Single Hard Problem Research Articles

A signature algorithm based on chaotic maps and factoring problems

There has been a great deal of interest in researching the behavior of chaotic systems over the past decade. They are distinguished by their sensitivity to initial conditions, continuous broad-band power spectrum, and similarity to random behavior. Chaos has possible applications in the encryption, compression, and modulation blocks of a digital communication system. The possibility of self-synchronization of chaotic oscillations has spawned a deluge of research on the cryptographic applications of chaos. FAC (Factoring) and CM (Chaotic maps) are used in this research to develop a new signature system (CM). Our system has a higher security level than any other based on a single hard number-theoretic problem since it is extremely unlikely that FAC and CM can be solved effectively at the same time. We further demonstrate that the scheme’s performance involves only minimal operations in signing and validating logarithms, and that it is impervious to attack.

A Strong Designated Verifier Signature Scheme with Hybrid Cryptographic Hard Problems

The security of the most of the existing strong designated verifier signature (SDVS) scheme are based on a single cryptographic hard problem. Although these schemes seem secure today, there is a possibility for an adversary to find a solution for this problem in the future and if this happens, then such SDVS schemes will no longer be secure. We develop a new SDVS scheme based on hybrid problems; factorization and discrete logarithm. The new developed scheme provides a greater security level than those previous designated SDVS schemes and satisfies the security properties and requirements of a SDVS scheme.

A new digital signature scheme with message recovery using hybrid problems

We present a new digital signature scheme with message recovery and its authenticated encryption based on elliptic curve discrete logarithm and quadratic residue. The main idea is to provide a higher level of security than all other techniques that use signatures with single hard problem including factoring, discrete logarithm, residuosity, or elliptic curves. The proposed digital signature schemes do not involve any modular exponentiation operations that leave no gap for attackers. The security analysis demonstrates the improved performance of the proposed schemes in comparison with existing techniques in terms of the ability to resist the most common attacks

Blind multi-signature scheme based on factoring and discrete logarithm problem

One of the important objectives of information security systems is providing authentication of the electronic documents and messages. In that, blind signature schemes are an important solution to protect the privacy of users in security electronic transactions by highlighting the anonymity of participating parties. Many studies have focused on blind signature schemes, however, most of the studied schemes are based on single computationally difficult problem. Also digital signature schemes from two difficult problems were proposed but the fact is that only finding solution to single hard problem then these digital signature schemes are breakable. In this paper, we propose a new signature schemes base on the combination of the RSA and Schnorr signature schemes which are based on two hard problems: IFP and DLP. Then expanding to propose a single blind signature scheme, a blind multi-signature scheme, which are based on new baseline schemes.

Modified ElGamal over RSA Digital Signature Algorithm (MERDSA)

Generally digital signature algorithms are based on a single hard problem like prime factorization problem, discrete logarithm problem, elliptic curve problem. If one finds solution of this single hard problem then these digital signature algorithms will no longer be secured and due to large computational power, this may be possible in future. There are many other algorithms which are based on the hybrid combination of prime factorization and discrete logarithms problem but different weaknesses and attacks have been developed against those algorithms. This paper also presents a new variant of digital signature algorithm which is based on two hard problems, prime factorization and discrete logarithm. Keyword-Digital Signature; Discrete logarithm; Factorization; Cryptanalysis

A new directed signature scheme with hybrid problems

In this paper, we proposed a new directed signature scheme based on hybrid problems; factoring and discrete logarithm. This scheme authorizes only an intended verifier to verify a resulting signature. In fact, both signer and verifier also should be able to prove the resulted signature to any third party whenever necessary. Until today, the security of many existing directed signatures is only based on a single hard problem like factoring, discrete logarithm or elliptic curve discrete logarithm. Although these schemes seem secure nowadays but in a near future, if an adversary finds a solution of these hard problems then the schemes will no longer be secured. Thus, we develop a newly designed scheme which provides greater security level than single hard problem-based scheme since it is impossible for the adversary to solve the two hard problems simultaneously.

An efficient mixed mode and paired cipher text cryptographic algorithm for effective key distribution

SUMMARYWidely used asymmetric key or public key systems such as RSA, Rabin system, ElGamal system, and elliptical curve system are based on a single hard mathematical problem such as factoring or discrete logarithm. Even if these algorithms are very secure now, in the future, the situation may change and someone can solve the single hard problem easily. In this work, a new mixed mode cryptographic algorithm based on RSA is designed, which incorporates three hard mathematical problems (hidden root problem, discrete logarithms, and factoring) to make the algorithm too secure and uses the properties of both symmetric and asymmetric key algorithms. The decryption of the cipher text by the cryptanalysts is very difficult without the knowledge of secret keys, because he or she needs to solve three hard mathematical problems, which is in fact impractical. Copyright © 2012 John Wiley & Sons, Ltd.

Development of a New Elliptic Curve Cryptosystem with Factoring Problem

Problem statement: The security of elliptic curve cryptosystems are based on elliptic curve discrete logarithm problem (ECDLP). However, if an attacker finds a solution to ECDLP, the elliptic curve-based systems will no longer be secure. Approach: To improve this, we develop a new elliptic curve cryptosystem using one of the old/novel problem in computational number theory; factoring problem (FAC). Specifically, our encrypting and decrypting equations will heavily depends on two public keys and two secret keys respectively. Results: We show that, the newly designed cryptosystem is heuristically secure against various algebraic attacks. The complexity of the scheme shows that the time complexity for each encryption and decryption are given by 299Tmul and 270Tmul. Conclusion: The new system provides greater security than that system based on a single hard problem. The attacker has not enough resources to solve the two hard problems simultaneously in a polynomial time.

