An Improved Montgomery Window Algorithm on Modular Exponentiation Secure against Side Channel Attacks

2013 ◽  
Vol 392 ◽  
pp. 862-866
Author(s):  
Mu Han ◽  
Jia Zhao ◽  
Shi Dian Ma
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
Side Channel ◽  
Modular Exponentiation ◽  
Side Channel Attacks ◽  
The Core

As one of the core algorithms in most public key cryptography, modular exponentiation has a flaw of its efficiency, which often uses the Montgomerys algorithm to realize the fast operation. But the Montgomerys algorithm has the issue of side channel leakage from the final conditional subtraction. Aiming at this problem, this paper presents an improved fast Montgomery window algorithm. The new algorithm generates the remainder table with odd power to reduce the amount of pre-computation, and combines with the improved Montgomerys algorithm to realize modular exponentiation, which can accelerate the speed and reduce the side channel leakage. The new algorithm cant only thwart side channel attacks, but also improve the efficiency.

scholarly journals Implementation Methodology of ECC to Overcome Side Channel Attacks

2018 ◽  
Vol 7 (3.27) ◽  
pp. 421
Author(s):  
M Maheswari ◽  
R A. Karthika ◽  
Anuska Chatterjee
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Public Key Cryptography ◽  
Public Key ◽  
Side Channel ◽  
Side Channel Attacks ◽  
Private Key ◽  
Wide Range ◽  
Cryptographic Algorithms ◽  
Implementation Methodology

Elliptic Curve Cryptography (ECC) is a form of public-key cryptography. This implies that there is the involvement of a private key and a public key for the purpose of cryptography. ECC can be used for a wide range of applications. The keys used are much smaller than the non-ECC cryptographic algorithms. 256 bit and 384 bit ECC are used by NSA for storage of classified intel as ECC is considered to be a part of suit B cryptography by the NSA. When it comes to normal usage, other versions of ECC are used. So, many of the applications protected by ECC are vulnerable to side channel attacks. So, the objective is to modify the existing method of implementation of ECC is some regular domains like media, smart grid, etc., such that the side-channel attacks [7], [3] vulnerabilities are fixed.  

scholarly journals Leakage-Resilient Outsourced Revocable Certificateless Signature with a Cloud Revocation Server

2020 ◽  
Vol 49 (4) ◽  
pp. 464-481
Author(s):  
Yuh–Min Tseng ◽  
Jui-Di Wu ◽  
Sen-Shan Huang ◽  
Tung-Tso Tsai
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
Side Channel ◽  
Key Generation ◽  
Side Channel Attacks ◽  
Signature Schemes ◽  
Certificateless Cryptography ◽  
Secret Keys ◽  
Leakage Resilient ◽  
Certificateless Signature

Certificateless public-key system (CL-PKS) is a significant public-key cryptography and it solves both the key escrow and certificate management problems. Outsourced revocable certificateless public-key system (ORCL-PKS) with a cloud revocation server (CRS) not only provides a revocation mechanism, but also further outsources the revocation functionality to the CRS to reduce the computational burden of the key generation center (KGC). Recently, side-channel attacks have threatened some existing conventional cryptography (including CL-PKS). Indeed, adversaries can apply side-channel attacks to derive fractional constituents of private (or secret) keys to damage the security of these cryptographic protocols (or schemes). To withstand such attacks, leakage-resilient cryptography is an attractive approach. However, little research concerns with leakage-resilient certificateless cryptography. In this paper, the first leakage-resilient outsourced revocable certificateless signature (LR-ORCLS) scheme is presented. The proposed scheme allows adversaries to continually derive fractional constituents of private (or secret) keys and possesses overall unbounded leakage property. In the generic bilinear group (GBG) model, our scheme is shown to be existential unforgeable against adversaries. Finally, the comparisons between the proposed scheme and the previous revocable certificateless signature schemes are provided to demonstrate the merits of the proposed scheme.

scholarly journals Lattice-Based Linearly Homomorphic Signature Scheme over F 2

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jie Cai ◽  
Han Jiang ◽  
Hao Wang ◽  
Qiuliang Xu
Keyword(s):  
Public Key ◽  
Side Channel ◽  
Signature Scheme ◽  
Side Channel Attacks ◽  
Sampling Function ◽  
Uniform Sampling ◽  
Restricted Condition ◽  
Gaussian Sampling

In this paper, we design a new lattice-based linearly homomorphic signature scheme over F 2 . The existing schemes are all constructed based on hash-and-sign lattice-based signature framework, where the implementation of preimage sampling function is Gaussian sampling, and the use of trapdoor basis needs a larger dimension m ≥ 5 n   log   q . Hence, they cannot resist potential side-channel attacks and have larger sizes of public key and signature. Under Fiat–Shamir with aborting signature framework and general SIS problem restricted condition m ≥ n   log   q , we use uniform sampling of filtering technology to design the scheme, and then, our scheme has a smaller public key size and signature size than the existing schemes and it can resist side-channel attacks.

scholarly journals Generic Side-channel attacks on CCA-secure lattice-based PKE and KEMs

