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Bits Security of the Elliptic Curve Diffie–Hellman Secret Keys [chapter]

Dimitar Jetchev, Ramarathnam Venkatesan
Lecture Notes in Computer Science  
We show that the least significant bits (LSB) of the elliptic curve Diffie-Hellman secret keys are hardcore.  ...  factor overhead, one can compute the entire Diffie-Hellman secret on a polynomial fraction of all the curves over the same finite field.  ...  The analogous problem for elliptic curves studies the bit security of the following function: Diffie-Hellman function: Let E be an elliptic curve over F p and let P ∈ E be a point of prime order q.  ... 
doi:10.1007/978-3-540-85174-5_5 fatcat:5mj7uxfq7vhbxc7ebg7ay4d3ku

The Performance of Elliptic Curve Based Group Diffie-Hellman Protocols for Secure Group Communication over Ad Hoc Networks

Yong Wang, Byrav Ramamurthy, Xukai Zou
2006 2006 IEEE International Conference on Communications  
The security of the two party Diffie-Hellman key exchange protocol is currently based on the discrete logarithm problem (DLP).  ...  However, it can also be built upon the elliptic curve discrete logarithm problem (ECDLP). Most proposed secure group communication schemes employ the DLP-based Diffie-Hellman protocol.  ...  Group Elliptic Curve Diffie-Hellman Protocol The Group Elliptic Curve Diffie-Hellman (GECDH) protocol is an extension of GDH based on ECDLP.  ... 
doi:10.1109/icc.2006.255104 dblp:conf/icc/WangRZ06 fatcat:zrryl4ndrbd5xnarqd2txdvmgm

RSA, DH, and DSA in the Wild [article]

Nadia Heninger
2022 IACR Cryptology ePrint Archive  
Martijn Stam for organizing and kitten-herding the editing of this wonderful book.  ...  Acknowledgements I am grateful to Shaanan Cohney, Matthew Green, Paul Kocher, Daniel Moghimi, Keegan Ryan and the anonymous reviewers for helpful suggestions, anecdotes and feedback, and to Joppe Bos and  ...  Small Secret Keys Because the security of (EC)DSA relies on the (elliptic-curve) discrete logarithm of the public key y or Y being hard to compute, the secret key x should be difficult to guess.  ... 
dblp:journals/iacr/Heninger22 fatcat:g24spdzscbdn7ojc3fvx7it7cy

SPDH - A Secure Plain Diffie-Hellman Algorithm

Henrik Tange, Birger Andersen
2012 Journal of Cyber Security and Mobility  
Secure communication in a wireless system or end-to-end communication requires setup of a shared secret. This shared secret can be obtained by the use of a public key cryptography system.  ...  Other algorithms as for instance ECMQV (Elliptic Curve Menezes Qo Vanstone) can handle this problem but is far more complex and slower because the algorithm is a three-pass algorithm whereas the DiffieHellman  ...  The secure Plain Diffie-Hellman algorithm is based on Elliptic Curve Cryptography and uses standard implementations of AES and HMAC to enhance security.  ... 
doi:10.13052/jcsm2245-1439.1231 fatcat:pulps7p2zjhfdjhmtyvj2ekivq

Fast Elliptic Curve Cryptography in OpenSSL [chapter]

Emilia Käsper
2012 Lecture Notes in Computer Science  
Our implementation is fully integrated into OpenSSL 1.0.1: full TLS handshakes using a 1024-bit RSA certificate and ephemeral Elliptic Curve Diffie-Hellman key exchange over P-224 now run at twice the  ...  We present a 64-bit optimized implementation of the NIST and SECG-standardized elliptic curve P-224.  ...  Acknowledgements The author is grateful to Daniel J. Bernstein, Ian Goldberg, Adam Langley and Bodo Möller for their comments on the implementation.  ... 
doi:10.1007/978-3-642-29889-9_4 fatcat:2rui4auv65eobl4wsldewhpn2e

Prospective Utilization of Elliptic Curve Cryptography for Security: Authentication, Encryption and Decryption

Shabnoor Qureshi, Prof. Somesh Dewangan
2014 IOSR Journal of Computer Engineering  
This paper presents the design principles of elliptic curve public key cryptography, Authentication, Encryption and Decryption with shorter key of RSA.  ...  To overcome such type of difficulties the elliptic curve discrete logarithm is introduced, which provides advantages, whose public key is short, network bandwidth is small and ability to defend against  ...  Somesh Dewangan involving Dept. of M. Tech Computer Science and Engineering, Disha Institute of Management And Technology for giving constant inspiration for this work. I am also thankful to Mrs.  ... 
doi:10.9790/0661-16383135 fatcat:ffm24xv7urfldh3ryihvtvaqpi

Network Security System with Optimized Randomized Multiple Key Exchange Algorithm

2020 VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE  
The proposed three algorithms namely 1) Modified Simple Password Key Exchange Scheme 2) Modified Diffie-Hellman Key exchange Scheme 3) Modified Elliptic Curve Scheme are meant to provide shared secret  ...  This paper illustrates three different algorithms to provide shared secret key for security of the system.  ...  Elliptic Curve Diffie-Hellman (ECDH) Key Exchange protocol provides a shared key between client and server .  ... 
doi:10.35940/ijitee.b6849.019320 fatcat:hcibov3rnng2xasgc5iq7g3zku

