Robust threshold digital signature schemes are group signature schemes aiming to depart from the ... more Robust threshold digital signature schemes are group signature schemes aiming to depart from the classical one person signer schemes. The term 'robust' means that such schemes can tolerate errors attempted by malicious adversary and the term 'threshold' means that given a total of n players, no coalition of players with cardinality less than or equal the threshold value can perform the signature while any coalition of players exceeding the threshold value can perform the signature correctly. The contributions in this paper are two fold. First, we propose a new verifiable secret sharing scheme (VSS) other than Feldman's (1987) and Pedersen's (1992) schemes suitable to protect elliptic curve secret keys. The proposed scheme utilizes a strong one way function provided by the elliptic curve cryptography based on a different type of group mathematics. Next, we employ the elliptic curve VSS to propose a robust threshold elliptic curve digital signature scheme that can withstand an n/2 eavesdropping, n/3 halting and an n/4 malicious adversary. The scheme is able to tolerate n/3 malicious adversary with the cost of higher complexity
"Certificateless public key cryptography" has very appealing features, namely it does not require... more "Certificateless public key cryptography" has very appealing features, namely it does not require any public key certification (traditional public key cryptography) nor having key escrow problem (identity-based cryptography). Unfortunately, construction of certificateless public key encryption (CLPKE) schemes has so far depended on the use of identity-based encryption, which results in the bilinear pairing-based schemes that need costly operations. In this paper, we consider a relaxation of the original model of CLPKE and propose a new CLPKE scheme that does not depend on the bilinear pairings
The nature of the RSA public modulus N as a composite of at least two secret large primes was alw... more The nature of the RSA public modulus N as a composite of at least two secret large primes was always considered as a major obstacle facing the RSA function sharing without the help of a trusted dealer. The incorporated parties must agree on a suitable RSA modulus with no information revealed to them about its prime factors. Enormous number of trials must be performed before a suitable modulus is established. According to the number theory, for two -bit primes modulus, the number of trials is in the order of O( 2 ). Efforts have been made to reduce the quadratic slowdown in the generation process, however, most of these protocols allow the joint generation of a multi-prime RSA modulus (an RSA modulus with at least three prime factors), which is a drift from standard. Other protocols require distributed primality tests over a shared secret modulus which is an extensive task. In this paper, we introduce a simple yet an efficient idea to allow two parties to jointly generate a two-prime RSA modulus with a running time complexity O( ). In our protocol, the distributed primality test is performed over a public modulus. Consequently, the expected running time will be reduced from several days to only few minutes. The protocol can be extended to the multiparty case. However, for clarity, in this paper, we focus on the two-party case.
The nature of the RSA public modulus N as a composite of at least two secret large primes was alw... more The nature of the RSA public modulus N as a composite of at least two secret large primes was always considered as a major obstacle facing the RSA function sharing without the help of a trusted dealer. The incorporated parties must agree on a suitable RSA modulus with no information revealed to them about its prime factors. Enormous number of trials must be performed before a suitable modulus is established. According to the number theory, for two -bit primes modulus, the number of trials is in the order of O( 2 ). Efforts have been made to reduce the quadratic slowdown in the generation process, however, most of these protocols allow the joint generation of a multi-prime RSA modulus (an RSA modulus with at least three prime factors), which is a drift from standard. Other protocols require distributed primality tests over a shared secret modulus which is an extensive task. In this paper, we introduce a simple yet an efficient idea to allow two parties to jointly generate a two-prime RSA modulus with a running time complexity O( ). In our protocol, the distributed primality test is performed over a public modulus. Consequently, the expected running time will be reduced from several days to only few minutes. The protocol can be extended to the multiparty case. However, for clarity, in this paper, we focus on the two-party case.
Distributed primality tests for the purpose of testing the factors of the jointly generated RSA m... more Distributed primality tests for the purpose of testing the factors of the jointly generated RSA modulus were always considered as a nightmare due to the large amount of time required for these tests to succeed. Enormous number of trials must be performed before a suitable RSA modulus is established. In the honest-but-curious scenario, in this paper we propose an efficient extention to the three-party protocol of to allow n parties to share the generation of a RSA modulus N and to share the secret key d. The protocol enjoys the following properties:
Fast Three-Party Shared Generation of RSA Keys Without Distributed Primality Tests
... One may compute mdmodqi−1modqi, i = (1, 2, 3), since the numbers and exponents are smaller, t... more ... One may compute mdmodqi−1modqi, i = (1, 2, 3), since the numbers and exponents are smaller, the generation of the sig-nature is twice as fast as using the Chinese remainder theorem for N = pq. ... Alice computes a = qara while carol computes c = qcrc ...
