Let p be a prime; then the multiplicative group ℤ_p* of the integers 0 < k < p modulo (see modulo n arithmetic) p is cyclic, and if r is a generator (a primitive root), then k = r^m for some 0 ≤ m < p–1. This integer m is the discrete logarithm, or index, of k to base r. This is written m = ind_rk. For p = 11 and r = 2 the powers of r are 1,2,4,8,5,10,9,7,3,6 and so ind₂3 = 8. In general though, for large primes p, there is no known efficient algorithm for calculating ind_rk; consequently, discrete logarithms have found various uses in cryptography.