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Table 4. Tablulation of reported SCA and their characteristics for the different procedures of Dilithium signature scheme

Table 4 Tablulation of reported SCA and their characteristics for the different procedures of Dilithium signature scheme

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security and Correctness of IND-CPA Secure Kyber PKE The key-generation procedure of Kyber PKE simply involves generation of an LWE instance (A, t) € (RE xRe where t = A-s+e (Line 9 in Alg.1). The module A is sampled from a uniform distribution (Line 4), while the secret s and errors e are sampled from the CBD distribution (Lines 5-6). Given that NTT is used for polynomia multiplication, the public key and secret key are directly represented in the NTT domain (Line 10). The LWI instance (A, t) is the public key, while the secret s forms the secret key.
security and Correctness of IND-CPA Secure Kyber PKE The key-generation procedure of Kyber PKE simply involves generation of an LWE instance (A, t) € (RE xRe where t = A-s+e (Line 9 in Alg.1). The module A is sampled from a uniform distribution (Line 4), while the secret s and errors e are sampled from the CBD distribution (Lines 5-6). Given that NTT is used for polynomia multiplication, the public key and secret key are directly represented in the NTT domain (Line 10). The LWI instance (A, t) is the public key, while the secret s forms the secret key.
a wrapper around the encryption and decryption procedures, resulting in encapsulation and decapsulatior procedures of a,(CCA secure KEM (Refer Alg.2).
a wrapper around the encryption and decryption procedures, resulting in encapsulation and decapsulatior procedures of a,(CCA secure KEM (Refer Alg.2).
Fig. 2. Key-Exchange protocol,using IND-CCA secure Kyber KEM
Fig. 2. Key-Exchange protocol,using IND-CCA secure Kyber KEM
Table 1. Tablulation of reported SCA and their characteristics for the different procedures of Kyber KEM
Table 1. Tablulation of reported SCA and their characteristics for the different procedures of Kyber KEM
respect, an attacker can target the NTT over the secrets or error e in the key-generation procedure (Line 5, 6 in Alg.1). This results in utilization of low-entropy secrets and errors to generate a faulty public key, which can be easily solved to recover the secret key. The same faulty secret key is also used within the decapsulation procedure, as Kyber saves the secret key in the NTT domain. This therefore ensures correctness of Kyber KEM, even upon injection of fault in the NTT, only during key generation. We refer to this attack using the label NTT_Twiddle_Fault attack. The attack characteristic can be defined using the tuple: (EMFI, Observe_DUT_IO, Targeted_Fault, 1, 1).
respect, an attacker can target the NTT over the secrets or error e in the key-generation procedure (Line 5, 6 in Alg.1). This results in utilization of low-entropy secrets and errors to generate a faulty public key, which can be easily solved to recover the secret key. The same faulty secret key is also used within the decapsulation procedure, as Kyber saves the secret key in the NTT domain. This therefore ensures correctness of Kyber KEM, even upon injection of fault in the NTT, only during key generation. We refer to this attack using the label NTT_Twiddle_Fault attack. The attack characteristic can be defined using the tuple: (EMFI, Observe_DUT_IO, Targeted_Fault, 1, 1).
Table 2. Tablulation of reported FIA and their characteristics for the different procedures of Kyber KEM
Table 2. Tablulation of reported FIA and their characteristics for the different procedures of Kyber KEM
Table 3. Tablulation of reported FIA and their characteristics for the different procedures of Dilithium signature scheme Countermeasure (Our Proposal): We propose to simply utilize a Dynamic_Loop_Counter countermeasure to keep track of the number of compared coefficients of the challenge polynomial. This loop counter information along with the result of the comparison operation can be used to protect against trivial skipping attacks. One can also adopt redundancy of varying degrees to further fortify the verification procedure. We agree that this is only an implementation level countermeasure and can therefore be circumvented by a more powerful attacker. However, these countermeasures do significantly increase the ability of an attacker to mount a successful attack. Rafer ta Tah 2 far a tahilatian af all faunlteiniectian attacke an the ver flare ro Aedes af Tilithinm cionatire
Table 3. Tablulation of reported FIA and their characteristics for the different procedures of Dilithium signature scheme Countermeasure (Our Proposal): We propose to simply utilize a Dynamic_Loop_Counter countermeasure to keep track of the number of compared coefficients of the challenge polynomial. This loop counter information along with the result of the comparison operation can be used to protect against trivial skipping attacks. One can also adopt redundancy of varying degrees to further fortify the verification procedure. We agree that this is only an implementation level countermeasure and can therefore be circumvented by a more powerful attacker. However, these countermeasures do significantly increase the ability of an attacker to mount a successful attack. Rafer ta Tah 2 far a tahilatian af all faunlteiniectian attacke an the ver flare ro Aedes af Tilithinm cionatire
Refer to Tab.6 for the performance overheads due to the Verify_Nonce_Fault countermeasure on the key- generation procedure, and CT_Sanity_Check, Message_Poly_Sanity_Check, Shuffle_Encode and Shuffled_Decode countermeasures for the decapsulation procedure for Kyber KEM, implemented on the ARM Cortex-Mé4 device. These countermeasures impose very reasonable overheads in the range of 10-11%, 15-34%, 12-30% and 4-5% for the different parameter sets of Kyber KEM. Thus, we can see that these dedicated countermeasures can be implemented in a cost-effective manner for Kyber KEM. Table 6. Performance Comparison of the custom SCA-FIA countermeasures for Kyber KEM, compared to the opti- mized unprotected implementation on the ARM Cortex-M4 device. Numbers were obtained on the STM32F407VG microcontroller mounted on the STM32F407DISCOVERY board, running at 24 MHz. Numbers are provided in terms of x10? clock cycles. Ovh denotes overhead in percentage.