In an efficient two-party, two-prime RSA function sharing protocol was proposed. The protocol pro... more In an efficient two-party, two-prime RSA function sharing protocol was proposed. The protocol proves efficiency over previously proposed protocols. When the sharing of standard RSA is considered, the protocol is faster than ever. In this paper, under the assumption that the adversary has eavesdropping and halting capabilities, we propose an efficient extension to the protocol of . Our protocol enjoys the following properties (some of which are inherit from ): The protocol is fully distributed (i.e. does not require an honest dealer). It is a t-private and t-resilient (t, n)-threshold structure against a stationary adversary and also t-proactive (t, n)threshold structure against a mobile adversary, where the number of players n > 3t. The players jointly generate two-prime RSA modulus in a number of trials of O( /lg ) since, the protocol avoids the inefficient distributed biprimality test. An extension of the protocol allows the generation of a RSA modulus which is a composite of two safe primes. Distributed primality tests are performed over a public modulus not a shared secret one, which reduces complexity on a per trial basis. We must emphasize that robustness against malicious adversaries (adversaries that masquerade the corrupted player by altering, deleting, sending wrong values, etc.) are beyond the scope of this paper.
Verifiable secret sharing schemes (VSS) are schemes for the purpose of ensuring that the players ... more Verifiable secret sharing schemes (VSS) are schemes for the purpose of ensuring that the players are sharing a unique secret and this secret is the secret originally distributed by the dealer if the dealer was honest. However, such schemes do not ensure that the shared secret has any special characteristics (such as being a prime, safe prime or being with a specific bit-length). In this paper, we introduce a secret sharing scheme to allow a set of players to have confidence that they are sharing a large secret prime. Next, we introduce another scheme that allows the players to have confidence that they are sharing a large secret safe prime. Finally we give a subroutine that allows the players to ensure that the shared primes are of the appropriate bit-length. What we have in mind is to add fault-tolerance property to the recent all honest RSA function sharing protocol of .
A comparison of prescription medication use by nursing home and homebound dental patients
Special Care in Dentistry, 1990
The elderly consume a disproportionate number of prescription medications dispensed in the United... more The elderly consume a disproportionate number of prescription medications dispensed in the United States. Although medication use among nursing home residents has been documented, little information is available regarding the medication use of homebound elderly. This study compared the medication use of nursing home and homebound patients treated by a mobile dental homecare program. A total of 338 dental records were reviewed, identifying the number and type of medications used. In addition, medications with xerostomic potential were identified.
Robust threshold digital signature schemes are group signature schemes aiming to depart from the ... more Robust threshold digital signature schemes are group signature schemes aiming to depart from the classical one person signer schemes. The term 'robust' means that such schemes can tolerate errors attempted by malicious adversary and the term 'threshold' means that given a total of n players, no coalition of players with cardinality less than or equal the threshold value can perform the signature while any coalition of players exceeding the threshold value can perform the signature correctly. The contributions in this paper are two fold. First, we propose a new verifiable secret sharing scheme (VSS) other than Feldman's (1987) and Pedersen's (1992) schemes suitable to protect elliptic curve secret keys. The proposed scheme utilizes a strong one way function provided by the elliptic curve cryptography based on a different type of group mathematics. Next, we employ the elliptic curve VSS to propose a robust threshold elliptic curve digital signature scheme that can withstand an n/2 eavesdropping, n/3 halting and an n/4 malicious adversary. The scheme is able to tolerate n/3 malicious adversary with the cost of higher complexity
"Certificateless public key cryptography" has very appealing features, namely it does not require... more "Certificateless public key cryptography" has very appealing features, namely it does not require any public key certification (traditional public key cryptography) nor having key escrow problem (identity-based cryptography). Unfortunately, construction of certificateless public key encryption (CLPKE) schemes has so far depended on the use of identity-based encryption, which results in the bilinear pairing-based schemes that need costly operations. In this paper, we consider a relaxation of the original model of CLPKE and propose a new CLPKE scheme that does not depend on the bilinear pairings
The nature of the RSA public modulus N as a composite of at least two secret large primes was alw... more The nature of the RSA public modulus N as a composite of at least two secret large primes was always considered as a major obstacle facing the RSA function sharing without the help of a trusted dealer. The incorporated parties must agree on a suitable RSA modulus with no information revealed to them about its prime factors. Enormous number of trials must be performed before a suitable modulus is established. According to the number theory, for two -bit primes modulus, the number of trials is in the order of O( 2 ). Efforts have been made to reduce the quadratic slowdown in the generation process, however, most of these protocols allow the joint generation of a multi-prime RSA modulus (an RSA modulus with at least three prime factors), which is a drift from standard. Other protocols require distributed primality tests over a shared secret modulus which is an extensive task. In this paper, we introduce a simple yet an efficient idea to allow two parties to jointly generate a two-prime RSA modulus with a running time complexity O( ). In our protocol, the distributed primality test is performed over a public modulus. Consequently, the expected running time will be reduced from several days to only few minutes. The protocol can be extended to the multiparty case. However, for clarity, in this paper, we focus on the two-party case.
