# Perfectly secure and indistinguishability property

I'm studying cryptography for my university course, but some doubts arose from reading a book. In this book the author says: "Now we present another equivalent definition of perfect secrecy. This is base on an experiment involving an adversary $$\mathcal{A}$$ and formalizes $$\mathcal{A}$$'s inability to distinguish the encryption of one plaintext from the encryption of another." referring to the eavesdropping indistinguishability experiment. Then he concludes saying that an encryption scheme is perfectly secure if $$Pr[PrivK^{eav}_{\mathcal{A}, \Pi} = 1] = 1/2$$.

In other pages, he says "Any scheme that has indistinguishable encryptions under a chosen-plaintext attack clearly also has indistinguishable encryptions in the presence of an eavesdropper."

My doubt is: if an encryption scheme is indistinguishable from an eavesdropper but it is weak against a chosen plaintext attacks, so how can the scheme be considered still perfectly secure?

Another doubt: "eavesdropping indistinguishability" and "perfectly secure" are both referred to information-theoretically secureness?

• Welcome to Cryptography. Not sure we can find duplicates, however, 1) Is One Time Pad considered Chosen-Plaintext Attack Secure? Mar 17 '20 at 18:16
• The second question has on the textbooks like Lindell&katz or here Please prove distinguishability given a non-perfectly secure cipher Mar 17 '20 at 18:46
• My ideas are more clear now, but doubt remains: can we talk about computational security of a scheme ("scheme that cannot be broken given enough time and computation), if this is scheme is CPA-insecure? Because in my book, computation security is equal to eavesdropping indistinguishability, but some schemes can be eavesdropping indistinguishability but CPA-insecure; are these scheme secure in the sense of computation security? Mar 18 '20 at 11:21
• Could you add the name of the book? Mar 18 '20 at 11:53
• Jonathan Katz, Yehuda Lindell - Introduction to Modern Cryptography_ Principles and Protocols-Chapman and Hall_CRC (2007) Mar 18 '20 at 12:26