scholarly journals Public-Key Cryptographic Primitives Provably as Secure as Subset Sum

2010 ◽  
pp. 382-400 ◽  
Author(s):  
Vadim Lyubashevsky ◽  
Adriana Palacio ◽  
Gil Segev
Keyword(s):  
Public Key ◽  
Cryptographic Primitives ◽  
Subset Sum

scholarly journals PKCHD: Towards A Probabilistic Knapsack Public-Key Cryptosystem with High Density

Information ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 75 ◽  
Author(s):  
Yuan Ping ◽  
Baocang Wang ◽  
Shengli Tian ◽  
Jingxian Zhou ◽  
Hui Ma
Keyword(s):  
Chinese Remainder Theorem ◽  
Success Probability ◽  
High Density ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
The Public ◽  
Attack Model ◽  
Simultaneous Diophantine Approximation ◽  
Subset Sum ◽  
Linearization Attack

By introducing an easy knapsack-type problem, a probabilistic knapsack-type public key cryptosystem (PKCHD) is proposed. It uses a Chinese remainder theorem to disguise the easy knapsack sequence. Thence, to recover the trapdoor information, the implicit attacker has to solve at least two hard number-theoretic problems, namely integer factorization and simultaneous Diophantine approximation problems. In PKCHD, the encryption function is nonlinear about the message vector. Under the re-linearization attack model, PKCHD obtains a high density and is secure against the low-density subset sum attacks, and the success probability for an attacker to recover the message vector with a single call to a lattice oracle is negligible. The infeasibilities of other attacks on the proposed PKCHD are also investigated. Meanwhile, it can use the hardest knapsack vector as the public key if its density evaluates the hardness of a knapsack instance. Furthermore, PKCHD only performs quadratic bit operations which confirms the efficiency of encrypting a message and deciphering a given cipher-text.

scholarly journals polarRLCE: A New Code-Based Cryptosystem Using Polar Codes

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Jingang Liu ◽  
Yongge Wang ◽  
Zongxiang Yi ◽  
Zhiqiang Lin
Keyword(s):  
Coding Theory ◽  
Public Key ◽  
Security Level ◽  
Polar Codes ◽  
Encryption Scheme ◽  
Cryptographic Primitives ◽  
The Public ◽  
Security Challenges ◽  
High Security Level ◽  
Code Based Cryptography

Security challenges brought about by the upcoming 5G era should be taken seriously. Code-based cryptography leverages difficult problems in coding theory and is one of the main techniques enabling cryptographic primitives in the postquantum scenario. In this work, we propose the first efficient secure scheme based on polar codes (i.e., polarRLCE) which is inspired by the RLCE scheme, a candidate for the NIST postquantum cryptography standardization in the first round. In addition to avoiding some weaknesses of the RLCE scheme, we show that, with the proper choice of parameters, using polar codes, it is possible to design an encryption scheme to achieve the intended security level while retaining a reasonably small public key size. In addition, we also present a KEM version of the polarRLCE scheme that can attain a negligible decryption failure rate within the corresponding security parameters. It is shown that our proposal enjoys an apparent advantage to decrease the public key size, especially on the high-security level.

Bitcoin

2020 ◽  
pp. 241-258
Author(s):  
Andreas Bolfing
Keyword(s):  
Elliptic Curve Cryptography ◽  
Peer To Peer ◽  
Third Party ◽  
Public Key ◽  
Cryptographic Primitives ◽  
The Public ◽  
A Chain ◽  
Basic Ideas ◽  
Electronic Coin ◽  
Electronic Payment System

Bitcoin was proposed by Nakamoto (2008) as the first electronic payment system, which fully relies on cryptographic primitives in order to work over a purely peer-to-peer system, where everyone can participate in spending funds to other users without the need for a trusted third party. This chapter first introduces the basic ideas of Satoshi Nakamoto, who defined an electronic coin as a chain of digital signatures. It explains how the addresses in Bitcoin are derived, and how the elliptic curve cryptography (ECC) key pair is used in order to transact funds from one user to another. For this, it shows how the transactions are constructed in Bitcoin, based on the most common transaction, which is the Pay-to-Public-Key-Hash transaction. The last section then shows how the transactions are permanently stored in the public ledger, the blockchain, and how the miners solve the Proof-of-Work in order to safeguard the records.

