💻 computer science

Integrating Random Number Generation with the Rabin Cryptosystem for a Robust Two-Way Authentication in RFID

This paper proposes a cost-effective, robust two-way authentication protocol for low-cost RFID systems in IoT environments that integrates the Rabin cryptosystem with random number generation to enhance privacy, prevent replay and brute force attacks, and ensure information freshness.

Original authors: Yuanjia Ma, Jikun Guo, Canpeng Zheng, Qiujin Zhang, Yang Zhang

Published 2026-08-24

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CC BY 4.0

Original authors: Yuanjia Ma, Jikun Guo, Canpeng Zheng, Qiujin Zhang, Yang Zhang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the invisible web that connects our modern world, tiny devices called radio frequency identification tags act as the silent sentinels of commerce and logistics. These small chips, often no larger than a postage stamp, allow everything from shipping containers to livestock to be tracked without physical contact. They are the backbone of the Internet of Things, enabling supply chains to move with speed and precision. However, this convenience comes with a significant vulnerability. Because these tags communicate over open airwaves, they are exposed to eavesdropping, where unseen listeners can intercept their messages, or to spoofing, where a criminal pretends to be a legitimate scanner to steal data. The challenge for engineers is to build a security system that is strong enough to stop these intruders but simple enough to run on a device with almost no battery or computing power. Traditional security methods used on computers are often too heavy and complex for these tiny chips, leaving a gap between the need for safety and the reality of the hardware.

Researchers at the Guangdong University of Petrochemical Technology have addressed this gap by designing a new way for these tags to prove their identity to a scanner. Their work focuses on a specific type of encryption known as the Rabin system, which relies on a mathematical trick involving the squaring of numbers. While standard encryption often requires complex calculations that drain a tag's energy, this method uses a simpler operation that is much faster and less demanding. The team combined this efficient encryption with a clever use of random numbers to create a two-way handshake. In this process, the scanner and the tag exchange secret codes that change every single time they communicate. This ensures that even if a criminal records a conversation between a tag and a scanner, that recording becomes useless the moment the next conversation begins, because the secret codes have already changed.

The core of their improvement lies in how they generate these changing codes. In previous attempts to secure these tags, the tiny chips themselves had to generate random numbers, a task that required extra circuitry and increased the cost and size of the tag. The new protocol shifts this burden entirely to the scanner. The scanner generates two random numbers using a Linear Feedback Shift Register (LFSR) and sends them to the tag in a scrambled form. The tag, which holds a secret key shared only with the scanner, can unscramble these numbers to prove it is the real thing. Because the tag no longer needs to generate its own random numbers, the researchers were able to remove the random number generator component from the tag's design entirely. This reduction in complexity directly translates to a cheaper, smaller, and more energy-efficient tag.

To ensure this new system was truly secure, the researchers subjected it to a rigorous logical test known as BAN analysis. This method allows scientists to formally prove that a protocol works as intended, checking whether the tag and the scanner can truly trust each other's messages. The analysis confirmed that the new method successfully prevents several common attacks. It stops replay attacks, where a criminal tries to reuse an old message to trick the system, because the random numbers ensure every message is fresh. It also prevents desynchronization attacks, where a criminal tries to force the tag and scanner to lose track of their shared secrets, by ensuring that key updates only happen when both sides have successfully verified each other. Furthermore, the system resists brute-force attacks, where an intruder tries every possible combination of numbers to guess the secret, because the way the data is scrambled makes such guessing mathematically impractical.

The study also compared the performance of this new protocol against existing methods. The results showed that while the amount of memory required on the tag remained the same, the computational effort needed to process the security check was significantly lower. By swapping out a standard hashing function for the Rabin encryption method, the researchers reduced the number of logical operations the tag had to perform. This efficiency is crucial for low-cost applications where every bit of processing power matters. The researchers demonstrated that their approach not only offers stronger protection against tracking and impersonation but also does so with a lighter footprint on the hardware. By proving that a robust security system can be built with fewer electronic components, this work offers a practical path forward for securing the vast network of connected devices that underpin our daily lives, making the invisible web of the Internet of Things both faster and safer.

Technical Summary: Integrating Random Number Generation with the Rabin Cryptosystem for Robust Two-Way Authentication in RFID

Problem Statement
The widespread adoption of Radio Frequency Identification (RFID) in Internet of Things (IoT) environments is hindered by significant security and privacy vulnerabilities, including eavesdropping, message tampering, spoofing, replay attacks, and tracking. These risks are exacerbated by the severe resource constraints of RFID tags, which possess limited computational power, storage, and energy. While lightweight protocols based on hash functions and bitwise operations have been proposed to address efficiency, recent analyses indicate they are susceptible to secret disclosure and brute-force attacks. Conversely, public-key cryptography offers stronger security but is often deemed too computationally intensive for passive tags. Specifically, existing protocols (such as the one in reference [12]) suffer from vulnerabilities where random numbers are transmitted in plaintext or generated via complex circuitry on the tag, increasing costs and exposing the system to brute-force attacks and desynchronization.

