2017 ISEA Asia Security and Privacy (ISEASP), 2017
The NTRU public key cryptosystem was proposed by Hoffstein, Pipher and Silverman in 1996. NTRU is... more The NTRU public key cryptosystem was proposed by Hoffstein, Pipher and Silverman in 1996. NTRU is one of the most widely used public key cryptosystems and its security has been an active research topic. In 1977, coppersmith and Shamir applied new lattice basis reduction techniques to cryptanalyze the scheme, to discover either the original secret key, or an alternative secret key which is equally useful in decoding the ciphertexts. In 2014, A. Nitaj gave cryptanalysis of NTRU with two public keys and compared with lattice attack given by Coppersmith and Shamir. In this paper, we are generalizing the idea of A. Nitaj and presenting cryptanalysis of NTRU with n public keys.
Various forms of Mean Value Theorems are available in the literature. If we use Flett's Mean ... more Various forms of Mean Value Theorems are available in the literature. If we use Flett's Mean Value Theorem in Extended Generalized Mean Value Theorem then what would the new theorem look like. A sincere effort is done to develop this theorem. This theorem is named as Extended Generalized Flett's Mean Value Theorem.
Untraceability of Partial Blind and Blind Signature Schemes
Information Security and Cryptology, 2020
Blind Signature is employed in privacy related protocols, where signer signs on a blinded message... more Blind Signature is employed in privacy related protocols, where signer signs on a blinded message. It provides anonymity in various cryptographic applications such as electronic voting, digital cash system etc. Concerning the need for quantum resistant scheme, Ruckert and Tian et al. proposed the lattice based blind signature and partial blind signature schemes respectively. But, both the schemes left out one of the security requirement of a blind i.e. Untraceability, where the signer can’t link the blinded signature with a valid message-signature pair even when it is revealed in public. In this article, we propose an attack on the untracebility property of both the schemes. The proposed attack opens the door for researchers to work on quantum resistant untraceable blind signature.
In this paper we analyze the security of Koyama scheme based on the singular cubic curve for some... more In this paper we analyze the security of Koyama scheme based on the singular cubic curve for some well known attacks. We provide an efficient algorithm for linearly related plaintext attack and identify isomorphic attack on Koyama scheme. Some other attacks are also discussed in this paper.
The cryptosystem proposed by Koyama is not semantically secure. Also, it is not secure against pa... more The cryptosystem proposed by Koyama is not semantically secure. Also, it is not secure against partial known plaintext attack, linearly related plaintext attack and low exponent attack. In this paper we propose a cryptosystem over singular cubic curve using the idea of Koyama and Kouichi et al. Our proposed cryptosystem is approximately two times faster than the cryptosystem given by Kouichi et al. with the same security label and more efficient than the Koyama scheme at higher security label. Further, the partially known plaintext attack and the linearly related plaintext attacks are analyzed and concluded that those are not possible in the proposed scheme.
The concept of self proxy signature (SPS) scheme was proposed by Kim and Chang in 2007. In a self... more The concept of self proxy signature (SPS) scheme was proposed by Kim and Chang in 2007. In a self proxy signatures, the signer wants to protect his original keys by generating temporary key pairs for a time period and then revoke them. The temporary keys can be generated by delegating the signing right to himself. Thus, in SPS the user can prevent the exposure of his private key from repeated use. If we are considering the existence of quantum computers, then scheme proposed by Kim and Chang’s is no more secure since its security is based on the hardness of discrete logarithm assumption. In this paper we propose the first lattice based self proxy signature scheme. Since hard problems of lattices are secure against quantum attacks, therefore, our proposed scheme is secure against quantum computer also. We designed our scheme on NTRU lattices since NTRU lattices are most efficient lattices than general lattices.
Multi-proxy signature (MPS) allows an original signer to authorize a group of proxy signers as hi... more Multi-proxy signature (MPS) allows an original signer to authorize a group of proxy signers as his proxy agent to sign co-operatively a message. As per the literature, the relative computation cost of a pairing is approximately more than ten times of the scalar multiplication over elliptic curve group which indicates that pairing is a very expensive operation. Moreover the map-to-point function is also very expensive. Therefore, we propose a new MPS scheme without pairings having general crypto-graphic hash function after formalizing a security model.Our proposal is provable secure and much efficient than previously proposed schemes in practice.
In this paper we generalize the idea given by Weger and Maitra & Sarkar. This generalization is c... more In this paper we generalize the idea given by Weger and Maitra & Sarkar. This generalization is coming from the concept of x9.31-1997 standard for public key cryptography, Section 4:1:2, i.e., there are a number of recommendations for the generalization of the primes of an RSA modulus. Among them, the ratio of the primes shall not be close to the ratio of small integers. Also we try to improve the range of weak keys of RSA cryptosystem for the Generalized Wiener's attack given by Blomer & May. We have shown that the range of weak keys can be extended by more than 8 times than the range given by Blomer & May. Further we have shown that for |ap - bq| ≤ N(superscript (α/2)) where 0 ＜α≤ 1, if e satisfies an equation ex + y = m∅(N), for m ＞ 0. Then N can be factored in( O poly(logN)) times when 0 ＜ x ≤ 1/6√∅ (N)/e N(superscript (1/2 -α/4)) and |y|≤ |ap - bq|/∅(N)N(superscript (1/4) ex.
