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Generating ElGamal signatures without knowing the secret key
, 1996
"... . We present a new method to forge ElGamal signatures if the public parameters of the system are not chosen properly. Since the secret key is hereby not found this attack shows that forging ElGamal signatures is sometimes easier than the underlying discrete logarithm problem. 1 Introduction ElGamal ..."
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. We present a new method to forge ElGamal signatures if the public parameters of the system are not chosen properly. Since the secret key is hereby not found this attack shows that forging ElGamal signatures is sometimes easier than the underlying discrete logarithm problem. 1 Introduction ElGamal's digital signature scheme [4] relies on the difficulty of computing discrete logarithms in the multiplicative group IF p and can therefore be broken if the computation of discrete logarithms is feasible. However, the converse has never been proved. In this paper we show that it is sometimes possible to forge signatures without breaking the underlying discrete logarithm problem. This shows that the ElGamal signature scheme and some variants of the scheme must be used very carefully. The paper is organized as follows. Section 2 describes the ElGamal signature scheme. In Section 3 we present a method to forge signatures if some additional information on the generator is known. We show that...
Generalized ElGamal signatures for one message block
, 1994
"... There have been many approaches in the past to generalize the ElGamal signature scheme. In this paper we integrate all these approaches in a generalized ElGamal signature scheme. We also investigate some new types of variations, that haven't been considered before. By this method we obtain nume ..."
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There have been many approaches in the past to generalize the ElGamal signature scheme. In this paper we integrate all these approaches in a generalized ElGamal signature scheme. We also investigate some new types of variations, that haven't been considered before. By this method we obtain numerous variants of the ElGamal scheme. From these variants, we can extract new, highly efficient signature schemes, which haven't been proposed before. 1. Introduction There have been many approaches to generalize the ElGamal signature scheme [ElGa84, Schn89, AgMV90, NIST91, Schn91, BrMc91, YeLa93, Knob93, NyR293, Har194, NyRu94, HoP194, HoP294, HoP394, Har294]. In this paper we try to integrate all these approaches in a generalized ElGamal signature scheme. We also investigate some new types of variation, that haven't been considered before. By this method we obtain various variants of the ElGamal scheme. The advantage of this proceeding is that we can extract highly efficient schemes out of thes...
MetaElGamal signature schemes using a composite module
, 1994
"... In 1984 ElGamal published the first signature scheme based on the discrete logarithm problem. Since then a lot of work was done to modify and generalize this signature scheme. Very important steps of recent research were the discovery of efficient signature schemes with appendix , e.g. by Schnorr, N ..."
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In 1984 ElGamal published the first signature scheme based on the discrete logarithm problem. Since then a lot of work was done to modify and generalize this signature scheme. Very important steps of recent research were the discovery of efficient signature schemes with appendix , e.g. by Schnorr, Nyberg/Rueppel or Harn. All these variants can be embedded into a MetaElGamal signature scheme. Until now all schemes except one have in common that the verification is done over a finite field. In this paper we focus on those schemes where a composite modul n = pq instead of a primemodul p is used in the MetaElGamal signature scheme. An unmodified scheme is cryptoanalysed in this composite mode, further we introduce some new refined modes and give a security and performance analysis of the various schemes. As a result, some schemes can be used in these modes with slight modifications. Although the security of these schemes can't be proven, the advantages are that ffl even existential for...
Digital Signature Scheme Based on Two Hard
 Problems,” IJCSNS International Journal of Computer Science and Network Security, December 2007, vol.7 No.12
"... In 1998, Shao Proposed two digital signature schemes based on factoring and discrete logarithms. At the same year, Li and Xiao showed that Shao’s schemes are insecure are not based on any hard problem. This paper modifies Shao’s schemes. Two new schemes whose security is based on both factorization ..."
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In 1998, Shao Proposed two digital signature schemes based on factoring and discrete logarithms. At the same year, Li and Xiao showed that Shao’s schemes are insecure are not based on any hard problem. This paper modifies Shao’s schemes. Two new schemes whose security is based on both factorization and discrete logarithms are proposed. Key words:
Cryptographic Identification of Users Based on Intermixed Approach
"... ABSTRACT This study presents three identitybased cryptographic schemes, based on twoknown assumptions. Most existing cryptosystem designs incorporate just one cryptographic assumption, such as factoring or discrete logarithms. These assumptions appear secure today; but, it is possible that effici ..."