Methodology
The authors propose an improved two-way authentication protocol that integrates random number generation with the Rabin cryptosystem to address these limitations. The core methodology involves the following architectural and algorithmic shifts:

Centralized Random Number Generation: To reduce tag complexity and cost, the protocol eliminates the need for random number generators (PRNGs) on the tag. Instead, the reader (unified with the backend database) generates two random numbers, $R_1$ and $R_2$ , using a Linear Feedback Shift Register (LFSR).
Rabin Cryptosystem Integration: The protocol replaces traditional Hash functions with the Rabin encryption algorithm. Rabin is selected for its mathematical proof that inverting the trapdoor function is as hard as integer factorization, while its encryption process requires only modular squaring, which is computationally lightweight.
Bitwise Operations for Transmission: The random numbers $R_1$ and $R_2$ are not transmitted directly. Instead, they are XORed with the tag's identifier segments ( $ID_L$ and $ID_R$ ) before transmission. This prevents attackers from guessing the random numbers or the key via exhaustive methods, as the attacker cannot ascertain the exact values of $R_1$ and $R_2$ without prior knowledge of $ID_L$ and $ID_R$ .
Authentication Flow:
- Reader to Tag: The reader sends a Query command along with $A = ID_L \oplus R_1$ and $B = ID_R \oplus R_2$ .
- Tag to Reader: The tag recovers $R_1$ and $R_2$ , then computes $C = [(KEY \& R_2 \& R_1)^2 \mod M]_k$ (taking the first $K$ digits) and sends it back.
- Reader Verification: The reader verifies $C$ against its database. If valid, it sends $D = [KEY^2 \mod M]_k \& R_2$ to the tag.
- Key Update: Both parties update their shared secret keys ( $K_{old} = K_{new}$ ; $K_{new} = [KEY^2 \mod M]_k$ ) to ensure backward security and prevent desynchronization.
Formal Verification: The protocol's security properties are formally analyzed using BAN (Burrows-Abadi-Needham) logic to verify mutual authentication and belief in the freshness of messages.

Key Contributions

Enhanced Security against Brute-Force and Replay Attacks: By XORing random numbers with the tag's unique identifiers ( $ID_L$ and $ID_R$ ) and utilizing the one-way property of the Rabin algorithm, the protocol prevents attackers from deducing the shared key or random numbers. Specifically, without prior knowledge of $ID_L$ and $ID_R$ , an attacker is unable to ascertain the exact values of $R_1$ and $R_2$ through brute-force methods, even if they intercept messages.
Cost and Efficiency Optimization: The protocol significantly reduces the hardware requirements for RFID tags. By moving random number generation to the reader and replacing Hash functions with the optimized Rabin algorithm, the number of required logic gates is decreased.
Robust Mutual Authentication: The design ensures that both the tag and the reader authenticate each other. The tag verifies the reader via message $D$ , and the reader verifies the tag via message $C$ , ensuring that neither party can be spoofed without the shared secret key and unique identifiers.
Desynchronization Resistance: The protocol incorporates mechanisms to handle key updates safely. The reader checks for a valid triplet using the current key ( $K_{new}$ ); if that fails, it examines whether a pair exists using the previous key ( $K_{old}$ ). If the previous key is found, the system reverts to it to maintain synchronization, ensuring the protocol is resilient against desynchronization attacks.

Results
The paper presents a comparative analysis against existing protocols (specifically reference [12] and others [16-18]):

Security Comparison: The proposed protocol successfully resists Replay, Desynchronization, Fake, Tracking, and Brute-force attacks, whereas reference [12] was found vulnerable to Brute-force attacks and reference [18] lacked Backward Security.
Performance Comparison: While storage space remains constant (3K bits) compared to reference [12], the computational complexity is reduced. The proposed protocol requires 2 XOR, 3 XAND, and 3 Rabin operations, whereas the reference protocol requires 4 XOR, 1 PRNG, and 4 Hash operations.
Gate Count Reduction: The elimination of the PRNG module on the tag and the use of the Rabin algorithm (which requires fewer gates than Hash functions) result in a lower total logic gate count for the tag.

Significance
The authors claim that this protocol offers a balanced solution for low-cost RFID systems in IoT environments. By leveraging the computational asymmetry of the Rabin cryptosystem and offloading random number generation to the reader, the protocol achieves robust two-way authentication without compromising the resource constraints of passive tags. The formal verification via BAN logic provides theoretical assurance of the protocol's correctness. Ultimately, the study demonstrates that high security and privacy (including resistance to tracking and brute-force attacks) can be achieved in RFID systems while simultaneously reducing the manufacturing cost and computational burden of the tags.

Technical Summary: Integrating Random Number Generation with the Rabin Cryptosystem for Robust Two-Way Authentication in RFID

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