Seongan Lim

Bio: Seongan Lim is an academic researcher from KISA. The author has contributed to research in topics: Cryptography & Cryptanalysis. The author has an hindex of 7, co-authored 17 publications receiving 489 citations.

A Countermeasure against One Physical Cryptanalysis May Benefit Another Attack

Abstract: Recently, many research works have been reported about how physical cryptanalysis can be carried out on cryptographic devices by exploiting any possible leaked information through side channels. In this paper, we demonstrate a new type of safe-error based hardware fault cryptanalysis which is mounted on a recently reported countermeasure against simple power analysis attack. This safe-error based attack is developed by inducing a temporary random computational fault other than a temporary memory fault which was explicitly assumed in the first published safe-error based attack (in which more precisions on timing and fault location are assumed) proposed by Yen and Joye. Analysis shows that the new safe-error based attack proposed in this paper is powerful and feasible because the cryptanalytic complexity (especially the computational complexity) is quite small and the assumptions made are more reasonable. Existing research works considered many possible countermeasures against each kind of physical cryptanalysis. This paper and a few previous reports clearly show that a countermeasure developed against one physical attack does not necessarily thwart another kind of physical attack. However, almost no research has been done on dealing the possible mutual relationship between different kinds of physical cryptanalysis when choosing a specific countermeasure. Most importantly, in this paper we wish to emphasize that a countermeasure developed against one physical attack if not carefully examined may benefit another physical attack tremendously. This issue has never been explicitely noticed previously but its importance can not be overlooked because of the attack found in this paper. Notice that almost all the issues considered in this paper on a modular exponentiation also applies to a scalar multiplication over an elliptic curve.

RSA speedup with Chinese remainder theorem immune against hardware fault cryptanalysis

Abstract: This article considers the problem of how to prevent RSA signature and decryption computation with a residue number system (CRT-based approach) speedup from a hardware fault cryptanalysis in a highly reliable and efficient approach. CRT-based speedup for an RSA signature has been widely adopted as an implementation standard ranging from large servers to very tiny smart IC cards. However, given a single erroneous computation result, hardware fault cryptanalysis can totally break the RSA system by factoring the public modulus. Countermeasures using a simple verification function (e.g., raising a signature to the power of a public key) or fault detection (e.g., an expanded modulus approach) have been reported in the literature; however, it is pointed out that very few of these existing solutions are both sound and efficient. Unreasonably, in these methods, they assume that a comparison instruction will always be fault-free when developing countermeasures against hardware fault cryptanalysis. Research shows that the expanded modulus approach proposed by Shamir (1997, 1999) is superior to the approach using a simple verification function when another physical cryptanalysis (e.g., timing cryptanalysis) is considered. So, we intend to improve Shamir's method. In this paper, the new concepts of fault infective CRT computation and fault infective CRT recombination are proposed. Based on the new concepts, two novel protocols are developed with a rigorous proof of security. Two possible parameter settings are provided for the protocols. One setting selects a small public key and the proposed protocols can have comparable performance to Shamir's scheme. The other setting has better performance than Shamir's scheme (i.e., having comparable performance to conventional CRT speedup), but with a large public key. Most importantly, we wish to emphasize the importance of developing and proving the security of physically secure protocols without relying on unreliable or unreasonable assumptions, e.g., always fault-free instructions. In this paper, related protocols are also considered and carefully examined to point out possible weaknesses.

RSA Speedup with Residue Number System Immune against Hardware Fault Cryptanalysis

Abstract: This article considers the problem of how to prevent the fast RSA signature and decryption computation with residue number system (or called the CRT-based approach) speedup from a hardware fault cryptanalysis in a highly reliable and efficient approach. The CRT-based speedup for RSA signature has been widely adopted as an implementation standard ranging from large servers to very tiny smart IC cards. However, given a single erroneous computation result, a hardware fault cryptanalysis can totally break the RSA system by factoring the public modulus. Some countermeasures by using a simple verification function (e.g., raising a signature to the power of public key) or fault detection (e.g., an expanded modulus approach) have been reported in the literature, however it will be pointed out in this paper that very few of these existing solutions are both sound and efficient. Unreasonably, in these methods, they assume that a comparison instruction will always be fault free when developing countermeasures against hardware fault cryptanalysis. Researches show that the expanded modulus approach proposed by Shamir is superior to the approach of using a simple verification function when other physical cryptanalysis (e.g., timing cryptanalysis) is considered. So, we intend to improve Shamir's method. In this paper, the new concept of fault infective CRT computation and fault infective CRT recombination are proposed. Based on the new concept, two novel protocols are developed with rigorous proof of security. Two possible parameter settings are provided for the protocols. One setting is to select a small public key e and the proposed protocols can have comparable performance to Shamir's scheme. The other setting is to have better performance than Shamir's scheme (i.e., having comparable performance to conventional CRT speedup) but with a large public key. Most importantly, we wish to emphasize the importance of developing and proving the security of physically secure protocols without relying on unreliable or unreasonable assumptions, e.g., always fault free instructions.

