# randomness of encrypt

In the paper "Efficient Encryption from Random Quasi-Cyclic Codes" of Gaborit et al. p.14, I read "Encrypt$$(pk=(G,Q,s),\mu,\theta)$$: uses randomness $$\theta$$ to generate $$\epsilon \xleftarrow{\\\}V,r=(r_1,r_2) \xleftarrow{\\\}V^2$$...". Does it mean exactly "uses randomness $$\theta$$"? Where Can I find a descryption of a PKE in this terms?

For an encryption scheme to satisfy the standard notion of security (IND-CPA), its encryption algorithm must be randomised. Therefore $$\textsf{Encrypt}$$ has access to random coins, denoted here by $$\theta$$. It is usually implicit in the syntax of $$\textsf{Encrypt}$$ $$c\leftarrow\textsf{Encrypt}(pk,m),$$ but it can be made explicit as $$c=\textsf{Encrypt}(pk,m;\theta).$$
For example, the encryption algorithm in El Gamal (which is IND-CPA secure under the DDH assumption) with public key $$pk=(G,g,h,q)$$ and message $$m\in G$$ can be described as $$(c_1=g^r,c_2=h^r\cdot m)=\mathsf{Encrypt}(pk,m;\theta),$$ where the random coin $$\theta$$ (interpreted as a string) is used to sample $$r\in[1,q-1]$$.