Towards post-quantum security for IoT endpoints with NTRU

Guillen, Oscar M.; Pöppelmann, Thomas; Mera, Jose Maria Bermudo; Bongenaar, Elena Fuentes; Sigl, Georg; Sepúlveda, Johanna

doi:10.23919/date.2017.7927079

Cited by 41 publications

(28 citation statements)

References 9 publications

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“…Thus, in (18), the plaintext, mm is revealed. It can be seen that CPKC encryption/decryption procedure (12), (13), (15), works correctly due to (14) holding. Note that the norm of the vector, ( f , g) = f 2 + g 2 = 302928.4 is small compared to √ q = 759250123.0.…”

Section: Example Of Cpkc Encryption/ Decryptionmentioning

confidence: 93%

“…Message, m, meets (35), and random integer, r, is selected from the range defined in (42), (44). Encryption and decryption follow (12), and (13), (15), respectively (see Sections 3.2.1, and 3.2.2). Decryption correctness condition 14is proved for RCPKC.1 in (41).…”

Section: Rcpkc1 Definitionmentioning

confidence: 99%

“…Contrary to RSA and ECC working with big numbers and homomorphic only in one operation, multiplication and addition, respectively, NTRU works with high degree, N, polynomial rings and is homomorphic with respect to both multiplication and addition [7]. These features of NTRU make it applicable to various applications, such as authentication for smart cards [10], encryption of user data in smart monitoring system [11], securing of SMS [12], mutual authentication and key agreement for wireless communications [13], embedded systems including microcontrollers and FPGAs [14], Internet of Things devices [15], and NTRU hardware implementation [16]. NTRU model expects that the public key is used for encryption only by a public user (sender), whereas the private key is used for decryption only by the keys owner (receiver).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks

Ibrahim¹,

Chefranov²,

Hamad³

et al. 2020

Preprint

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Wireless Sensor Networks (WSN) are the core of Internet of Things and require cryptographic protection due to the increase number of attacks. Cryptographic methods for WSN should be fast and consume low power as these networks consist of battery-powered devices and constrained microcontrollers. NTRU, the fastest and secure public key cryptosystem, uses high degree polynomials, and is susceptible to the lattice basis reduction attack (LBRA). CPKC, proposed by NTRU authors, works on integers modulo $q$ and is easily attackable by LBRA since it uses small numbers for the sake of the correct decryption. Herein, RCPKC, a random congruential public key cryptosystem working on integers modulo $q$ is proposed, such that the norm of a two-dimensional vector formed by its private key is greater than $\sqrt{q}$. RCPKC works similar to NTRU, and it is a secure version of insecure CPKC. RCPKC specifies a range from which the random numbers shall be selected, and it provides correct decryption for valid users and incorrect decryption for an attacker using LBRA by Gaussian lattice reduction. Because of its resistance to LBRA, RCPKC is more secure. Simultaneously, due to the use of big numbers instead of high degree polynomials, RCPKC is about 24 (7) times faster in encryption (decryption) than NTRU. Also, RCPKC is more three times faster than the most effective known NTRU variant, BQTRU. Compared to NTRU, RCPKC reduces energy consumption at least seven times that allows increasing life-time of unattended WSN more than seven times.

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Section: Example Of Cpkc Encryption/ Decryptionmentioning

confidence: 93%

Section: Rcpkc1 Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks

Ibrahim¹,

Chefranov²,

Hamad³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…However, it did not address memory optimization, and KEM was not covered. In 2017, Oscar et al [15] presented a method for improving the performance of the NTRUEncryption algorithm in ARM Cortex-M0. To improve the speed of multiplication of polynomials, which consumes the most CPU cycles among operations, the product form [16] was applied to polynomial multiplication to show faster operation than conventional algorithms.…”

Section: Related Workmentioning

confidence: 99%

Improving the Performance of RLizard on Memory-Constraint IoT Devices with 8-Bit ATmega MCU

et al. 2020

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We propose an improved RLizard implementation method that enables the RLizard key encapsulation mechanism (KEM) to run in a resource-constrained Internet of Things (IoT) environment with an 8-bit micro controller unit (MCU) and 8–16 KB of SRAM. Existing research has shown that the proposed method can function in a relatively high-end IoT environment, but there is a limitation when applying the existing implementation to our environment because of the insufficient SRAM space. We improve the implementation of the RLizard KEM by utilizing electrically erasable, programmable, read-only memory (EEPROM) and flash memory, which is possessed by all 8-bit ATmega MCUs. In addition, in order to prevent a decrease in execution time related to their use, we improve the multiplication process between polynomials utilizing the special property of the second multiplicand in each algorithm of the RLizard KEM. Thus, we reduce the required MCU clock cycle consumption. The results show that, compared to the existing code submitted to the National Institute of Standard and Technology (NIST) PQC standardization competition, the required MCU clock cycle is reduced by an average of 52%, and the memory used is reduced by approximately 77%. In this way, we verified that the RLizard KEM works well in our low-end IoT environments.

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“…Contrary to RSA and ECC working with big numbers and homomorphic only in one operation, multiplication and addition, respectively, NTRU works with high degree, N, polynomial rings and is homomorphic with respect to both multiplication and addition [11]. These features of NTRU allow its use in various applications, such as authentication for smart cards [12], encryption of user data in smart monitoring systems [13], securing of SMS [14], mutual authentication and key agreement for wireless communications [15], embedded systems including microcontrollers and FPGAs [16], Internet of Things devices [17], and NTRU hardware implementation [18]. The NTRU model expects that the public key is used for encryption only by a public user (sender), whereas the private key is used for decryption by the key's owner (receiver).…”

Section: Introductionmentioning

confidence: 99%

NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks

Ibrahim

Chefranov

Hamad

et al. 2020

Sensors

View full text Add to dashboard Cite

Wireless sensor networks (WSNs) are the core of the Internet of Things and require cryptographic protection. Cryptographic methods for WSN should be fast and consume low power as these networks rely on battery-powered devices and microcontrollers. NTRU, the fastest and secure public key cryptosystem, uses high degree, N, polynomials and is susceptible to the lattice basis reduction attack (LBRA). Congruential public key cryptosystem (CPKC), proposed by the NTRU authors, works on integers modulo q and is easily attackable by LBRA since it uses small numbers for the sake of the correct decryption. Herein, RCPKC, a random congruential public key cryptosystem working on degree N=0 polynomials modulo q, is proposed, such that the norm of a two-dimensional vector formed by its private key is greater than q. RCPKC works as NTRU, and it is a secure version of insecure CPKC. RCPKC specifies a range from which the random numbers shall be selected, and it provides correct decryption for valid users and incorrect decryption for an attacker using LBRA by Gaussian lattice reduction. RCPKC asymmetric encryption padding (RAEP), similar to its NTRU analog, NAEP, is IND-CCA2 secure. Due to the use of big numbers instead of high degree polynomials, RCPKC is about 27 times faster in encryption and decryption than NTRU. Furthermore, RCPKC is more than three times faster than the most effective known NTRU variant, BQTRU. Compared to NTRU, RCPKC reduces energy consumption at least thirty times, which allows increasing the life-time of unattended WSNs more than thirty times.

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Towards post-quantum security for IoT endpoints with NTRU

Cited by 41 publications

References 9 publications

NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks

NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks

Improving the Performance of RLizard on Memory-Constraint IoT Devices with 8-Bit ATmega MCU

NTRU-Like Random Congruential Public-Key Cryptosystem for Wireless Sensor Networks

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