For modular multi-exponentiation, in average case, the proposed algorithm can reduce the number of modular multiplications (MMs) from 1.503 k to 1.306 k, where k is the bit-length of the exponent. We can therefore efficiently speed up the overall performance of the modular multi-exponentiation ...
And finally here’s the most optimized exponentiation by squaring algorithm I have seen around. It’s an iterative version where at each step you divide the exponent by two and square the base, and then for the iterations where the exponent is odd you multiply the result by the base. In ...
For modular multi-exponentiation AXBY(modN), assume the value k is the maximum bit-length of two exponents X and Y, i.e. k=⌈log2max(X,Y)⌉. Consider the average case. Pekmestzi’s algorithm [1] uses 1.75k modular multiplications. Directly employing the minimal weight binary ...
3) Fast modular exponentiation This might be a well-known technique which has been used in RSA cryptosystem. The main idea is that to calculate (a^n)%P, if n is an even number, then we can compute (a^2)^(n/2)%P; while if n is an odd number, we can calculate (a)*(a^2)^...
Figure 1: Performance of algorithms for batch verification of modular exponentiation. We indicate the number of multiplications each method uses to get error 2 −l . See the text for explanations of the parameters. algorithm with respect to some fixed public key.) The verification proble...
Scalar multiplication, modular exponentiation, and pairing evaluation are in general considered expensive. (iii) Fine-grained revocable. Any one credential of the user can be revoked while leaving his other credentials untouched. In other words, revocation of credentials is on a per-user per-access...
Public-key cryptosystems may be used to provide data confidentiality, author authentication and data integrity. Some public-key cryptosystems (e.g., Rivest-Shamir-Adleman (RSA)) rely on modular exponentiation of large numbers, which requires repeated modular multiplications. To increase security, the ...
NSP algorithm for modular exponentiation; 模幂运算的并行算法NSP 2. In this paper,a new modular exponentiation algorithm named window NAF algorithm is proposed. 将椭圆曲线的定点标量乘的窗口NAF方法应用在模幂运算中,通过采用预处理技术,与SMM算法进行组合得到一种新的求模幂乘算法-窗口NAF方法。
This paper proposes a fast parallel Montgomery multiplication algorithm based on Residue Number Systems (RNS). It is easy to construct a fast modular exponentiation by applying the algorithm repeatedly. To realize an efficient RNS Montgomery multiplication, the main contribution of this paper is to pr...
2) Fast modular algorithm 快速模运算3) High speed multiplication and division 快速乘除法运算4) Fast Modular Exponentiation 快速模幂运算5) rapid division 快速除法运算6) fast parallel arithmetic 快速并行运算器补充资料:不定积分的运算法则 又称为“不定积分的性质”,包含如下两个性质: (1)设函数...