Diffie-Hellman Key Agreement with Elliptic Curve Discrete Logarithm Problem

Samta Gajbhiye, Sanjeev Karmakar, Monisha Sharma
2015 International Journal of Computer Applications  
Elliptic curve cryptography, Elliptic Curve Diffiee Hellman(ECDH)  ...  This paper implements Diffie -Hellman Key aggrement Procotocol using Elliptic Curve as the mathematical technique over prime field F p Keywords Diffie-Hellman key Agreement protocol.  ...  Section 2 and 3 discusses the background of Elliptic Curve Cryptography and Elliptic Curve Diffie Hellman Key Exchange Protocol. Section 4 shows the implementation results ECDLP-based Diffie Hellman.  ... 
doi:10.5120/ijca2015907030 fatcat:4hmuhvu4pvfn5g5pxp4x5pqk3i

Survey on Public Key Cryptography Scheme for Securing Data in Cloud Computing

J. Athena, V. Sumathy
2017 Circuits and Systems  
This paper presents the brief review of major cryptographic techniques such as Rivest, Shamir Adleman (RSA), Dffie Hellman and the Elliptic Curve Cryptography (ECC) associated key sizes.  ...  The initialization of random prime numbers and the key computation based on the points on the elliptic curve assures the high-security compared to the existing schemes with the minimum time consumption  ...  Security is attractive feature of elliptic curve cryptography. Elliptic curve cryptosystems also are more computationally efficient RSA and Diffie-Hellman.  ... 
doi:10.4236/cs.2017.83005 fatcat:5s4pj3vzrvekla6nnyb2diizpu

Security Analysis of the Strong Diffie-Hellman Problem [chapter]

Jung Hee Cheon
2006 Lecture Notes in Computer Science  
Further we apply this algorithm to the schemes based on the Diffie-Hellman problem on an abelian group of prime order p.  ...  As a result, we reduce the complexity of recovering the secret key from O( √ p) to O( p/d) for Boldyreva's blind signature and the original ElGamal scheme when p − 1 (resp. p + 1) has a divisor d ≤ p 1  ...  I would also like to thank the anonymous reviewers for their valuable suggestions.  ... 
doi:10.1007/11761679_1 fatcat:rtjmtgc5xzcfncfq5wnevfnqym

Diffie Hellman Stand the Test of Time (Protocol's Limitations, Applications and Functional Divergence)

Avenash Kumar, Sufian Hameed
2020 International Journal of Computer Applications  
The Diffie-Hellman Key Exchange (DHKE) protocol is the well-known asymmetric algorithm formulated by its namesakes Whitfield Diffie and Martin Hellman in 1976.  ...  Cryptography plays a vital role in protecting secret information, as secure communication between two parties over the internet is the necessity and cannot be overstated.  ...  In doing so, we have discussed the limitations in different variants of DHKE protocol which are supposed to be secure compare to the classical DHKE protocol.  ... 
doi:10.5120/ijca2020920380 fatcat:aiibf3ocajgs5ned6gm23lzna4

Page 5697 of Mathematical Reviews Vol. , Issue 2003g [page]

2003 Mathematical Reviews  
Our results show that just predicting one bit of the elliptic curve Diffie- Hellman secret in a family of curves is as hard as computing the entire secret.”  ...  of the bits of the Diffie- Hellman secret is as hard as computing the entire secret.  ... 

The energy cost of cryptographic key establishment in wireless sensor networks

Johann Großschädl, Alexander Szekely, Stefan Tillich
2007 Proceedings of the 2nd ACM symposium on Information, computer and communications security - ASIACCS '07  
The second protocol is based on ECMQV, an authenticated version of the elliptic curve Diffie-Hellman key exchange, and uses a 256-bit prime field GF(p) as underlying algebraic structure.  ...  Therefore, the implementation of effective and secure techniques for setting up a shared secret key between sensor nodes is a challenging task.  ...  ACKNOWLEDGEMENTS The authors are grateful to Erkay Savaş and Ingrid Verbauwhede for valuable comments on a draft version of this paper.  ... 
doi:10.1145/1229285.1229334 dblp:conf/ccs/GrossschadlST07 fatcat:z36lp7i6crdrlocgovkadk5u7m

SDR implementation of a D2D security cryptographic mechanism

Titus N. Balan, Alexandra C. Balan, Florin D. Sandu
2019 IEEE Access  
This paper proposes a security mechanism for D2D communication involving the use of physically unclonable functions (PUF) for unique key generation, elliptic-curve cryptography (ECC) and Diffie-Hellman  ...  INDEX TERMS Device to device, Diffie-Hellman key exchange, encryption, elliptic-curve cryptography, key management, physically unclonable function, proximity services (ProSe), security, software defined  ...  DIFFIE HELLMAN KEY EXCHANGE Elliptic curve Diffie-Hellman is an anonymous key agreement protocol that allows two parties, each having an elliptic curve public-private key pair, to establish a shared ''  ... 
doi:10.1109/access.2019.2904909 fatcat:wmwxxef77fhzhkqj6z4xwle654

An Enhanced Elliptic Curve Cryptosystem for Securing Data

Edward Kwadwo, James Ben, Frimpong Twum
2018 International Journal of Computer Applications  
The first phase of the project involves understanding the key exchange of Diffie-Hellman and applying the properties of the Elliptic Curves.  ...  Elliptic Curve cryptosystem (ECC) is a technique of public-key encryption, which is rooted on the arithmetical construction of elliptic curves over finite fields.  ...  Diffie-Hellman object Proposed Procedure The steps involved in the proposed procedure involves standard techniques such as the Diffie-Hellman key exchange algorithm, elliptic curve properties and computations  ... 
doi:10.5120/ijca2018917688 fatcat:sbn4oplcfnd2xjn7axxddpak6a
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