Efficient ID-based proxy multi-signature scheme secure in random oracle
Frontiers of Computer Science, 2012
Abstract Proxy signature schemes enable an entity to delegate its signing rights to any other par... more Abstract Proxy signature schemes enable an entity to delegate its signing rights to any other party, called proxy signer. As a variant of proxy signature primitive, proxymultisignature allows a group of original signers to delegate their signing capabilities to a single proxy signer in such a way that the proxy signer can sign a message on behalf of the group of original signers. We propose a concrete ID-based proxy multi-signature scheme from bilinear pairings. The proposed scheme is existential unforgeable against adaptively ...
An attack is possible upon all three RSA analogue PKCs based on singular cubic curves given by Ko... more An attack is possible upon all three RSA analogue PKCs based on singular cubic curves given by Koyama. While saying so, Seng et al observed that the scheme become insecure if a linear relation is known between two plaintexts. In this case, attacker has to compute greatest common divisor of two polynomials corresponding to those two plaintexts. However, the computation of greatest common divisor of two polynomials is not efficient. For the reason, the degree e of both polynomials, an encryption exponent, is quite large. In this paper, we propose an algorithm, which makes the attack considerably efficient. Subsequently, we identify isomorphic attack on the Koyama schemes by using the isomorphism between two singular cubic curves.
In the last few years, the traditonal certificate-based setting is replaced by the ID-based setti... more In the last few years, the traditonal certificate-based setting is replaced by the ID-based setting. Proxy signatures allow the delegation of signing rights from an original user to its proxy agent. Normally, the original signer can authorize a group of proxy agents to sign any document on its behalf. Currently in our study, we have proposed an ID-based multi-proxy signature scheme, from bilinear pairings based on 'k-plus problem'. We document that the proposed scheme is secure under the inverse computational Die-Hellman (INV-CDH) assumption. Besides, we have proven that the new scheme is computationally more efficient and takes less running time than other existing schemes [5, 10]. Our proposed method meets all the security requirements of a proxy signature scheme proposed by Lee.
2017 ISEA Asia Security and Privacy (ISEASP), 2017
The NTRU public key cryptosystem was proposed by Hoffstein, Pipher and Silverman in 1996. NTRU is... more The NTRU public key cryptosystem was proposed by Hoffstein, Pipher and Silverman in 1996. NTRU is one of the most widely used public key cryptosystems and its security has been an active research topic. In 1977, coppersmith and Shamir applied new lattice basis reduction techniques to cryptanalyze the scheme, to discover either the original secret key, or an alternative secret key which is equally useful in decoding the ciphertexts. In 2014, A. Nitaj gave cryptanalysis of NTRU with two public keys and compared with lattice attack given by Coppersmith and Shamir. In this paper, we are generalizing the idea of A. Nitaj and presenting cryptanalysis of NTRU with n public keys.
Various forms of Mean Value Theorems are available in the literature. If we use Flett's Mean ... more Various forms of Mean Value Theorems are available in the literature. If we use Flett's Mean Value Theorem in Extended Generalized Mean Value Theorem then what would the new theorem look like. A sincere effort is done to develop this theorem. This theorem is named as Extended Generalized Flett's Mean Value Theorem.
Untraceability of Partial Blind and Blind Signature Schemes
Information Security and Cryptology, 2020
Blind Signature is employed in privacy related protocols, where signer signs on a blinded message... more Blind Signature is employed in privacy related protocols, where signer signs on a blinded message. It provides anonymity in various cryptographic applications such as electronic voting, digital cash system etc. Concerning the need for quantum resistant scheme, Ruckert and Tian et al. proposed the lattice based blind signature and partial blind signature schemes respectively. But, both the schemes left out one of the security requirement of a blind i.e. Untraceability, where the signer can’t link the blinded signature with a valid message-signature pair even when it is revealed in public. In this article, we propose an attack on the untracebility property of both the schemes. The proposed attack opens the door for researchers to work on quantum resistant untraceable blind signature.
In this paper we analyze the security of Koyama scheme based on the singular cubic curve for some... more In this paper we analyze the security of Koyama scheme based on the singular cubic curve for some well known attacks. We provide an efficient algorithm for linearly related plaintext attack and identify isomorphic attack on Koyama scheme. Some other attacks are also discussed in this paper.
