Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Mathematics of Computation
Elliptic curves in cryptography
Elliptic curves in cryptography
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Improving the parallelized Pollard lambda search on anomalous binary curves
Mathematics of Computation
On random walks for Pollard's Rho method
Mathematics of Computation
Faster Attacks on Elliptic Curve Cryptosystems
SAC '98 Proceedings of the Selected Areas in Cryptography
Speeding Up Pollard's Rho Method for Computing Discrete Logarithms
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Factoring Large Numbers with the Twinkle Device (Extended Abstract)
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
CAIRN 2: An FPGA Implementation of the Sieving Step in the Number Field Sieve Method
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
IEEE Transactions on Computers
Factorization of a 768-bit RSA modulus
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
On the correct use of the negation map in the Pollard rho method
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
A heterogeneous computing environment to solve the 768-bit RSA challenge
Cluster Computing
Using equivalence classes to accelerate solving the discrete logarithm problem in a short interval
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Curve25519: new diffie-hellman speed records
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Reducing elliptic curve logarithms to logarithms in a finite field
IEEE Transactions on Information Theory
Hi-index | 0.00 |
At present, the RSA cryptosystem is most widely used in public key cryptography. On the other hand, elliptic curve cryptography (ECC) has recently received much attention since smaller ECC key sizes provide the same security level as RSA. Although there are a lot of previous works that analyze the security of ECC and RSA, the comparison of strengths varies depending on analysis. The aim of this paper is once again to compare the security strengths, considering state-of-the-art of theory and experiments. The security of RSA is closely related to the hardness of the integer factorization problem (IFP), while the security of ECC is closely related to the elliptic curve discrete logarithm problem (ECDLP). In this paper, we compare the computing power required to solve the ECDLP and the IFP, respectively, and estimate the sizes of the problems that provide the same level of security.