The nature of the RSA public modulus N as a composite of at least two secret large primes was alw... more The nature of the RSA public modulus N as a composite of at least two secret large primes was always considered as a major obstacle facing the RSA function sharing without the help of a trusted dealer. The incorporated parties must agree on a suitable RSA modulus with no information revealed to them about its prime factors. Enormous number of trials must be performed before a suitable modulus is established. According to the number theory, for two -bit primes modulus, the number of trials is in the order of O( 2 ). Efforts have been made to reduce the quadratic slowdown in the generation process, however, most of these protocols allow the joint generation of a multi-prime RSA modulus (an RSA modulus with at least three prime factors), which is a drift from standard. Other protocols require distributed primality tests over a shared secret modulus which is an extensive task. In this paper, we introduce a simple yet an efficient idea to allow two parties to jointly generate a two-prime RSA modulus with a running time complexity O( ). In our protocol, the distributed primality test is performed over a public modulus. Consequently, the expected running time will be reduced from several days to only few minutes. The protocol can be extended to the multiparty case. However, for clarity, in this paper, we focus on the two-party case.
Distributed primality tests for the purpose of testing the factors of the jointly generated RSA m... more Distributed primality tests for the purpose of testing the factors of the jointly generated RSA modulus were always considered as a nightmare due to the large amount of time required for these tests to succeed. Enormous number of trials must be performed before a suitable RSA modulus is established. In the honest-but-curious scenario, in this paper we propose an efficient extention to the three-party protocol of to allow n parties to share the generation of a RSA modulus N and to share the secret key d. The protocol enjoys the following properties:
Fast Three-Party Shared Generation of RSA Keys Without Distributed Primality Tests
... One may compute mdmodqi−1modqi, i = (1, 2, 3), since the numbers and exponents are smaller, t... more ... One may compute mdmodqi−1modqi, i = (1, 2, 3), since the numbers and exponents are smaller, the generation of the sig-nature is twice as fast as using the Chinese remainder theorem for N = pq. ... Alice computes a = qara while carol computes c = qcrc ...
In an efficient two-party, two-prime RSA function sharing protocol was proposed. The protocol pro... more In an efficient two-party, two-prime RSA function sharing protocol was proposed. The protocol proves efficiency over previously proposed protocols. When the sharing of standard RSA is considered, the protocol is faster than ever. In this paper, under the assumption that the adversary has eavesdropping and halting capabilities, we propose an efficient extension to the protocol of . Our protocol enjoys the following properties (some of which are inherit from ): The protocol is fully distributed (i.e. does not require an honest dealer). It is a t-private and t-resilient (t, n)-threshold structure against a stationary adversary and also t-proactive (t, n)threshold structure against a mobile adversary, where the number of players n > 3t. The players jointly generate two-prime RSA modulus in a number of trials of O( /lg ) since, the protocol avoids the inefficient distributed biprimality test. An extension of the protocol allows the generation of a RSA modulus which is a composite of two safe primes. Distributed primality tests are performed over a public modulus not a shared secret one, which reduces complexity on a per trial basis. We must emphasize that robustness against malicious adversaries (adversaries that masquerade the corrupted player by altering, deleting, sending wrong values, etc.) are beyond the scope of this paper.
Verifiable secret sharing schemes (VSS) are schemes for the purpose of ensuring that the players ... more Verifiable secret sharing schemes (VSS) are schemes for the purpose of ensuring that the players are sharing a unique secret and this secret is the secret originally distributed by the dealer if the dealer was honest. However, such schemes do not ensure that the shared secret has any special characteristics (such as being a prime, safe prime or being with a specific bit-length). In this paper, we introduce a secret sharing scheme to allow a set of players to have confidence that they are sharing a large secret prime. Next, we introduce another scheme that allows the players to have confidence that they are sharing a large secret safe prime. Finally we give a subroutine that allows the players to ensure that the shared primes are of the appropriate bit-length. What we have in mind is to add fault-tolerance property to the recent all honest RSA function sharing protocol of .
A comparison of prescription medication use by nursing home and homebound dental patients
Special Care in Dentistry, 1990
The elderly consume a disproportionate number of prescription medications dispensed in the United... more The elderly consume a disproportionate number of prescription medications dispensed in the United States. Although medication use among nursing home residents has been documented, little information is available regarding the medication use of homebound elderly. This study compared the medication use of nursing home and homebound patients treated by a mobile dental homecare program. A total of 338 dental records were reviewed, identifying the number and type of medications used. In addition, medications with xerostomic potential were identified.
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