Integer decomposition for fast scalar multiplication on elliptic curves

Abstract: Since Miller and Koblitz applied elliptic curves to cryptographic system in 1985[3,6], a lot of researchers have been interested in this field and various speedup techniques for the scalar multiplication have been developed. Recently, Gallant et al. published a method that accelerates the scalar multiplication and is applicable to a larger class of curves[4]. In the process of their method, they assumed the existence of a special pair of two short linearly independent vectors. Once a pair of such vectors exists, their decomposition method improves the efficiency of the scalar multiplication roughly about 50%. In this paper, we state and prove a necessary condition for the existence of a pair of desired vectors and we also present an algorithm to find them.

A Generalized Takagi-Cryptosystem with a modulus of the form prqs

Abstract: In this paper, we propose a generalized Takagi-Cryptosystem with a modulus of the form pr qs. We've studied for the optimal choice for r, s that gives the best efficiency while maintaining a prescribed security level, and we show that the choice of either pr qr+1, pr-1 qr+1, or pr-2qr+2 depending on the value r + s is the optimal. We also present comparison tables for the efficiency of RSA, the multiprime technology, Takagi's scheme, and our proposed scheme.

Guide to Elliptic Curve Cryptography

Abstract: After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application. Features & Benefits: * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology * Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic* Distills complex mathematics and algorithms for easy understanding* Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software toolsThis comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.

The Montgomery Powering Ladder

Abstract: This paper gives a comprehensive analysis of Montgomery powering ladder. Initially developed for fast scalar multiplication on elliptic curves, we extend the scope of Montgomery ladder to any exponentiation in an abelian group. Computationally, the Montgomery ladder has the triple advantage of presenting a Lucas chain structure, of being parallelized, and of sharing a common operand. Furthermore, contrary to the classical binary algorithms, it behaves very regularly, which makes it naturally protected against a large variety of implementation attacks.

Fault Injection Attacks on Cryptographic Devices: Theory, Practice, and Countermeasures

Abstract: Implementations of cryptographic algorithms continue to proliferate in consumer products due to the increasing demand for secure transmission of confidential information. Although the current standard cryptographic algorithms proved to withstand exhaustive attacks, their hardware and software implementations have exhibited vulnerabilities to side channel attacks, e.g., power analysis and fault injection attacks. This paper focuses on fault injection attacks that have been shown to require inexpensive equipment and a short amount of time. The paper provides a comprehensive description of these attacks on cryptographic devices and the countermeasures that have been developed against them. After a brief review of the widely used cryptographic algorithms, we classify the currently known fault injection attacks into low-cost ones (which a single attacker with a modest budget can mount) and high-cost ones (requiring highly skilled attackers with a large budget). We then list the attacks that have been developed for the important and commonly used ciphers and indicate which ones have been successfully used in practice. The known countermeasures against the previously described fault injection attacks are then presented, including intrusion detection and fault detection. We conclude the survey with a discussion on the interaction between fault injection attacks (and the corresponding countermeasures) and power analysis attacks.

Fault Based Cryptanalysis of the Advanced Encryption Standard (AES)

Abstract: In this paper we describe several fault attacks on the Ad- vanced Encryption Standard (AES). First, using optical/eddy current fault induction attacks as recently publicly presented by Skorobogatov, Anderson and Quisquater, Samyde (SA,QS), we present an implemen- tation independent fault attack on AES. This attack is able to deter- mine the complete 128-bit secret key of a sealed tamper-proof smart- card by generating 128 faulty cipher texts. Second, we present several implementation-dependent fault attacks on AES. These attacks rely on the observation that due to the AES's known timing analysis vulnera- bility (as pointed out by Koeune and Quisquater (KQ)), any implemen- tation of the AES must ensure a data independent timing behavior for the so called AES's xtime operation. We present fault attacks on AES based on various timing analysis resistant implementations of the xtime- operation. Our strongest attack in this direction uses a very liberal fault model and requires only 256 faulty encryptions to determine a 128-bit key.

Side-Channel Attacks: Ten Years After Its Publication and the Impacts on Cryptographic Module Security Testing.

Abstract: Side-channel attacks are easy-to-implement whilst powerful attacks against cryptographic implementations, and their targets range from primitives, protocols, modules, and devices to even systems. These attacks pose a serious threat to the security of cryptographic modules. In consequence, cryptographic implementations have to be evaluated for their resistivity against such attacks and the incorporation of different countermeasures has to be considered. This paper surveys the methods and techniques employed in these attacks, the destructive effects of such attacks, the countermeasures against such attacks and evaluation of their feasibility and applicability. Finally, the necessity and feasibility of adopting this kind of physical security testing and evaluation in the development of FIPS 140-3 standard are explored. This paper is not only a survey paper, but also more a position paper.