Secure Hybrid Mode-Based Cryptosystem

Problem statement: A cryptosystem provides two parties; a sender and a receiver to communicate interactively via an insecure channel in which, the sender is able to send any confidential message, document or data in a disguised form to the intended receiver. Upon receiving the disguised message, the receiver converts it to the intelligible message using his secret key. The security of the existing cryptosystems was based on a single hard problem such as factorization, discrete logarithm, quadratic residue, or elliptic curve discrete logarithm. Although these schemes appear secure, one day in a near future they may be broken if one finds a solution of a single hard problem. Approach: To overcome the disadvantage of using a single hard problem, we developed a secure hybrid mode-based cryptosystem based on the two well-known hard problems; factoring and discrete logarithm. We inject the element of the hard problems into our encrypting and decrypting equations respectively in such a way that the former equation depends on two public keys whereas the latter depends on two corresponding secret keys. Results: The new cryptosystem is shown heuristically secure against various algebraic attacks. The efficiency analysis confirms that our scheme only needs 3Texp+Thash time complexity for encryption and 2Texp time complexity for decryption and this magnitude of complexity is considered minimal for multiple hard problems-like cryptosystems. Conclusion: The newly developed hybrid mode based-cryptosystem provides greater security level than that schemes based on a single hard problem. The enemy or adversary has to solve the two problems simultaneously which is unlikely to happen in order to read any secret message.

A New Signature Scheme Based on Multiple Hard Number Theoretic Problems

The past years have seen many attempts to construct digital signature schemes based on a single hard problem, like factoring or discrete logarithm. But in the near future, those systems will no longer be secure if the solution of factoring or discrete logarithms problems is discovered. In this paper, we propose a new signature scheme based on two hard number theoretic problems, factoring and discrete logarithms. The major advantage of our scheme is that it is very unlikely that factoring and discrete logarithms can be efficiently solved simultaneously, and; therefore, the security of our scheme is longer or higher than that of any scheme based on a single hard number theoretic problem. We also show that the performance of the scheme requires only minimal operation both in signing and verifying logarithms and is resistant to attack.

A New Cryptosystem Based on Factoring and Discrete Logarithm Problems

Problem statement: A cryptosystem allows a sender to send any confide ntial or private message using a receiver's public key and later the receiver confirms the integrity of the received message using his secret key. Currently the existin g cryptosystems were developed based on a single hard problem like factoring, discrete logarithm, re siduosity, knapsack or elliptic curve discrete logarithm. Although these schemes appear secure, one day in a near future they may be broken if one finds a solution of a single hard problem. Approach: To solve this problem, we developed a new cryptosystem based on two hard problems; factoring and discrete logarithm. We integrated the two problems in our encrypting and decrypting equations so that the former depends on two public keys whereas the latter depends on two corresponding sec ret keys. Results: The new cryptosystem is shown secure against the most three considering attacks. The efficiency performance of our scheme only requires 3T exp +T mul + T hash time complexity for encryption and 2T exp + T mul time complexity for decryption and this magnitude of complexity is cons idered minimal for multiple hard problems-like cryptosystems. Conclusion: The new cryptosystem based on multiple hard problems provides longer and higher security level than that schemes based o n a single hard problem. The adversary has to solve the two problems simultaneously in order to recover a corresponding plaintext (message) from the received ciphertext (encrypted message).

A new signature scheme based on factoring and discrete logarithms

In this paper, we propose a new signature scheme based on factoring and discrete logarithms. We develop this scheme because it provides a longer or higher level security than that scheme based on a single hard problem since it is very unlikely to solve the two hard problems simultaneously. The newly developed scheme on the other hand requires only minimal and low-complexity computations, thus makes it very efficient.

A New Digital Signature Scheme Based on Factoring and Discrete Logarithms

Problem statement: A digital signature scheme allows one to sign an electronic message and later the produced signature can be validated by the owner of the message or by any verifier. Most of the existing digital signature schemes were developed based on a single hard problem like factoring, discrete logarithm, residuosity or elliptic curve discrete logarithm problems. Although these schemes appear secure, one day in a near future they may be exploded if one finds a solution of the single hard problem. Approach: To overcome this problem, in this study, we proposed a new signature scheme based on multiple hard problems namely factoring and discrete logarithms. We combined the two problems into both signing and verifying equations such that the former depends on two secret keys whereas the latter depends on two corresponding public keys. Results: The new scheme was shown to be secure against the most five considering attacks for signature schemes. The efficiency performance of our scheme only requires 1203Tmul+Th time complexity for signature generation and 1202Tmul+Th time complexity for verification generation and this magnitude of complexity is considered minimal for multiple hard problems-like signature schemes. Conclusions: The new signature scheme based on multiple hard problems provides longer and higher security level than that scheme based on one problem. This is because no enemy can solve multiple hard problems simultaneously.

A New Partially Blind Signature Based on Factoring and Discrete Logarithms

Partially blind signatures played an important role in many electronic commerce applications. Many existing partially blind signature scheme based on a single hard problem but not secure. In this study, we propose a secure partially blind signature scheme based on factoring and discrete logarithms and show that the proposed scheme satisfies the partial blindness, randomization, unlinkability and unforgeability properties. We also analyse the computation cost of the proposed scheme.