2020 ◽  
pp. 307-335 ◽  
Author(s):  
Prasanna Ravi ◽  
Sujoy Sinha Roy ◽  
Anupam Chattopadhyay ◽  
Shivam Bhasin
Keyword(s):  
Experimental Validation ◽  
Error Correcting Codes ◽  
Public Key ◽  
Side Channel ◽  
Public Key Encryption ◽  
Side Channel Attacks ◽  
Key Recovery ◽  
Binary Information ◽  
Channel Information ◽  
Standardization Process

In this work, we demonstrate generic and practical EM side-channel assisted chosen ciphertext attacks over multiple LWE/LWR-based Public Key Encryption (PKE) and Key Encapsulation Mechanisms (KEM) secure in the chosen ciphertext model (IND-CCA security). We show that the EM side-channel information can be efficiently utilized to instantiate a plaintext checking oracle, which provides binary information about the output of decryption, typically concealed within IND-CCA secure PKE/KEMs, thereby enabling our attacks. Firstly, we identified EM-based side-channel vulnerabilities in the error correcting codes (ECC) enabling us to distinguish based on the value/validity of decrypted codewords. We also identified similar vulnerabilities in the Fujisaki-Okamoto transform which leaks information about decrypted messages applicable to schemes that do not use ECC. We subsequently exploit these vulnerabilities to demonstrate practical attacks applicable to six CCA-secure lattice-based PKE/KEMs competing in the second round of the NIST standardization process. We perform experimental validation of our attacks on implementations taken from the open-source pqm4 library, running on the ARM Cortex-M4 microcontroller. Our attacks lead to complete key-recovery in a matter of minutes on all the targeted schemes, thus showing the effectiveness of our attack.

scholarly journals Efficiency through Diversity in Ensemble Models applied to Side-Channel Attacks

2021 ◽  
pp. 60-96
Author(s):  
Gabriel Zaid ◽  
Lilian Bossuet ◽  
Amaury Habrard ◽  
Alexandre Venelli
Keyword(s):  
Deep Learning ◽  
Model Performance ◽  
Public Key ◽  
Side Channel ◽  
Ensemble Model ◽  
Secret Key ◽  
Side Channel Attacks ◽  
Ensemble Models ◽  
Remaining Time ◽  
Multiple Scenarios

Deep Learning based Side-Channel Attacks (DL-SCA) are considered as fundamental threats against secure cryptographic implementations. Side-channel attacks aim to recover a secret key using the least number of leakage traces. In DL-SCA, this often translates in having a model with the highest possible accuracy. Increasing an attack’s accuracy is particularly important when an attacker targets public-key cryptographic implementations where the recovery of each secret key bits is directly related to the model’s accuracy. Commonly used in the deep learning field, ensemble models are a well suited method that combine the predictions of multiple models to increase the ensemble accuracy by reducing the correlation between their errors. Linked to this correlation, the diversity is considered as an indicator of the ensemble model performance. In this paper, we propose a new loss, namely Ensembling Loss (EL), that generates an ensemble model which increases the diversity between the members. Based on the mutual information between the ensemble model and its related label, we theoretically demonstrate how the ensemble members interact during the training process. We also study how an attack’s accuracy gain translates to a drastic reduction of the remaining time complexity of a side-channel attacks through multiple scenarios on public-key implementations. Finally, we experimentally evaluate the benefits of our new learning metric on RSA and ECC secure implementations. The Ensembling Loss increases by up to 6.8% the performance of the ensemble model while the remaining brute-force is reduced by up to 222 operations depending on the attack scenario.

scholarly journals Practical Evaluation of Protected Residue Number System Scalar Multiplication

2018 ◽  
pp. 259-282
Author(s):  
Louiza Papachristodoulou ◽  
Apostolos P. Fournaris ◽  
Kostas Papagiannopoulos ◽  
Lejla Batina
Keyword(s):  
Public Key Cryptography ◽  
Number System ◽  
Residue Number System ◽  
Scalar Multiplication ◽  
Public Key ◽  
Side Channel ◽  
Evaluation Approach ◽  
Rings Of Integers ◽  
Residue Number ◽  
Template Attacks

The Residue Number System (RNS) arithmetic is gaining grounds in public key cryptography, because it offers fast, efficient and secure implementations over large prime fields or rings of integers. In this paper, we propose a generic, thorough and analytic evaluation approach for protected scalar multiplication implementations with RNS and traditional Side Channel Attack (SCA) countermeasures in an effort to assess the SCA resistance of RNS. This paper constitutes the first robust evaluation of RNS software for Elliptic Curve Cryptography against electromagnetic (EM) side-channel attacks. Four different countermeasures, namely scalar and point randomization, random base permutations and random moduli operation sequence, are implemented and evaluated using the Test Vector Leakage Assessment (TVLA) and template attacks. More specifically, variations of RNS-based Montgomery Powering Ladder scalar multiplication algorithms are evaluated on an ARM Cortex A8 processor using an EM probe for acquisition of the traces. We show experimentally and theoretically that new bounds should be put forward when TVLA evaluations on public key algorithms are performed. On the security of RNS, our data and location dependent template attacks show that even protected implementations are vulnerable to these attacks. A combination of RNS-based countermeasures is the best way to protect against side-channel leakage.

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