On XTR and Side-Channel Analysis

The acceleration of cryptographic applications on embedded devices is a topic of increasingly importance, due to their massive use. In this paper, the efficiency of these devices when operating as cryptographic accelerators is assessed, using a two-tiered parallelism model, where not only multi-core, but also Single Instruction Multiple Data (SIMD) parallelism is exploited to increase the throughput of modular multiplications. In addition, the applicability of the developed parallel modular multiplications are tested for the Rivest-Shavir-Adleman (RSA) and Elliptic Curve (EC) cryptosystems. The relative efficiency of the two-tiered model for implementing cryptosystems on general purpose processors and embedded devices is analysed and experimentally evaluated. It can be concluded that it is possible to achieve the same levels of execution enhancement on both platforms. Moreover, speedups of up to 7.3 and 3.9 are obtained for the RSA and EC cryptosystems on the ARM A15 quad-core processor, respectively.

The concept of public key cryptography was first introduced by Diffie and Hellman in 1976 using discrete logarithm problem as base of difficulty. In 1985, T. ElGamal proposed public key cryptosystem scheme based on discrete logarithm problem. Elliptic curve cryptosystems were first proposed in 1985 independently by Neil Koblitz and Victor Miller. Elliptic curve cryptosystems are unique in using elliptic curve groups for arithmetic. This cryptosystem is based on discrete logarithm problem in the group of points of an elliptic curve defined over a finite field. The discrete logarithm problem in an elliptic curve group appears to be much harder than the discrete logarithm problem in other groups. Hence elliptic curves cryptosystem can match the security of other cryptosystems while using smaller key. In this paper we will discuss a VLSl implementation of elliptic curves cryptosystem for ElGamal encryption scheme.

Since their invention in the mid 1980s, Elliptic Curve Cryptosystems (ECC) have become an alternative to common Public-Key (PK) cryptosystems such as, e.g., RSA. The utilization of Elliptic Curves (EC) in cryptography is very promising because of their resistance against powerful index-calculus attacks. Providing a similar level of security as RSA, ECC allows for efficient implementation due to a significantly smaller bit size of the operands. It is widely accepted that the only feasible way to attack actual cryptosystems, if at all, is the application of dedicated hardware. In times of continuous technological improvements and increasing computing power, the question of the security of ECC against attacks based on special-purpose hardware and, in particular based on recently emerged low-cost FPGAs, arises.This work presents the first architecture with a corresponding FPGA implementation of an attack against ECC over prime fields. We describe an FPGA-based multi-processing hardware architecture for the Pollard-Rho method which is, to our knowledge, currently the most efficient attack against ECC. The implementation is running on a contemporary low-cost FPGA which allows for a much better cost-performance ratio than conventional CPUs. With the implementation at hand, a fairly accurate estimate about the cost of an FPGA-based attack can be given. We will extrapolate the results on actual ECC key lengths (128 bits and above) and estimate the expected runtimes for a successful attack. Since FPGA-based attacks are out of reach for key lengths exceeding 128 bits, we provide estimates for an ASIC design.Based on our results, currently used elliptic curve cryptosystems (160 bit and above) are infeasible to break with available computational and financial resources. However, some of the security standards proposed by the SECG in [2, 3] become subject to attacks based on low-cost FPGAs.

In the 1970s researchers noticed that radioactive particles produced by elements naturally present in packaging material could cause bits to flip in sensitive areas of electronic chips. Research into the effect of cosmic rays on semiconductors, an area of particular interest in the aerospace industry, led to methods of hardening electronic devices designed for harsh environments. Ultimately various mechanisms for fault creation and propagation were discovered, and in particular it was noted that many cryptographic algorithms succumb to so-called fault attacks. Preventing fault attacks without sacrificing performance is nontrivial and this is the subject of this book. Part I deals with side-channel analysis and its relevance to fault attacks. The chapters in Part II cover fault analysis in secret key cryptography, with chapters on block ciphers, fault analysis of DES and AES, countermeasures for symmetric-key ciphers, and countermeasures against attacks on AES. Part III deals with fault analysis in public key cryptography, with chapters dedicated to classical RSA and RSA-CRT implementations, elliptic curve cryptosystems and countermeasures using fault detection, devices resilient to fault injection attacks, lattice-based fault attacks on signatures, and fault attacks on pairing-based cryptography. Part IV examines fault attacks on stream ciphers and how faults interact with countermeasures used to prevent power analysis attacks. Finally, Part V contains chapters that explain how fault attacks are implemented, with chapters on fault injection technologies for microprocessors, and fault injection and key retrieval experiments on a widely used evaluation board. This is the first book on this topic and will be of interest to researchers and practitioners engaged with cryptographic engineering.

