Almost all primes can be quickly certified
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Attacks on some RSA signatures
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
On using RSA with low exponent in a public key network
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A course in number theory and cryptography
A course in number theory and cryptography
A pseudo-random bit generator based on elliptic logarithms
Proceedings on Advances in cryptology---CRYPTO '86
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Fast generation of secure RSA-moduli with almost maximal diversity
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Factoring with two large primes (extended abstract)
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Primality and Cryptography
On taking roots in finite fields
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Riemann's hypothesis and tests for primality
Journal of Computer and System Sciences
Non-interactive public-key cryptography
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
A new elliptic curve based analogue of RSA
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
On the importance of securing your bins: the garbage-man-in-the-middle attack
Proceedings of the 4th ACM conference on Computer and communications security
Reducing the Elliptic Curve Cryptosystem of Meyer-Müllerto the Cryptosystem of Rabin-Williams
Designs, Codes and Cryptography
Complexity and Fast Algorithms for Multiexponentiations
IEEE Transactions on Computers
The State of Elliptic Curve Cryptography
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
How to Choose Secret Parameters for RSA-Type Cryptosystems over Elliptic Curves
Designs, Codes and Cryptography
Generalised Cycling Attacks on RSA and Strong RSA Primes
ACISP '99 Proceedings of the 4th Australasian Conference on Information Security and Privacy
New Public-Key Cryptosystem Using Braid Groups
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
An Efficient Digital Signature Scheme Based on an Elliptic Curve Over the Ring Zn
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Speeding up Elliptic Cryptosystems by Using a Signed Binary Window Method
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
A Group Signature Scheme with Improved Efficiency
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Trapdooring Discrete Logarithms on Elliptic Curves over Rings
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Cryptanalysis of short secret exponents modulo RSA primes
Information Sciences—Informatics and Computer Science: An International Journal
A public-key cryptosystem scheme on conic curves over the ring Z n
ISP'06 Proceedings of the 5th WSEAS International Conference on Information Security and Privacy
Verifiable secret sharing schemes based on non-homogeneous linear recursions and elliptic curves
Computer Communications
Two Generic Constructions of Probabilistic Cryptosystems and Their Applications
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
Low exponent attack against elliptic curve RSA
Information Processing Letters
A public key cryptosystem based on elliptic curves over Z/nZ equivalent to factoring
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Counting the number of points on elliptic curves over finite fields: strategies and performances
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Fast RSA-type schemes based on singular cubic curves y2 + axy ≡ x3 (mod n)
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Proving in zero-knowledge that a number is the product of two safe primes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Trading one-wayness against chosen-ciphertext security in factoring-based encryption
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Spreading alerts quietly and the subgroup escape problem
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
ECC based threshold cryptography for secure data forwarding and secure key exchange in MANET (i)
NETWORKING'05 Proceedings of the 4th IFIP-TC6 international conference on Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile and Wireless Communication Systems
A provably secure elliptic curve scheme with fast encryption
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
IWSEC'06 Proceedings of the 1st international conference on Security
Pairings on elliptic curves over finite commutative rings
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
An efficient probabilistic public-key cryptosystem over quadratic fields quotients
Finite Fields and Their Applications
Additively homomorphic encryption with a double decryption mechanism, revisited
ISC'12 Proceedings of the 15th international conference on Information Security
| Hi-index | 0.00 |
Three new trapdoor one-way functions are proposed that are based on elliptic curves over the ring Zn. The first class of functions is a naive construction, which can be used only in a digital signature scheme, and not in a public-key cryptosystem. The second, preferred class of function, does not suffer from this problem and can be used for the same applications as the RSA trapdoor one-way function, including zero-knowledge identification protocols. The third class of functions has similar properties to the Rabin trapdoor one-way functions. Although the security of these proposed schemes is based on the difficulty of factoring n, like the RSA and Rabin schemes, these schemes seem to be more secure than those schemes from the viewpoint of attacks without factoring such as low multiplier attacks. The new schemes are somewhat less efficient than the RSA and Rabin schemes.