Refer to Tab.6 for the performance overheads due to the Verify_Nonce_Fault countermeasure on the key- generation procedure, and CT_Sanity_Check, Message_Poly_Sanity_Check, Shuffle_Encode and Shuffled_Decode countermeasures for the decapsulation procedure for Kyber KEM, implemented on the ARM Cortex-Mé4 device. These countermeasures impose very reasonable overheads in the range of 10-11%, 15-34%, 12-30% and 4-5% for the different parameter sets of Kyber KEM. Thus, we can see that these dedicated countermeasures can be implemented in a cost-effective manner for Kyber KEM. Table 6. Performance Comparison of the custom SCA-FIA countermeasures for Kyber KEM, compared to the opti- mized unprotected implementation on the ARM Cortex-M4 device. Numbers were obtained on the STM32F407VG microcontroller mounted on the STM32F407DISCOVERY board, running at 24 MHz. Numbers are provided in terms of x10? clock cycles. Ovh denotes overhead in percentage.
on the ARM Cortex-A53 device *. These countermeasures impose very reasonable overheads in the range of 3 —4%, ~ 0%, 7 — 18% and.19 — 39% for the different parameter sets of Kyber KEM. Table 8. Performance Comparison of the custom SCA-FIA countermeasures for Kyber KEM, compared to the optimized unprotected implementations on the ARM Cortex-A53 device. Numbers were obtained on the Raspberry Pi 3 Model B Plus Rev 1.3 based on the ARM Cortex-A53 processor, running Debian GNU/Linux 11 at 1.4 GHz. Numbers are provided in terms of x10? clock cycles. Ovh denotes overhead in percentage.
on the ARM Cortex-A53 device *. These countermeasures impose very reasonable overheads in the range of 3 —4%, ~ 0%, 7 — 18% and.19 — 39% for the different parameter sets of Kyber KEM. Table 8. Performance Comparison of the custom SCA-FIA countermeasures for Kyber KEM, compared to the optimized unprotected implementations on the ARM Cortex-A53 device. Numbers were obtained on the Raspberry Pi 3 Model B Plus Rev 1.3 based on the ARM Cortex-A53 processor, running Debian GNU/Linux 11 at 1.4 GHz. Numbers are provided in terms of x10? clock cycles. Ovh denotes overhead in percentage.
Table 9. Performance Comparison of the Shuffled_Masked_NTT countermeasures for Dilithium, compared to the optimized unprotected implementation on the ARM Cortex-M4 devices Numbers were obtained on the STM32F407VG microcontroller mounted on the STM32F407DISCOVERY board, running at 24 MHz. Numbers are provided in terms of x10° clock cycles. Ovh denotes overhead in percentage.
Table 9. Performance Comparison of the Shuffled_Masked_NTT countermeasures for Dilithium, compared to the optimized unprotected implementation on the ARM Cortex-M4 devices Numbers were obtained on the STM32F407VG microcontroller mounted on the STM32F407DISCOVERY board, running at 24 MHz. Numbers are provided in terms of x10° clock cycles. Ovh denotes overhead in percentage.
these countermeasures are only implemented in C language, while assembly optimized implementations can result in much smaller overheads. Table 12. Performance Comparison of the different SCA-FIA countermeasures for Dilithium and the overheads they incur on optimized implementations on the ARM Cortex-A53 device. Numbers were obtained on the Raspberry Pi 3 Model B Plus Rev 1.3 based on the ARM Cortex-A53 processor, running Debian GNU/Linux 11 at 1.4 GHz. Numbers are provided in terms of X10° clock cycles. Ovh denotes overhead in percentage.
these countermeasures are only implemented in C language, while assembly optimized implementations can result in much smaller overheads. Table 12. Performance Comparison of the different SCA-FIA countermeasures for Dilithium and the overheads they incur on optimized implementations on the ARM Cortex-A53 device. Numbers were obtained on the Raspberry Pi 3 Model B Plus Rev 1.3 based on the ARM Cortex-A53 processor, running Debian GNU/Linux 11 at 1.4 GHz. Numbers are provided in terms of X10° clock cycles. Ovh denotes overhead in percentage.
Table 11. Performance Comparison of the Shuffled_Masked_NTT countermeasures for Dilithium, compared to the optimized unprotected implementation on the ARM Cortex-A53 device. Numbers were obtained on the Raspberry Pi : Model B Plus Rev 1.3 based on the ARM Cortex-A53 processor, running Debian GNU/Linux 11 at 1.4 GHz. Number: are provided in terms of x10% clock cycles. Ovh denotes overhead in percentage.
Table 11. Performance Comparison of the Shuffled_Masked_NTT countermeasures for Dilithium, compared to the optimized unprotected implementation on the ARM Cortex-A53 device. Numbers were obtained on the Raspberry Pi : Model B Plus Rev 1.3 based on the ARM Cortex-A53 processor, running Debian GNU/Linux 11 at 1.4 GHz. Number: are provided in terms of x10% clock cycles. Ovh denotes overhead in percentage.
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