Convertible group signatures

Kim, Seungjoo; Park, Sung Jun; Won, Dong Ho

doi:10.1007/bfb0034857

Cited by 31 publications

(25 citation statements)

References 4 publications

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“…A clever idea to solve this contradiction is to define zero-knowledge protocols working in a prime order subgroup of Z * n , with the order disclosed without leading to discovery of (p − 1)(q − 1). A widely adopted method [1,8,9,11,13]) to achieve this is to construct p and q with the structures given in (3), and make g and ord n (g) public. Here g is chosen such that ord n (g) = ord p (g) = ord q (g).…”

Section: Class 2: Difficult Problem Made Easy Due To Disclosure Of a mentioning

confidence: 99%

“…The widely adopted method for disclosing a subgroup of Z * n [1,8,9,11,13]) is in such a structure. Let…”

Section: Class 3: Significant Complexity Reduction For Integer Factormentioning

confidence: 99%

“…(In [11], an additional factor, which is a factor of p , is also made public. We will examine that case in a moment.)…”

Section: Class 3: Significant Complexity Reduction For Integer Factormentioning

confidence: 99%

“…In the literature we also often see cryptosystems and cryptographic protocols (crypto schemes) that make use of prime order subgroups of Z * n (e.g., [1,2,8,9,11,13]). In the sequel, whenever we say subgroup, we refer to a prime order subgroup of Z We will analyze each of the crypto schemes referred in the above paragraph and itemize three classes of security failures from our analysis.…”

Section: Introductionmentioning

confidence: 99%

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Cryptanalysis in Prime Order Subgroups of Zn*

Mao

Lim²

1998

Lecture Notes in Computer Science

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Abstract. Many cryptographic protocols and cryptosystems have been proposed to make use of prime order subgroups of Z * n where n is the product of two large distinct primes. In this paper we analyze a number of such schemes. While these schemes were proposed to utilize the difficulty of factoring large integers or that of finding related hidden information (e.g., the order of the group Z * n ), our analyzes reveal much easier problems as their real security bases. We itemize three classes of security failures and formulate a simple algorithm for factoring n with a disclosed non-trivial factor of φ(n) where the disclosure is for making use of a prime order subgroup in Z * n . The time complexity of our algorithm is O(n 1/4 /f ) where f is a disclosed subgroup order. To factor such n of length up to 800 bits with the subgroup having a secure size against computing discrete logarithm, the new algorithm will have a feasible running time on use of a trivial size of storage.

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Section: Class 2: Difficult Problem Made Easy Due To Disclosure Of a mentioning

confidence: 99%

“…The widely adopted method for disclosing a subgroup of Z * n [1,8,9,11,13]) is in such a structure. Let…”

Section: Class 3: Significant Complexity Reduction For Integer Factormentioning

confidence: 99%

“…(In [11], an additional factor, which is a factor of p , is also made public. We will examine that case in a moment.)…”

Section: Class 3: Significant Complexity Reduction For Integer Factormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Cryptanalysis in Prime Order Subgroups of Zn*

Mao

Lim²

1998

Lecture Notes in Computer Science

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“…The lengths of the public key and of the signatures 1 The only previously proposed schemes with fixed size public keys [21,17] were broken. are, as well as the computational effort for signing and verifying, independent o] the number of group members.…”

Section: Introductionmentioning

confidence: 99%

Efficient group signature schemes for large groups

Camenisch

Stadler

1997

Lecture Notes in Computer Science

789

610

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Abstract.A group signature scheme allows members of a group to sign messages on the group's behalf such that the resulting signature does not reveal their identity. Only a designated group manager is able to identify the group member who issued a given signature. Previously proposed realizations of group signature schemes have the undesirable property that the length of the public key is linear in the size of the group. In this paper we propose the first group signature scheme whose public key and signatures have length independent of the number of group members and which can therefore also be used for large groups. Furthermore, the scheme allows the group manager to add new members to the group without modifying the public key. The realization is based on methods for proving the knowledge of signatures.

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An (n–t)-out-of-n Threshold Ring Signature Scheme

Isshiki

Tanaka

2005

Information Security and Privacy

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Convertible group signatures

Cited by 31 publications

References 4 publications

Cryptanalysis in Prime Order Subgroups of Zn*

Cryptanalysis in Prime Order Subgroups of Zn*

Efficient group signature schemes for large groups

An (n–t)-out-of-n Threshold Ring Signature Scheme

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