中文摘要：

椭圆曲线已经广泛应用于密码学领域中的公钥密码系统,数字签名验证等。在椭圆曲线密码系统中,标量乘法占据着十分重要的地位。目前已经有一些算法来加快这些十分关键的计算,它们均基于整数的不同表示,以尽量减少一般乘法或点加法的数目。在椭圆曲线现有的各种计算方法中,联合稀疏表式（JSF）,w-NAF,双基方法是目前常用并且有效的算法。基于多基整数表示系统,提出一种联合多基稀疏表示方法。多基联合稀疏表示需要较少的位数,并且比JSF和w-NAF更加稀疏,（2,3,5）基表示与（2,3）基表示相比,可以使椭圆曲线标量乘法的运算提高约16%的效益。

英文摘要：

Elliptic curve has been widely used in public key cryptography of cryptology field and in digital signature verification, etc. In elliptic curve cryptology, scalar muhiplication occupies very important position. At present there have been some algorithms to speed up these critical calculations, and they are all based on integer representations in order to minimise as much as possible the number of general multiplication or point addition. In various existing calculation approaches of elliptic curve, joint sparse form （JSF） and w-NAF, the dual-base approach is the commonly used and effective algorithms at present. In this paper, we propose a joint muhibase sparse form based on muhibase integer representation system. Muhibase joint sparse form requires fewer digits and is sparser than JSF and w-NAF, comparing the （2,3,5） base representation and the （2,3） base representation, the operation efficiency of elliptic curve scalar multiplication can be increased about 16%.