Cryptographic Primitives

2020 ◽  
pp. 57-134
Author(s):  
Andreas Bolfing
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Public Key ◽  
Public Key Encryption ◽  
Cryptographic Primitives ◽  
Digital Signature Algorithm ◽  
Digital Signature Scheme ◽  
Current Standards

This chapter provides a very detailed introduction to cryptography. It first explains the cryptographic basics and introduces the concept of public-key encryption which is based on one-way and trapdoor functions, considering the three major public-key encryption families like integer factorization, discrete logarithm and elliptic curve schemes. This is followed by an introduction to hash functions which are applied to construct Merkle trees and digital signature schemes. As modern cryptoschemes are commonly based on elliptic curves, the chapter then introduces elliptic curve cryptography which is based on the Elliptic Curve Discrete Logarithm Problem (ECDLP). It considers the hardness of the ECDLP and the possible attacks against it, showing how to find suitable domain parameters to construct cryptographically strong elliptic curves. This is followed by the discussion of elliptic curve domain parameters which are recommended by current standards. Finally, it introduces the Elliptic Curve Digital Signature Algorithm (ECDSA), the elliptic curve digital signature scheme.

An Improvement for Fully Homomorphic Encryption over Integers with Shorter Public Keys

2014 ◽  
Vol 989-994 ◽  
pp. 4326-4331
Author(s):  
Ze Tao Jiang ◽  
Xiao Te Huang
Keyword(s):  
Quadratic Form ◽  
Homomorphic Encryption ◽  
Public Key ◽  
Encryption Scheme ◽  
Fully Homomorphic Encryption ◽  
The Public ◽  
Cubic Form ◽  
Public Keys ◽  
Subset Sum ◽  
Approximate Gcd

This paper puts forward a more efficient fully homomorphic encryption scheme with a view to improving the oversized public key based on the Dijk’s scheme.Encrypted with a cubic form in the public key elements instead of quadratic form by adopting Gentry’s fully homomorphic techonology.The results show that the public key size reduce from to compared to the Coron’s scheme.The security of the proposed scheme is based on both the approximate GCD problem and the sparse-subset sum problem.

An Extended Knapsack Public Key Cryptosystem

2013 ◽  
Vol 441 ◽  
pp. 678-681
Author(s):  
Xiao Ping Ji ◽  
Hai Bin Zhang ◽  
Bo Ying Wu ◽  
Guang Yu Li
Keyword(s):  
High Density ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Low Density ◽  
Subset Sum Problem ◽  
Encryption And Decryption ◽  
Subset Sum

We analyzed a typical cryptosystem and an easy extended knapsack subset sum problem is proposed. The solution is not chosen from any longer but from. Based on the problem, we construct a public key cryptosystem in which the plaintext is divided into some groups and each group has bits, so that the encryption and decryption can be very fast. The possible attacks are analyzed. Our cryptosystem not only can resist Shamir's attack but also can resist the low density attack, because of its high density. The number of the sequence is also much shorter than before with the same density.

scholarly journals Efficient and Provable Secure Pairing-Free Security-Mediated Identity-Based Identification Schemes

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Ji-Jian Chin ◽  
Syh-Yuan Tan ◽  
Swee-Huay Heng ◽  
Raphael C.-W. Phan
Keyword(s):  
Discrete Logarithm ◽  
Bilinear Pairings ◽  
Public Key ◽  
Encryption Scheme ◽  
Secret Key ◽  
Cryptographic Primitives ◽  
Main Motivation ◽  
Identification Scheme ◽  
Identification Schemes ◽  
Identity Based

Security-mediated cryptography was first introduced by Boneh et al. in 2001. The main motivation behind security-mediated cryptography was the capability to allow instant revocation of a user’s secret key by necessitating the cooperation of a security mediator in any given transaction. Subsequently in 2003, Boneh et al. showed how to convert a RSA-based security-mediated encryption scheme from a traditional public key setting to an identity-based one, where certificates would no longer be required. Following these two pioneering papers, other cryptographic primitives that utilize a security-mediated approach began to surface. However, the security-mediated identity-based identification scheme (SM-IBI) was not introduced until Chin et al. in 2013 with a scheme built on bilinear pairings. In this paper, we improve on the efficiency results for SM-IBI schemes by proposing two schemes that are pairing-free and are based on well-studied complexity assumptions: the RSA and discrete logarithm assumptions.

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