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Guide to Elliptic Curve Cryptography
, 2004
"... Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves ..."
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Cited by 610 (18 self)
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also figured prominently in the recent proof of Fermat's Last Theorem by Andrew Wiles. Originally pursued for purely aesthetic reasons, elliptic curves have recently been utilized in devising algorithms for factoring integers, primality proving, and in publickey cryptography. In this article, we
Cryptography
"... The Rivest Shamir Adleman (RSA) cryptosystem, named after its creators, is one of the most popular public key cryptosystems. It is most widely used for its strong security feature and easy implementation. The RSA cryptosystem has been utilized for many ecommerce applications, various forms of authe ..."
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of authentication, and virtual private networks in any organizations. The importance of high security and faster implementations paved the way for hardware implementations of the RSA algorithm. This work consists of describing a new approach to enhance RSA security. In this paper we will enhance the security
Hardware Architectures for Public Key Cryptography
, 2002
"... This paper presents an overview of hardware implementations for the two commonly used types of Public Key Cryptography, i.e. RSA and Elliptic Curve Cryptography (ECC), both based on modular arithmetic. We first discuss the mathematical background and the algorithms to implement these cryptosystems. ..."
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Cited by 30 (7 self)
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This paper presents an overview of hardware implementations for the two commonly used types of Public Key Cryptography, i.e. RSA and Elliptic Curve Cryptography (ECC), both based on modular arithmetic. We first discuss the mathematical background and the algorithms to implement these cryptosystems
Comparing elliptic curve cryptography and RSA on 8bit CPUs
 in Proc. of the Sixth Workshop on Crypto graphic Hardware and Embedded Systems (CHES’04
, 2004
"... Abstract. Strong publickey cryptography is often considered to be too computationally expensive for small devices if not accelerated by cryptographic hardware. We revisited this statement and implemented elliptic curve point multiplication for 160bit, 192bit, and 224bit NIST/SECG curves over GF ..."
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Cited by 189 (2 self)
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Abstract. Strong publickey cryptography is often considered to be too computationally expensive for small devices if not accelerated by cryptographic hardware. We revisited this statement and implemented elliptic curve point multiplication for 160bit, 192bit, and 224bit NIST/SECG curves over
Hardware Assisted Elliptic Curve Cryptography
, 2001
"... The increased vulnerability of network attached computers has elevated the need for strong security methods. At the same time, advancements in the the area of cryptography have risen to meet this challenge. This report concerns one particular form of cryptography which uses the mathematics of ellipt ..."
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The increased vulnerability of network attached computers has elevated the need for strong security methods. At the same time, advancements in the the area of cryptography have risen to meet this challenge. This report concerns one particular form of cryptography which uses the mathematics
Efficient Unified Arithmetic for Hardware Cryptography
"... The basic arithmetic operations (i.e. addition, multiplication, and inversion) in finite fields, GF (q), where q = pk and p is a prime integer, have several applications in cryptography, such as RSA algorithm, DiffieHellman key exchange algorithm [1], the US federal Digital Signature Standard [2], ..."
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The basic arithmetic operations (i.e. addition, multiplication, and inversion) in finite fields, GF (q), where q = pk and p is a prime integer, have several applications in cryptography, such as RSA algorithm, DiffieHellman key exchange algorithm [1], the US federal Digital Signature Standard [2
Practical symmetric key cryptography on modern graphics hardware
 In Proc. USENIX ’08
"... Graphics processors are continuing their trend of vastly outperforming CPUs while becoming more general purpose. The latest generation of graphics processors have introduced the ability handle integers natively. This has increased the GPU’s applicability to many fields, especially cryptography. This ..."
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Cited by 40 (3 self)
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Graphics processors are continuing their trend of vastly outperforming CPUs while becoming more general purpose. The latest generation of graphics processors have introduced the ability handle integers natively. This has increased the GPU’s applicability to many fields, especially cryptography
Analysis of AES Hardware Implementations
 PREPRINT
, 2003
"... Following paper examines hardware implementation methods regarding Advanced Encryption Standard (AES). Compared to software implementation, migrating to hardware provides higher level of security and faster encryption speed. An overview of existing AES hardware implementation techniques are summariz ..."
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Cited by 3 (0 self)
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are summarized. Then the direction of recon#12;gurable coprocessor as a cryptography hardware is proposed.
Founding Cryptography on TamperProof Hardware Tokens
"... A number of works have investigated using tamperproof hardware tokens as tools to achieve a variety of cryptographic tasks. In particular, Goldreich and Ostrovsky considered the goal of software protection via oblivious RAM. Goldwasser, Kalai, and Rothblum introduced the concept of onetime program ..."
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Cited by 19 (5 self)
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A number of works have investigated using tamperproof hardware tokens as tools to achieve a variety of cryptographic tasks. In particular, Goldreich and Ostrovsky considered the goal of software protection via oblivious RAM. Goldwasser, Kalai, and Rothblum introduced the concept of one
Efficient Acceleration of Asymmetric Cryptography on Graphics Hardware
 AFRICACRYPT 2009
, 2009
"... Graphics processing units (GPU) are increasingly being used for general purpose computing. We present implementations of large integer modular exponentiation, the core of publickey cryptosystems such as RSA, on a DirectX 10 compliant GPU. DirectX 10 compliant graphics processors are the latest gene ..."
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Cited by 20 (1 self)
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Graphics processing units (GPU) are increasingly being used for general purpose computing. We present implementations of large integer modular exponentiation, the core of publickey cryptosystems such as RSA, on a DirectX 10 compliant GPU. DirectX 10 compliant graphics processors are the latest generation of GPU architecture, which provide increased programming flexibility and support for integer operations. We present high performance modular exponentiation implementations based on integers represented in both standard radix form and residue number system form. We show how a GPU implementation of a 1024bit RSA decrypt primitive can outperform a comparable CPU implementation by up to 4 times and also improve the performance of previous GPU implementations by decreasing latency by up to 7 times and doubling throughput. We present how an adaptive approach to modular exponentiation involving implementations based on both a radix and a residue number system gives the best allaround performance on the GPU both in terms of latency and throughput. We also highlight the usage criteria necessary to allow the GPU to reach peak performance on public key cryptographic operations.
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