𝑖 . The goal is to compute a function inputs or intermediate results. 𝑓 (𝑣1 , 𝑣2 , . . . , 𝑣𝑛 ) securely. Mathematically, SPDZ employs techniques from lin- ear secret-sharing schemes to ensure zero-knowledge Secret sharing in WSN properties. A sensor node’s private value 𝑣𝑖 is split into additive secret shares distributed among other nodes such that: ∑︁𝑛 𝑣𝑖 = 𝑠ℎ𝑎𝑟𝑒𝑖𝑗 (8) 𝑖=1 For shared values 𝑥 and 𝑦, use preprocessed triples Node Failures (𝑎, 𝑏, 𝑐) where 𝑐 = 𝑎 × 𝑏. Solution: Employ error-correcting codes for share re- Calculate and open covery and design the protocol to be resilient to node dropouts. 𝛿𝑥 = 𝑥 − 𝑎, (9) Security Considerations In WSN, the threat model may differ, with concerns of and node capture or eavesdropping. The security of SPDZ-2 𝛿𝑦 = 𝑦 − 𝑏, (10) in such a model ensures: to all nodes. Each node locally computes • Privacy: Individual sensor readings are kept con- 𝑥 × 𝑦 = 𝑐 + 𝛿𝑥 × 𝑏 + 𝛿𝑦 × 𝑎 + 𝛿𝑥 × 𝛿𝑦 . (11) fidential. • Integrity: The outcome of the computation is cor- Zero-Knowledge Proofs rect even if some nodes are malicious. To ensure consistency of shares and validity of the triples, MACs (Message Authentication Codes) [17] are utilized. 3. Case study Given a MAC key 𝛼, and a value 𝑣, the MAC is: 3.1. Sensor Data Communication 𝑀 𝐴𝐶 𝑣 = 𝛼 × 𝑣. (12) Overhead in the SPDZ-2 Protocol Sensor nodes verify the validity of MACs without reveal- The SPDZ-2 protocol, when applied to sensor networks, ing their private values. still has a significant communication overhead. This is especially problematic for wireless sensor networks, Communication Model in WSN which may have limited bandwidth or be subjected to high-latency communication environments. Given the energy and bandwidth constraints in WSN, the application of SPDZ-2 requires efficient communi- Communication Overhead in SPDZ cation models, possibly hierarchical or cluster-based, to minimize overhead. The communication overhead in the SPDZ protocol pri- In WSN, sensor nodes can be viewed as parties in marily arises from: the MPC. Each node can hold a piece of the secret (i.e., its measurement) and wants to perform computations • Calculation, sharing and, reconstructing values without revealing its exact measurement to others. in the preprocessing phase. • Exchanging values during the online phase for op- Sensor Data Aggregation erations like multiplication using Beaver’s triples. • Zero-knowledge proofs ensure honesty and cor- For an aggregate function 𝑓 over sensor data rectness. 𝑑1 , 𝑑 2 , . . . , 𝑑 𝑛 : ∑︁𝑛 Strategies to Reduce Communication Overhead 𝑓 (𝑑1 , 𝑑2 , . . . , 𝑑𝑛 ) = 𝑓 (𝑑𝑖 ). (13) 𝑖=1 Before initiating the SPDZ protocol, sensors can locally Using SPDZ-2, the function 𝑓 can be computed in a dis- aggregate or summarize their data. For instance, instead tributed manner without revealing individual 𝑑𝑖 values. of sending individual readings, sensors can send averages or other statistical summaries over a time window. Challenges and Solutions in WSN Group multiple operations together, especially during the preprocessing phase. This can help amortize the cost Bandwidth Constraint of generating and distributing values like Beaver’s triples Solution: Use compact secret sharing schemes and over multiple operations. optimize communication patterns, possibly adopting hi- Instead of running individual proofs for each operation, erarchical sensor node structures where cluster heads consider batched or aggregated proofs that can cover manage intra-cluster communication. multiple operations at once. Energy Constraint Implement secret sharing schemes that are tailored Solution: Minimize interactive rounds in the protocol for sensor networks. These can focus on minimizing and consider energy-efficient cryptographic operations. the number of shares or using techniques like error- Asynchronous operations can be adapted to allow nodes correcting codes to handle lost or delayed shares without to enter low-energy states when not actively participat- retransmission. ing. Employ data compression algorithms to reduce the size Function FixedKey_DDESES_Encrypt(input_block): of the transmitted data. This can be especially effective // Define a fixed key; this remains constant. if sensor readings or intermediate values in the SPDZ FIXED_KEY = "32-byte key derived protocol have redundancy or predictable patterns. from a secure process" Instead of all-to-all communication, consider using re- lay nodes or hierarchical structures where a subset of // Use DES encryption with the fixed key. sensors aggregates data and communicates with other ciphertext = DES_Encrypt(FIXED_KEY, groups, reducing the total communication across the net- input_block) work. return ciphertext Instead of continuous computation, synchronize the End Function computation in intervals. This allows for more batched operations and fewer real-time communication require- Function FixedKey_DES_Decrypt(ciphertext): ments. Reducing the communication overhead in the // Define the same fixed key. SPDZ protocol when applied to sensor networks requires FIXED_KEY = "32-byte key derived from a combination of algorithmic optimizations, architectural a secure process" considerations, and leveraging domain-specific knowl- // Use DES decryption with the fixed key. edge of sensor data. Implementing the above strategies plaintext = DES_Decrypt(FIXED_KEY, can significantly enhance the efficiency of the SPDZ pro- ciphertext) tocol in sensor environments. return plaintext The current paper focuses on the algorithms related to End Function reducing the communication overhead in the preprocess- ing phase of the SPZD-2 protocol. One of the possible The FIXED_KEY should be securely generated, prefer- ways to reduce the communication overhead in the pre- ably using a cryptographically secure random number processing phase of the SPDZ protocol in WSNs is to use generator, and then kept constant for all future opera- technique such Fixed-key block ciphers. tions. Storing cryptographic keys securely is essential. Fixed-key block ciphers [18], as the name suggests, Depending on the application, you might consider using involve the use of block ciphers with a fixed, predefined hardware security modules, secure key storage services, key. The idea behind using a fixed key is to transform or other best practices. the block cipher into a deterministic function with pseu- It is essential to ensure that the input_block has an dorandom behavior. appropriate size for the block cipher is used. For DES, Standard Block Cipher: A standard block cipher can this would typically be 128 bits (or 16 bytes). For the be denoted as: same input, the output will always be the same since the key remains constant. 𝐸 : {0, 1}𝑘 × {0, 1}𝑛 → {0, 1}𝑛 (14) Since block ciphers are permutations for a given key, the process is reversible. If you know the fixed key, you where 𝐸 is the encryption function. The first parameter is can decrypt any ciphertext produced by the fixed-key a key of length 𝑘 bits. The second parameter is a plaintext block cipher to retrieve the original input. block of length 𝑛 bits. The output is a ciphertext block In the context of secure multi-party computation of length 𝑛 bits. For a given key 𝐾 and plaintext 𝑃 , the (SMPC), fixed-key block ciphers can be used to produce encryption is denoted as correlated randomness between parties or derive other types of structured randomness efficiently. 𝐶 = 𝐸 (𝐾, 𝑃 ) (15) One notable application is in the generation of "oblivi- ous pseudorandom functions" (OPRFs) where one party Fixed-Key Block Cipher: When we talk about a learns the output of a PRF on a specific input without fixed-key block cipher, the key remains constant. This the other party learning anything about the input or the can be represented as: output. 𝐸𝐾𝑓 𝑖𝑥𝑒𝑑 : {0, 1}𝑛 → {0, 1}𝑛 (16) Integration between Beaver triple and Fixed-Key where 𝐾𝑓 𝑖𝑥𝑒𝑑 is a predefined constant key. For any input Block Ciphers block 𝑃 , the output is 𝐸 (𝐾𝑓 𝑖𝑥𝑒𝑑 , 𝑃 ). Beaver triples and fixed-key block ciphers are both tech- With the key fixed, a block cipher behaves like a pseu- niques used within the realm of secure multi-party com- dorandom permutation (PRP) over the set of 𝑛-bit strings. putation (SMPC). While they serve different primary This means that for every input 𝑃 , there is a unique out- functions and can sometimes be complementary, they can put 𝐶, and the relationship appears random unless you also be seen as alternative techniques in specific settings. know the fixed key. Primarily used for securely computing multiplication Generation of 𝑎: Each party 𝑃𝑖 generates a random in SMPC protocols, Beaver triples [19] consist of prepro- value. Each party computes: cessed random multiplicative triples (a,b,c) where c=a×b. These triples allow parties to perform multiplication on 𝐴𝑖 = 𝐸𝑛𝑐𝑟𝑦𝑝𝑡𝑘𝑒𝑦𝑖 (𝑎𝑖 ) (17) secret-shared values without revealing their actual in- and broadcast it. The shared value 𝑎 is the sum of the 𝑎𝑖 puts. values. The generation of Beaver triples can be computation- Generation of 𝑏: Each party 𝑃𝑖 generates a random ally intensive, especially in protocols that require a large value 𝑏𝑖 . Each party computes: number of such triples. However, once