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ABSTRACT This study presents three identitybased cryptographic schemes, based on twoknown assumptions. Most existing cryptosystem designs incorporate just one cryptographic assumption, such as factoring or discrete logarithms. These assumptions appear secure today; but, it is possible that efficient algorithms will be developed in the future to break one or more of these assumptions. The security of the proposed scheme follows from the difficulties in simultaneously solving the factoring (FAC) and discrete logarithms (DL) problems with arithmetic modulo of almost the same size. Each user in the system uses common arithmetic modulo and only requires one public key and one private key. The proposed schemes support user identification, digital signature, and key distribution.
Implementing Swati Verma’s Digital Signature Schemes based on Integer Factorization and
"... A digital signature is a cryptographic method for verifying the identity of an individual. It can be a process, computer system, or any other entity, in much the same way as a handwritten signature verifies the identity of a person. Digital signatures use the properties of publickey cryptography to ..."
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A digital signature is a cryptographic method for verifying the identity of an individual. It can be a process, computer system, or any other entity, in much the same way as a handwritten signature verifies the identity of a person. Digital signatures use the properties of publickey cryptography to produce pieces of information that verify the origin of the data. Several digital schemes have been proposed as on date based on factorization, discrete logarithm and elliptical curve. However, the Swati Verma and Birendra Kumar Sharma [8] digital signature scheme which combines factorization and discrete logarithm together making it difficult for solving two hard problems from the hackers point of view. This paper presents the implementation of same, with the help of different tools and further analyzes them from different perceptions.
Generating ElGamal signatures without knowing the secret key
, 1996
"... . We present a new method to forge ElGamal signatures if the public parameters of the system are not chosen properly. Since the secret key is hereby not found this attack shows that forging ElGamal signatures is sometimes easier than the underlying discrete logarithm problem. 1 Introduction El ..."
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. We present a new method to forge ElGamal signatures if the public parameters of the system are not chosen properly. Since the secret key is hereby not found this attack shows that forging ElGamal signatures is sometimes easier than the underlying discrete logarithm problem. 1 Introduction ElGamal's digital signature scheme [4] relies on the difficulty of computing discrete logarithms in the multiplicative group IF p and can therefore be broken if the computation of discrete logarithms is feasible. However, the converse has never been proved. In this paper we show that it is sometimes possible to forge signatures without breaking the underlying discrete logarithm problem. This shows that the ElGamal signature scheme and some variants of the scheme must be used very carefully. The paper is organized as follows. Section 2 describes the ElGamal signature scheme. In Section 3 we present a method to forge signatures if some additional information on the generator is known. We show ...
Improved Shao’s Signature Scheme
"... In 1998, Shao proposed two digital signature schemes and claimed that the security of which is based on the difficulties of computing both integer factorization and discrete logarithm. However, in 1999, Lee demonstrated that Shao’s signature schemes can be broken if the factorization problem can be ..."
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In 1998, Shao proposed two digital signature schemes and claimed that the security of which is based on the difficulties of computing both integer factorization and discrete logarithm. However, in 1999, Lee demonstrated that Shao’s signature schemes can be broken if the factorization problem can be solved. This paper presents an improvement of Shao’s signature schemes and shows that it can resist Lee’s attack. This makes our proposed scheme based on two hard problems. Some possible common attacks are considered. We show that the problem of recovering the signer’s secret key from his/her public key is equivalent to solve both the discrete logarithm problem and the factorization problem; the problem of forging a valid signature for a message is at least equivalent to solve the discrete logarithm problem or the factorization problem. In addition, our proposed scheme is immune from substitution and homomorphism attacks.
An Improved RSA Cryptographic System
"... Paper introduced RSA cryptosystem and its security aspects. RSA is a public key algorithm that applied widely in the field of information security in the InternetBanking and ECommerce applications. The proposed scheme for RSA cryptosystem contains three prime numbers and overcome several attack po ..."
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Paper introduced RSA cryptosystem and its security aspects. RSA is a public key algorithm that applied widely in the field of information security in the InternetBanking and ECommerce applications. The proposed scheme for RSA cryptosystem contains three prime numbers and overcome several attack possible on RSA. The proposed scheme has speed improvement on RSA decryption side by using the Chinese Reminder Theorem (CRT) and the scheme is semantically secure also.
A New Digital Signature Scheme Based on Factoring and Discrete Logarithms
"... Abstract: 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 factori ..."
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Abstract: 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 problemslike 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.