Elliptic curve cryptosystem (ECC) was proposed by Miller [10] and Koblitz [9] which relies on the difficulty of elliptic curve discrete logarithmic problem (ECDLP). It is gaining wide acceptance as an alternative to the conventional public key cryptosystem such as RSA [24], DSA [25], DH [26]. Also it is noted that the wireless sensor networks (WSN) based on the rapid progress of wireless communications and embedded micro electro mechanical systems technologies are becoming important part in our daily life. The security of the WSN becomes one of the major concerns in its applications. Even ECC prominently offers great potential benefits for WSN security there is still a lot of work needs to be done due to WSN has very restraint running conditions such as limited energy source, capability of computing, etc. It is well known that scalar multiplication operation in ECC accounts for about 80% of key calculation time on wireless sensor network motes. In this paper we present an optimized dynamic window based on our previous research works. The whole quality of service (QoS) has been improved under this algorism in particularly the power consuming is more efficiently. The simulation results showed that the average calculation time, due to fuzzy conditions decreased from previous 26 to current 9 as a whole the calculation time, decreased by approximately 18% in comparison to our previous algorithms in an ECC wireless sensor network [23].

Elliptic curve cryptosystems (ECCs) are becoming more popular because of the reduced number of key bits required in comparison to other cryptosystems (e.g. a 160 bit ECC has roughly the same security as 1024 bit RSA). ECCs are especially suited to smart cards because of the limited memory and computational power available on these devices. However, the side-channel attacks which have recently been proposed can obtain information about the cryptosystem by measuring side-channel information such as power consumption and processing time. This information may be used to break implementations that have not incorporated defences against these attacks. This paper presents a new defence against Simple Power Analysis (SPA). This new defence is based on the NAF (non-adjacent form) representation of a scalar and requires 44% fewer additions and 11% extra doublings than the commonly recommended defence of performing a point addition in every loop of the binary scalar multiplication algorithm.

Elliptic curve cryptosystem — The answer to strong, fast public-key cryptography for securing constrained environments

One of the main barriers to the development of multi-application smart card is the limitation of the memory size and processing power. This paper gives a solution to it by using an elliptic curve cryptosystem (ECC) as the public key scheme. The basic mathematics principles of ECC are discussed. Based on the ECC, we also put a digital certificate inside the smart card. This paper presents a prototype of a multi-application smart card system using the ECC certificate. Several security issues are also discussed.

In this digital world, communication systems have witnessed abundant usage of media over the platforms. Among these, providing security in transmission of images is highly important, and attained a lot of research interest due to its high consideration in both the industry and the academic community. This paper proposes a hybrid asymmetric image encryption algorithm using Elliptic curve cryptosystem (ECC), Hadamard transform and Hill cipher algorithms. Based on the Diffie–Hellman public key exchange method a point on the elliptic curve is selected and agreed between both the sender and receiver. The key relies upon the ECC and it is difficult to resolve the ECDLP to get it. The proposed algorithm involves two stages of encryption, primarily, the XOR function is applied on the Elliptic curve Diffie-Hellman (ECDH) shared secret key and the hadamard image. In the subsequent stage, ECC is combined with the hill cipher algorithm. Encryption and decryption uses self-invertible key matrix, hence the process of finding inverse key becomes redundant during decryption which improves the speed of execution. It also enhances the security and efficiency compared to original hill cipher method. The results are compared with other ECC methods proves that the current cryptosystem attains large key space, highly key sensitive, low correlation and can resist against differential and statistical attacks.