generated, they make the online phase of the computation faster. Used 𝐵𝑖 = 𝐸𝑛𝑐𝑟𝑦𝑝𝑡𝑘𝑒𝑦𝑖 (𝑏𝑖 ) (18) widely in SMPC protocols like SPDZ and its variants. and broadcast it. The shared value 𝑏 is the sum of the 𝑏𝑖 They are fundamental for protocols that rely on secret values. sharing and require multiplication operations. Generation of 𝑐: The shared value 𝑐 = 𝑎 × 𝑏 is Beaver Triples offer strong security guarantees when computed. However, instead of interacting to verify the generated correctly. Their security relies on the fact that correctness of this multiplication, the sensor modules the triples are random and independent of the inputs on can use the fact that they have encryption of the values which they will be used. 𝑎𝑖 and 𝑏𝑖 . They can derive the product of the encrypted Fixed-Key Block Ciphers: Used to generate certain values, given the properties of the fixed-key block cipher types of correlated randomness in SMPC. A fixed-key and the determinism of their chosen function. This step block cipher is a pseudo-random function where the key avoids the need for complex interactive proofs, hence remains constant. Given the same input, it will always removing the original need for Beaver triples. produce the same output, but changing even one bit of the input will produce a substantially different output. function generate_triples_using_block_cipher(): Typically, block ciphers are relatively efficient, espe- # a-values cially in hardware implementations. Using them to pro- a_i = random_value() duce correlated randomness can sometimes be more effi- A_i = Encrypt_with_fixed_key(key_i, a_i) cient than generating Beaver triples, depending on the broadcast(A_i) protocol and context. Often used in oblivious pseudo- a = sum_of_broadcasted_A_values random function (OPRF) [20] contexts and other settings # b-values where correlated randomness or specific patterns of ran- b_i = random_value() domness are required. B_i = Encrypt_with_fixed_key(key_i, b_i) The security here typically depends on the underlying broadcast(B_i) block cipher’s robustness and resistance against cryp- b = sum_of_broadcasted_B_values tographic attacks. If a cryptographically secure block # Compute c using encrypted values and cipher is used, the fixed-key variant can provide strong # properties of the block cipher security guarantees for its purpose. c= compute_all_A_values, all_B_values) return (a, b, c) 3.2. Reducing the Sensor Data This approach dramatically simplifies the preprocess- Communication Overhead in the ing phase compared to the standard SPDZ protocol with SD-SPDZ Protocol Beaver triples and reduces the sensor data communica- tion overhead. However, it assumes that the fixed-key Utilizing fixed-key block ciphers to substitute the Beaver block cipher has certain properties that make this method triple generation in the SPDZ preprocessing phase is an secure and that the encryption/decryption operations are advanced topic in secure multi-party computation, and performed in a secure manner. this approach is at the core of the new proposed SD-SPDZ protocol. Lab environment The idea behind this technique is to use block ciphers, like DES, to deterministically generate shared random- The lab environment consists of a cluster-based sensor ness, which can be used to produce Beaver triples. network consisting of five sensor modules based on NUCs The high-level approach for this is: Gigabyte and control center shown in the picture below: Key Generation: Each party selects a secret key for The testing software is implemented in each sensor the block cipher (e.g., DES). module and at the cluster head (CH). The experimental Beaver triple generation using Fixed-Key Block Ci- results are shown in the table below which describes the phers: average time in seconds to compute 10.000 triples in a WSN cluster consisting of five sensor nodes: Table 1 Experimental results MPC protocol Preprocessing phase Standard Beaver Triple calculation Fixed-Key Block Ciphers triple calculation SPDZ 7 - SPDZ-2 4 - SD-SPDZ 4 0.7 The integration of SD-SPDZ in WSNs could improve performance sensitively and change the way sensor data is securely processed in sensor networks. It provides a promising pathway to ensure that as technology ad- vances, the integrity and confidentiality of the data in these networks remain uncompromised. In summary, as WSNs play an increasingly critical role in modern-day applications, the need for advanced high-performance security mechanisms such as the SD- SPDZ protocol becomes more evident. 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