A Novel Digital Signature based on Error Correcting Codes

Computer Communications, 1997

A new cryptographic system is presented in this paper which combines error-correction techniques with cryptographic protection as secure as one might want. The proposed system is based on the following: given a linear block code (n, k), n > k, we have a lot of possibilities to distribute 'k' information symbols among 'n' symbols composing the code word. A method for the cryptanalysis of the system is also proposed. These possibilities increase when n > > k and include the order and place of the 'k' symbols among the 'n' symbols. Practical results were obtained via simulation on a PC486,66 MHz, where the proposed system and its cryptographic analysis were implemented. 0 1997 Elsevier Science B.V.

2013 21st Telecommunications Forum Telfor (TELFOR), 2013

Error-correcting codes based on quasigroups are defined elsewhere. These codes are a combination of cryptographic algorithms and error correcting codes. In a paper of ours we succeed to improve the speed of the decoding process by defining new algorithm for coding and decoding, named "cut-decoding algorithm". Here, a new modification of the cut-decoding algorithm is considered in order to obtain further improvements of the code performances. We present several experimental results obtained with different decoding algorithms for these codes.

Applicable Algebra in Engineering, Communication and Computing, 2008

In this paper, we give and explain some illustrative examples of research topics where error-correcting codes overlap with cryptography. In some of these examples, error-correcting codes employed in the implementation of secure cryptographic protocols. In the others, the codes are used in attacks against cryptographic schemes. Throughout this paper, we show the interrelation between errorcorrecting codes and cryptography, as well as point out the common features and the differences between these two fields.

International Journal of Electrical and Computer Engineering (IJECE), 2023

Digital signatures are in high demand because they allow authentication and non-repudiation. Existing digital signature systems, such as digital signature algorithm (DSA), elliptic curve digital signature algorithm (ECDSA), and others, are based on number theory problems such as discrete logarithmic problems and integer factorization problems. These recently used digital signatures are not secure with quantum computers. To protect against quantum computer attacks, many researchers propose digital signature schemes based on error-correcting codes such as linear, Goppa, polar, and so on. We studied 16 distinct papers based on various error-correcting codes and analyzed their various features such as signing and verification efficiency, signature size, public key size, and security against multiple attacks.

Nowadays, all our information are kept in electronic form using the internet and trust that it cannot be accessed by anyone except the intended recipient. For the sake of this purpose, digital signature schemes play a significant role in providing authenticity and record management efficiency. A digital signature is an encoded record that moves with the electronically available document which needs to be signed and returns after the transaction has been completed. In code-based cryptography many digital signature scheme were given among them is CFS code-based digital signature scheme introduced in 2001. It is still considered to be the most popular electronically based signature scheme. The major drawback of this algorithm is its large publickey size. Due to this problem of CFS algorithm, new scheme is presented in this paper using the modified Quasi Cyclic LDPC code and LLR-BP decoding algorithm by replacing the Goppa code and the Patternson decoding scheme for the signing process. This scheme provides a fast and secure signature with public key size smaller than the previously existing schemes and it also strengthens the signature without being compromised with its security.

Tatra Mountains Mathematical Publications, 2019

In this paper we introduce a new cryptographic system which is based on the idea of encryption due to [McEliece, R. J. A public-key cryptosystem based on algebraic coding theory, DSN Progress Report. 44, 1978, 114–116]. We use the McEliece encryption system with a new linear error-correcting code, which was constructed in [Hannusch, C.—Lakatos, P.: Construction of self-dual binary 22 k, 22 k−1, 2 k-codes, Algebra and Discrete Math. 21 (2016), no. 1, 59–68]. We show how encryption and decryption work within this cryptosystem and we give the parameters for key generation. Further, we explain why this cryptosystem is a promising post-quantum candidate.

2012

The purpose of introducing of this algorithm is a new method for designing a simple mechanism for producing a digital signature. Some applications like multi agent systems transfer messages with low size and capacity. The new algorithm minimizes the size of original file and gives us a dynamic and smaller size output. In this algorithm read the input file then hash the message and encode it. Finally modify the established code into a unique ID at Base 16. We concentrate on designing and implementation of functions of algorithm.

Cryptography is the science of encrypting the information so that it is rendered unreadable for an intruder. Cryptographic techniques are of utmost importance in today’s world as the information to be sent might be of invaluable importance to both the sender and the receiver. Various cryptographic techniques ensure that even if an intruder intercepts the sent information, he is not able to decipher it thus render ending it useless for the intruder. Cryptography can be grouped into two types, that is Symmetric key cryptography and Asymmetric key cryptography. Symmetric key cryptography uses the same key for encryption as well as decryption thus making it faster compared to Asymmetric Key cryptography which uses different keys for encryption and decryption. Generation of dynamic keys for Symmetric key cryptography is an interesting field and in this we have tapped this field so as to generate dynamic keys for symmetric key cryptography. In this work, we have devised an algorithm for generating dynamic keys for sending messages over a communication channel and also solving key refreshment problem.

eprint.iacr.org

Signcryption is a cryptographic protocol that provides authentication and confidentiality as a single primitive at a cost lower than the combined cost of sign and encryption. Due to the improved efficiency, signcryption schemes have found significant applications in areas related to E-commerce. Shor's algorithm poses a threat to number-theoretic algorithms, as it can solve the number-theoretic hard problems in polynomial time using quantum computers. Therefore, code-based cryptography offers an exciting alternative to number-theoretic cryptography, as it is not only resistant to quantum algorithms, but also, the base operation (matrix-vector multiplication) is far less computationally intensive compared to the modular exponentiation required in number-theoretic schemes. Courtois, Finiasz and Sendrier proposed the only practical code-based signature(CFS signature) . It can be used to realise many cryptographic primitives. But the signature is currently not provably secure due to the existence of the high rate distinguisher . In this paper, we make use of an alternate key-construct for the CFS signature, and thus prove its existential unforgeability under chosen message attacks (EUF-CMA). Also, we propose a code-based signcryption scheme and proved its security. To the best of our knowledge, this is the first code-based, provably secure signature and signcryption scheme in literature.

People have traditionally used signatures as a means of informing others that the signature has read and understood a document. Digital signature in a document is bound to that document in such a way that altering the signed document or moving the signature to a different document invalidates the signature. This security eliminates the need for paper copies of documents and can speed the processes involving documents that require signatures. Digital Signatures are messages that identify and authenticate a particular person as the source of the electronic message, and indicate such persons approval of the information contained in the electronic message. Emerging applications like electronic commerce and secure communications over open networks have made clear the fundamental role of public key cryptosystem as unique security solutions. On the other hand, these solutions clearly expose the fact, that the protection of private keys is a security bottleneck in these sensitive applications. This problem is further worsened in the cases where a single and unchanged private key must be kept secret for very long time (such is the case of certification authority keys, and e-cash keys). They help users to achieve basic security building blocks such as identification, authentication, and integrity.