In 2009, Yang and Chang proposed an ID-based remote mutual authentication with key agreement scheme on elliptic curve cryptosystem (ECC). Based upon ID-based concept, Yang and Chang scheme (YC scheme) does not require additional computations for certificate and is not constructed by bilinear-pairings, which is an expensive operation on elliptic curve. In addition, YC scheme not only provides mutual authentication but also supports a session key agreement between the user and the server. Therefore, YC scheme is more efficient and practical than the related works. However, we find YC scheme is vulnerable to an impersonation attack and does not provide perfect forwardsecrecy in spite of efforts to perform mutual authentication and session key agreement between the user and the remote server and reduce the computational costs than the related works. Therefore, this paper proposes an improved ID-based remote mutual authentication with key agreement scheme for mobile devices on ECC. Compared with YC scheme, the proposed scheme is more secure, efficient, and practical for mobile devices because the proposed scheme not only eliminates the security flaws of YC scheme but also reduces the computational costs between the user and the server.

Elliptic curve cryptosystems (ECCs) are becoming more popular because of the reduced number of key bits required in comparison to other cryptosystems (for example, a 160 bit ecc has roughly the same security as 1024 bit RSA). ECCs are especially suited to smart cards because of the limited memory and computational power available on these devices. This paper discusses an optimized implementation of the elliptic curve Digital Signature Algorithm implemented over the field $GF(p)$ on a Motorola smart card. Algorithms for point addition, point doubling and scalar multiplication are compared according to their timings. The effects of different memory usage, code size and speed tradeoffs which were considered during the implementation are discussed. Also, optimized point addition and doubling algorithms are presented.

An efficient key-management scheme for hierarchical access control based on elliptic curve cryptosystem

Existing power analysis techniques rely on strong adversary models with prior knowledge of the leakage or training data. We introduce side-channel analysis with unsupervised learning (SCAUL) that can recover the secret key without requiring prior knowledge or profiling (training). We employ an LSTM auto-encoder to extract features from power traces with high mutual information with the data-dependent samples of the measurements. We demonstrate that by replacing the raw measurements with the auto-encoder features in a classical DPA attack, the efficiency, in terms of required number of measurements for key recovery, improves by 10X. Further, we employ these features to identify a leakage model with sensitivity analysis and multi-layer perceptron (MLP) networks. SCAUL uses the auto-encoder features and the leakage model, obtained in an unsupervised approach, to find the correct key. On a lightweight implementation of AES on Artix-7 FPGA, we show that SCAUL is able to recover the correct key with 3,700 power measurements with random plaintexts, while a DPA attack requires at least 17,400 measurements. Using misaligned traces, with an uncertainty equal to 20 percent of the hardware clock cycle, SCAUL is able to recover the secret key with 12,300 measurements while the DPA attack fails to detect the key.

Side channel attacks (SCA) are serious attacks on mobile devices. In SCA, the attacker can observe the side channel information while the device performs the cryptographic operations, and he/she can detect the secret stored in the device using such side channel information. Ha-Moon proposed a novel countermeasure against side channel attacks in elliptic curve cryptosystems (ECC). The countermeasure is based on the signed scalar multiplication with randomized concept, and does not pay the penalty of speed. Ha-Moon proved that the countermeasure is secure against side channel attack theoretically, and confirmed its immunity experimentally. Thus Ha-Moon’s countermeasure seems to be very attractive. In this paper we propose a novel attack against Ha-Moon’s countermeasure, and show that the countermeasure is vulnerable to the proposed attack. The proposed attack utilizes a Markov chain for detecting the secret. The attacker determines the transitions in the Markov chain using side channel information, then detects the relation between consecutive two bits of the secret key, instead of bits of the secret key as they are. The use of such relations drastically reduces the search space for the secret key, and the attacker can easily reveal the secret. In fact, around twenty observations of execution of the countermeasure are sufficient to detect the secret in the case of the standard sizes of ECC. Therefore, Ha-Moon’s countermeasure is not recommended for cryptographic use.

An ID-based remote mutual authentication with key agreement scheme for mobile devices on elliptic curve cryptosystem