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Register a new userCode based Cryptography: Classic McEliece
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Added by
Harshdeep Singh
Publication date
2019
fields
Informatics Engineering
and research's language is
English
Authors
Harshdeep Singh
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This article addresses code-based cryptography and is designed to depict the complete outline of a code based public key cryptosystem. This report includes basic mathematics and fundamentals of coding theory which are useful for studying code-based cryptography. Here, we briefly describe the first scheme of code based public key cryptosystems given by R. J. McEliece in 1978 and its improved version given by H. Niederreiter in 1986. We discuss the hard problems of coding theory which are used in code based cryptography and some classic attacks on it like information-set decoding (ISD). Successful implementation of the ISD attack on McEliece cryptosystem for some small parameters set is executed and the code for the same is provided in the Appendix. This report elaborates a key encapsulation mechanism (KEM), namely Classic McEliece, based on algebraic coding theory to establish a symmetric key for two users.
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In this paper we proposed an authentication technique based on the user cards, to improve the authentication process in systems that allows remote access for the users, and raise the security rate during an exchange of their messages. in this technique the server performs two functions, the first function, register the users, and give him user ID, PIN code, and user private card contains secrecy information, which is used to encrypt user messages by using two kinds of encryption symmetric using RC4-Pr and asymmetric using RSA encryption., the second function, distribute the users public card if the user demand that, in which the user sends the own authentication code with their own user ID and recipient user ID to the authentication check, and then the server sends the user public card to the recipient user, thus the sender user can send the messages to recipient user without back to the server again. We attained confidentiality using RC4-Pr and RSA encryption and message authentication, user signature, and mutual secret key by using RSA encryption. in this paper we also implement the proposal in [1] RC4-pr algorithm which is modified to improve the key weakness of basic RC4.
Recently, it has been shown how McEliece public-key cryptosystems based on moderate-density parity-check (MDPC) codes allow for very compact keys compared to variants based on other code families. In this paper, classical (iterative) decoding schemes for MPDC codes are considered. The algorithms are analyzed with respect to their error-correction capability as well as their resilience against a recently proposed reaction-based key-recovery attack on a variant of the MDPC-McEliece cryptosystem by Guo, Johansson and Stankovski (GJS). New message-passing decoding algorithms are presented and analyzed. Two proposed decoding algorithms have an improved error-correction performance compared to existing hard-decision decoding schemes and are resilient against the GJS reaction-based attack for an appropriate choice of the algorithms parameters. Finally, a modified belief propagation decoding algorithm that is resilient against the GJS reaction-based attack is presented.
Differential privacy (DP) has arisen as the state-of-the-art metric for quantifying individual privacy when sensitive data are analyzed, and it is starting to see practical deployment in organizations such as the US Census Bureau, Apple, Google, etc. There are two popular models for deploying differential privacy - standard differential privacy (SDP), where a trusted server aggregates all the data and runs the DP mechanisms, and local differential privacy (LDP), where each user perturbs their own data and perturbed data is analyzed. Due to security concerns arising from aggregating raw data at a single server, several real world deployments in industry have embraced the LDP model. However, systems based on the LDP model tend to have poor utility - a gap in the utility achieved as compared to systems based on the SDP model. In this work, we survey and synthesize emerging directions of research at the intersection of differential privacy and cryptography. First, we survey solutions that combine cryptographic primitives like secure computation and anonymous communication with differential privacy to give alternatives to the LDP model that avoid a trusted server as in SDP but close the gap in accuracy. These primitives introduce performance bottlenecks and necessitate efficient alternatives. Second, we synthesize work in an area we call DP-Cryptography - cryptographic primitives that are allowed to leak differentially private outputs. These primitives have orders of magnitude better performance than standard cryptographic primitives. DP-cryptographic primitives are perfectly suited for implementing alternatives to LDP, but are also applicable to scenarios where standard cryptographic primitives do not have practical implementations. Through this unique lens of research taxonomy, we survey ongoing research in these directions while also providing novel directions for future research.
We present an attack against a code-based signature scheme based on the Lyubashevsky protocol that was recently proposed by Song, Huang, Mu, Wu and Wang (SHMWW). The private key in the SHMWW scheme contains columns coming in part from an identity matrix and in part from a random matrix. The existence of two types of columns leads to a strong bias in the distribution of set bits in produced signatures. Our attack exploits such a bias to recover the private key from a bunch of collected signatures. We provide a theoretical analysis of the attack along with experimental evaluations, and we show that as few as 10 signatures are enough to be collected for successfully recovering the private key. As for previous attempts of adapting Lyubashevskys protocol to the case of code-based cryptography, the SHMWW scheme is thus proved unable to provide acceptable security. This confirms that devising secure code-based signature schemes with efficiency comparable to that of other post-quantum solutions (e.g., based on lattices) is still a challenging task.
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