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Horizontal and Vertical Side Channel Analysis of a McEliece Cryptosystem

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Abstract

This paper presents horizontal and vertical side channel analysis techniques for an implementation of the McEliece cryptosystem. The target of this side-channel attack is a state-of-the-art field-programmable gate array (FPGA) implementation of the efficient quasi-cyclic moderate-density parity-check McEliece decryption operation, as presented at Design, Automation and Test in Europe (DATE) 2014. The presented cryptanalysis succeeds to recover the complete secret key after a few observed decryptions. It consists of a combination of a differential leakage analysis during the syndrome computation followed by an algebraic step that exploits the relation between the public key and the private key.

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... Power analysis (PA) has especially been employed to compromise the security of different crypto-systems running on a computing platform. Examples include secret key recovery from elliptic-curve cryptography (ECC) running on iOS and Android devices [1] and McEliece cryptosystem implemented on FPGA [2], attacks on Xilinx bitstream encryption [3], recovering the secret key of postquantum key exchange protocols [4], [5], key recovery of Advanced Encryption Standard (AES) [6], symmetric encryption systems [7], [8] and breaking the security of smart cards [9]. ...
... The architecture of the MLP used in this work is shown in Fig. 6 To facilitate training of the MLP, the input power features are normalized over all measurements. Let c (2) j , j = 1, 2, · · · , S denote the power features, extracted at the toplayer encoder cell of the auto-encoder in Fig. 5, correspond-ing to S power measurements. The input to the MLP is theñ ...
... Processing of power traces as in Fig. 7 is similar to the horizontal attacks of [2], [4] in which similar patterns of power consumption through time, corresponding to the same key subset, are analyzed to recover the key. However, in the SCAUL attack on AES, the power traces correspond to different key subsets. ...
Preprint
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... A single trace is used as a side-channel on PQC lattice-based encryption schemes to perform key recovery [25]. Power side-channels on FPGA implementations of McEliece PQC was shown in [45]. Differential power side-channels were revealed in PQC XMSS and SPHINCS [46]. ...
Preprint
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NIST is standardizing Post Quantum Cryptography (PQC) algorithms that are resilient to the computational capability of quantum computers. Past works show malicious subversion with cryptographic software (algorithm subversion attacks) that weaken the implementations. We show that PQC digital signature codes can be subverted in line with previously reported flawed implementations that generate verifiable, but less-secure signatures, demonstrating the risk of such attacks. Since, all processors have built-in Hardware Performance Counters (HPCs), there exists a body of work proposing a low-cost Machine Learning (ML)-based integrity checking of software using HPC fingerprints. However, such HPC-based approaches may not detect subversion of PQC codes. A miniscule percentage of qualitative inputs when applied to the PQC codes improve this accuracy to 98%. We propose grey-box fuzzing as a pre-processing step to obtain inputs to aid the HPC-based method.
... Fault attacks on the variables used during encryption by McEliece and Niederreiter schemes are examined in [10]. A Differential Power Analysis (DPA) attack is presented in [11] that recovers the secret key of a QC-MDPC McEliece FPGA implementation by measuring the leakage of the carry occurring during the key rotation operation. A similar attack on a software implementation is presented in [15], using the detection of counter overflows. ...
Chapter
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... Some side-channel attacks have been attempted on the McEliece cryptosystem using QC-MDPC codes [26,27]. Side-channel attacks try to gain information by measuring time (time analysis attacks) or power usage (power analysis attacks) differences in performed calculations in the encryption or decryption process. ...
Thesis
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... [15] implements a lightweight MDPC-McEliece on FPGAs by sequentially manipulating cyclic rotations of the private key in block RAMs. This work is found to be vulnerable to differential power analysis attacks [16], [17] in 2015. [18] introduces mask operations to large keys as a countermeasure against differential power analysis. ...
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Article
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Preface 1. Basic concepts of linear codes 2. Bounds on size of codes 3. Finite fields 4. Cyclic codes 5. BCH and Reed-Soloman codes 6. Duadic codes 7. Weight distributions 8. Designs 9. Self-dual codes 10. Some favourite self-dual codes 11. Covering radius and cosets 12. Codes over Z4 13. Codes from algebraic geometry 14. Convolutional codes 15. Soft decision and iterative decoding Bibliography Index.
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Book
Power analysis attacks allow the extraction of secret information from smart cards. Smart cards are used in many applications including banking, mobile communications, pay TV, and electronic signatures. In all these applications, the security of the smart cards is of crucial importance. Power Analysis Attacks: Revealing the Secrets of Smart Cards is the first comprehensive treatment of power analysis attacks and countermeasures. Based on the principle that the only way to defend against power analysis attacks is to understand them, this book explains how power analysis attacks work. Using many examples, it discusses simple and differential power analysis as well as advanced techniques like template attacks. Furthermore, this volume provides an extensive discussion of countermeasures like shuffling, masking, and DPA-resistant logic styles. By analyzing the pros and cons of the different countermeasures, Power Analysis Attacks: Revealing the Secrets of Smart Cards allows practitioners to decide how to protect smart cards. This book also provides valuable information for graduate and advanced undergraduate students, and researchers working in information security. © 2007 Springer Science+Business Media, LLC. All rights reserved.