The cryptosystem proposed by Koyama is not semantically secure. Also, it is not secure against pa... more The cryptosystem proposed by Koyama is not semantically secure. Also, it is not secure against partial known plaintext attack, linearly related plaintext attack and low exponent attack. In this paper we propose a cryptosystem over singular cubic curve using the idea of Koyama and Kouichi et al. Our proposed cryptosystem is approximately two times faster than the cryptosystem given by Kouichi et al. with the same security label and more efficient than the Koyama scheme at higher security label. Further, the partially known plaintext attack and the linearly related plaintext attacks are analyzed and concluded that those are not possible in the proposed scheme.
The concept of self proxy signature (SPS) scheme was proposed by Kim and Chang in 2007. In a self... more The concept of self proxy signature (SPS) scheme was proposed by Kim and Chang in 2007. In a self proxy signatures, the signer wants to protect his original keys by generating temporary key pairs for a time period and then revoke them. The temporary keys can be generated by delegating the signing right to himself. Thus, in SPS the user can prevent the exposure of his private key from repeated use. If we are considering the existence of quantum computers, then scheme proposed by Kim and Chang’s is no more secure since its security is based on the hardness of discrete logarithm assumption. In this paper we propose the first lattice based self proxy signature scheme. Since hard problems of lattices are secure against quantum attacks, therefore, our proposed scheme is secure against quantum computer also. We designed our scheme on NTRU lattices since NTRU lattices are most efficient lattices than general lattices.
Multi-proxy signature (MPS) allows an original signer to authorize a group of proxy signers as hi... more Multi-proxy signature (MPS) allows an original signer to authorize a group of proxy signers as his proxy agent to sign co-operatively a message. As per the literature, the relative computation cost of a pairing is approximately more than ten times of the scalar multiplication over elliptic curve group which indicates that pairing is a very expensive operation. Moreover the map-to-point function is also very expensive. Therefore, we propose a new MPS scheme without pairings having general crypto-graphic hash function after formalizing a security model.Our proposal is provable secure and much efficient than previously proposed schemes in practice.
In this paper we generalize the idea given by Weger and Maitra & Sarkar. This generalization is c... more In this paper we generalize the idea given by Weger and Maitra & Sarkar. This generalization is coming from the concept of x9.31-1997 standard for public key cryptography, Section 4:1:2, i.e., there are a number of recommendations for the generalization of the primes of an RSA modulus. Among them, the ratio of the primes shall not be close to the ratio of small integers. Also we try to improve the range of weak keys of RSA cryptosystem for the Generalized Wiener's attack given by Blomer & May. We have shown that the range of weak keys can be extended by more than 8 times than the range given by Blomer & May. Further we have shown that for |ap - bq| ≤ N(superscript (α/2)) where 0 ＜α≤ 1, if e satisfies an equation ex + y = m∅(N), for m ＞ 0. Then N can be factored in( O poly(logN)) times when 0 ＜ x ≤ 1/6√∅ (N)/e N(superscript (1/2 -α/4)) and |y|≤ |ap - bq|/∅(N)N(superscript (1/4) ex.
Efficient ID-based proxy multi-signature scheme secure in random oracle
Frontiers of Computer Science, 2012
Abstract Proxy signature schemes enable an entity to delegate its signing rights to any other par... more Abstract Proxy signature schemes enable an entity to delegate its signing rights to any other party, called proxy signer. As a variant of proxy signature primitive, proxymultisignature allows a group of original signers to delegate their signing capabilities to a single proxy signer in such a way that the proxy signer can sign a message on behalf of the group of original signers. We propose a concrete ID-based proxy multi-signature scheme from bilinear pairings. The proposed scheme is existential unforgeable against adaptively ...
An attack is possible upon all three RSA analogue PKCs based on singular cubic curves given by Ko... more An attack is possible upon all three RSA analogue PKCs based on singular cubic curves given by Koyama. While saying so, Seng et al observed that the scheme become insecure if a linear relation is known between two plaintexts. In this case, attacker has to compute greatest common divisor of two polynomials corresponding to those two plaintexts. However, the computation of greatest common divisor of two polynomials is not efficient. For the reason, the degree e of both polynomials, an encryption exponent, is quite large. In this paper, we propose an algorithm, which makes the attack considerably efficient. Subsequently, we identify isomorphic attack on the Koyama schemes by using the isomorphism between two singular cubic curves.
In the last few years, the traditonal certificate-based setting is replaced by the ID-based setti... more In the last few years, the traditonal certificate-based setting is replaced by the ID-based setting. Proxy signatures allow the delegation of signing rights from an original user to its proxy agent. Normally, the original signer can authorize a group of proxy agents to sign any document on its behalf. Currently in our study, we have proposed an ID-based multi-proxy signature scheme, from bilinear pairings based on 'k-plus problem'. We document that the proposed scheme is secure under the inverse computational Die-Hellman (INV-CDH) assumption. Besides, we have proven that the new scheme is computationally more efficient and takes less running time than other existing schemes [5, 10]. Our proposed method meets all the security requirements of a proxy signature scheme proposed by Lee.
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Papers by Sahadeo Padhye