Authoritarianism cannot be solely identified with the left or right because rather than being an intrinsic element of leftist or rightist thought, it's simply a means of reaching certain ideological goals. However, authoritarianism may be intrinsic to an ideology insofar as that ideology requires it as a means of reaching those ideological goals.

With regard to anarchism and socialism, both ideologies are means of reaching a communist society, which is a society premised upon common ownership of the means of production and the absence of class, money and the state, this in of itself isn't authoritarian. However, certain means of reaching a communist society may be considered authoritarian. For example, Marxism holds that it is necessary to develop a socialist state as a transitory phase to a communist society. Marxism-Leninism holds that the socialist state ought to be established via the leadership of a revolutionary vanguard; a dictatorship of the proletariat. The ultimate aim of the proletarian dictatorship is the full realisation of a communist society, but meeting this aim requires the authority of a revolutionary leadership to direct the people to this goal via the advancement of the material and social conditions of the people and the elimination of false consciousness.

Anarchism differs insofar as it seeks the immediate abolition of capitalism, private property and the state without a transitory period. Anarchists reject Marxism and the socialist state, instead seeking to immediately produce a society based on common ownership of the means of production, direct democracy and voluntary associations.

Ultimately, this demonstrates my earlier point that authoritarianism isn't intrinsic to leftism or rightism, it's simply a tool which may be embraced or rejected by a given ideology. If you're asking whether the left or right are authoritarian, then you're asking the wrong question.