In Chapter 11, History of Cryptographic Key Sizes, Nigel P. Smart and Emmanuel Thomé provide an overview of improvements over the years in estimating the security level of the main cryptographic hardness assumptions. These improvements heavily rely on the algorithmic innovations discussed in Chapters 2 to 5, but combining all those ideas into concrete key-size recommendations is not immediate. Smart and Thomé have been at the forefront of cryptanalytic research and recommending cryptographic key sizes and conclude with current recommendations in Chapter 11.