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The power consumed by a circuit varies according to the activity of its individual transistors and other components. As a result, measurements of the power used by actual computers or microchips contain information about the operations being performed and the data being processed. Cryptographic designs have traditionally assumed that secrets are manipulated in environments that expose no information beyond the specified inputs and outputs. This paper examines how information leaked through power consumption and other side channels can be analyzed to extract secret keys from a wide range of devices. The attacks are practical, non-invasive, and highly effective—even against complex and noisy systems where cryptographic computations account for only a small fraction of the overall power consumption. We also introduce approaches for preventing DPA attacks and for building cryptosystems that remain secure even when implemented in hardware that leaks.
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In the rst of two papers on Magma, a new system for computational algebra, we present the Magma language, outline the design principles and theoretical background, and indicate its scope and use. Particular attention is given to the constructors for structures, maps, and sets. c 1997 Academic Press Limited Magma is a new software system for computational algebra, the design of which is based on the twin concepts of algebraic structure and morphism. The design is intended to provide a mathematically rigorous environment for computing with algebraic struc- tures (groups, rings, elds, modules and algebras), geometric structures (varieties, special curves) and combinatorial structures (graphs, designs and codes). The philosophy underlying the design of Magma is based on concepts from Universal Algebra and Category Theory. Key ideas from these two areas provide the basis for a gen- eral scheme for the specication and representation of mathematical structures. The user language includes three important groups of constructors that realize the philosophy in syntactic terms: structure constructors, map constructors and set constructors. The util- ity of Magma as a mathematical tool derives from the combination of its language with an extensive kernel of highly ecient C implementations of the fundamental algorithms for most branches of computational algebra. In this paper we outline the philosophy of the Magma design and show how it may be used to develop an algebraic programming paradigm for language design. In a second paper we will show how our design philoso- phy allows us to realize natural computational \environments" for dierent branches of algebra. An early discussion of the design of Magma may be found in Butler and Cannon (1989, 1990). A terse overview of the language together with a discussion of some of the implementation issues may be found in Bosma et al. (1994).
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A public-key cryptosystem which appears quite secure while at the same time allowing extremely rapid data rates, is constructed for use in multi-user communication networks, such as those envisioned by NASA for the distribution of space-acquired data.
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A low-density parity-check code is a code specified by a parity-check matrix with the following properties: each column contains a small fixed number j geq 3 of l's and each row contains a small fixed number k > j of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j . When used with maximum likelihood decoding on a sufficiently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixed j . A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described. Both the equipment complexity and the data-handling capacity in bits per second of this decoder increase approximately linearly with block length. For j > 3 and a sufficiently low rate, the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length. Some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound.
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MEMBER, IEEE, AND HENK C. A. V~ TILBORG The fact that the general decoding problem for linear codes and the general problem of finding the weights of a linear code are both NP-complete is shown. This strongly suggests, but does not rigorously imply, that no algorithm for either of these problems which runs in polynomial time exists.
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. Cryptosystem designers frequently assume that secrets will be manipulated in closed, reliable computing environments. Unfortunately, actual computers and microchips leak information about the operations they process. This paper examines specific methods for analyzing power consumption measurements to find secret keys from tamper resistant devices. We also discuss approaches for building cryptosystems that can operate securely in existing hardware that leaks information. Keywords: differential power analysis, DPA, SPA, cryptanalysis, DES 1 Background Attacks that involvemultiple parts of a security system are difficult to predict and model. If cipher designers, software developers, and hardware engineers do not understand or review each other's work, security assumptions made at each level of a system's design may be incomplete or unrealistic. As a result, security faults often involveunanticipated interactions between components designed by different people. Manytechniques ...
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The author advocates two specific mathematical notations from his popular course and joint textbook, "Concrete Mathematics". The first of these, extending an idea of Iverson, is the notation "[P]" for the function which is 1 when the Boolean condition P is true and 0 otherwise. This notation can encourage and clarify the use of characteristic functions and Kronecker deltas in sums and integrals. The second notation puts Stirling numbers on the same footing as binomial coefficients. Since binomial coefficients are written on two lines in parentheses and read "n choose k", Stirling numbers of the first kind should be written on two lines in brackets and read "n cycle k", while Stirling numbers of the second kind should be written in braces and read "n subset k". (I might say "n partition k".) The written form was first suggested by Imanuel Marx. The virtues of this notation are that Stirling partition numbers frequently appear in combinatorics, and that it more clearly presents functional relations similar to those satisfied by binomial coefficients.
The myth of generic DPA
  • C Whitnall
  • E Oswald
  • F.-X Standaert
  • J Benaloh