Zero Knowledge Proof


Zero-Knowledge proofs are fascinating and extremely useful constructs. Their fascinating nature is due to their seemingly contradictory definition; zero-knowledge proofs are both convincing and yet yield nothing beyond the validity of the assertion being proven. Their applicability in the domain of cryptography is vast; they are typically used to force malicious parties to behave according to a predetermined protocol. In addition to their direct applicability in Cryptography, zero-knowledge proofs serve as a good bench-mark for the study of various problems regarding cryptographic protocols (e.g., “secure composion of protocols” and the “use of of the adversary’s program within the proof of security”).

In this tutorial we will present the basic definitions and results regarding zero-knowledge as well as some recent developments regarding this notion.

The Basics

Loosely speaking, zero-knowledge proofs are proofs that yield nothing beyond the validity of the assertion. That is, a verifier obtaining such a proof only gains conviction in the validity of the assertion. This is formulated by saying that anything that is feasibly computable from a zero-knowledge proof is also feasibly computable from the (valid) assertion itself (by a so-called simulator). Variants on the basic definition include:

  • Consideration of auxiliary inputs.
  • Universal and black-box simulations.
  • Restricting attention to honest verifiers.
  • The level of similarity required of the simulation.

It is well-known that zero-knowledge proofs exist for any NP-set, provided that one-way functions exist. This result is a powerful tool in the design of cryptographic protocols, because it enables to force parties to behave according to a predetermined protocol (i.e., the protocol requires parties to provide zero-knowledge proofs of the correctness of their secret-based actions, without revealing these secrets).

Advanced Topics

We focus on two basic problems regarding zero-knowledge, which actually arise also with respect to the security of other cryptographic primitives. The first question refers to the preservation of security (i.e., zero-knowledge in our case) under various types of composition operations. We survey the known results regarding sequential, parallel and concurrent execution of (arbitrary and/or specific) zero-knowledge protocols. The main facts are:

  • Zero-knowledge (w.r.t auxiliary inputs) is closed under sequential composition.
  • In general, zero-knowledge is not closed under parallel composition. Yet, some zero-knowledge proofs (for NP) preserve their security when many copies are executed in parallel. Furthermore, some of these protocol use a constant number of rounds.
  • Some zero-knowledge proofs (for NP) preserve their security when many copies are executed concurrently, but such a result is not known for constant-round protocols.

The second basic question regarding zero-knowledge refers to the usage of the adversary’s program within the proof of security (i.e., demonstration of the zero-knowledge property). For 15 years, all known proofs of security used the adversary’s program as a black-box (i.e., a universal simulator was presented using the adversary’s program as an oracle). Furthermore, it was believed that there is no advantage in having access to the code of the adversary’s program. Consequently it was conjectured that negative results regarding black-box simulation represent an inherent limitation of zero-knowledge. This belief has been refuted recently by a zero-knowledge argument (for NP) that has important properties that are unachievable by black-box simulation.

Other topics treated in the full version of the tutorial (but not in its oral presentation) include proofs of knowledge, Non-Interactive Zero-Knowledge proofs, Statistical Zero-Knowledge, Knowledge Complexity, and the resettability of a party’s random-tape.
http://www.wisdom.weizmann.ac.il/~oded/zk-tut02.html

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Lyrics of Pee Loon Hoto Ki Sargam Song


Song Details:-
Song Name: Pee Loon Hoto Ki Sargam
Film/Album: Once Upon A Time In Mumbaai
Singer(s): Mohit Chauhan
Music Director: Pritam
Lyricist: Irshad Kamil
Picturised on: Emraan Hashmi, Prachi Desai
Choreography: Raju Khan
Length: 4:48
Music Label: T-Series

Lyrics of Pee Loon Hoto Ki Sargam Song

Pee loon tere neelay neelay nainon se shabnam
Pee loon tere geelay geelay hoto ki sargam
Pee loon hai peenay ka mausam
Tere sang ishq taari hai
Tere sang ik khumari hai
Tere sang chain bhi mujhko
Tere sang bekraari hai
Tere sang ishq taari hai
Tere sang ik khumari hai
Tere sang chain bhi mujhko
Tere sang bekraari hai
Tere bin jee nahi lagda, tere bin jee nahi sakda
Tujhpe hai haare maine vaare do jahan, kurbaan, meharbaan, ke main toh kurbaan
Sun le zara, tera kurbaan

Hosh mein rahun kyun aaj main
Tu meri baahon mein simti hai, mujh mein samayi hai yun
Jis tarah ki koi hum nadi, tu mere seenay mein chupti hai sagar tumhara main hoon
Pee loon teri dheemi dheemi lehron ki cham cham
Pee loon teri saundi saundi saanson ko har dum
Pee loon hai peenay ka mausam
Tere sang ishq taari hai
Tere sang ik khumari hai
Tere sang chain bhi mujhko
Tere sang bekraari hai
Tere sang ishq taari hai
Tere sang ik khumari hai
Tere sang chain bhi mujhko
Tere sang bekraari hai

Shaam ko milun jo main tujhe
Toh bura subah na jaane kyun kuch maan jaati hai yeh
Har lamha, har gadi har pehar
Hi teri yaadon se tadpa ke mujhko jalati hai yeh
Pee loon main dheere dheere jalne ka yeh gumm
Pee loon inn gore gore haanthon se hum dum
Pee loon hai peenay ka mausam
Tere sang ishq taari hai
Tere sang ik khumari hai
Tere sang chain bhi mujhko
Tere sang bekraari hai
Tere sang ishq taari hai
Tere sang ik khumari hai
Tere sang chain bhi mujhko
Tere sang bekraari hai
Tere bin jee nahi lagda, tere bin jee nahi sakda
Tujhpe hai haare maine vaare do jahan, kurbaan, meharbaan, ke main toh kurbaan
Sun le zara, tera kurbaan

Lyrics of Tum Jo Aaye Song


Lyrics of Tum Jo Aaye Song

Paaya maine, paaya tumhe, rab ne milaya tumhe, honthon pe sajaya tumhe, nag mein sagaya tumhe

Paaya maine, paaya tumhe, sab se chupaya tumhe, sapna banaya tumhe, neendhon mein bulaya tumhe

Tum jo aaye zindagi mein baat ban gayi

Ishq mazhab, ishq meri zaat ban gayi

Paaya maine, paaya tumhe, rab ne milaya tumhe, honthon pe sajaya tumhe, nag mein sagaya tumhe

Paaya maine, paaya tumhe, sab se chupaya tumhe, sapna banaya tumhe, neendhon mein bulaya tumhe

Ho tum jo aaye zindagi mein baat ban gayi

Sapne teri chahaton ke, sapne teri chahaton ke

Dekhti hoon ab gayi

Din hai sona aur chaandi raat ban gayi

Hoo tum jo aaye zindagi mein baat ban gayi

Paaya maine, paaya tumhe, rab ne milaya tumhe, honthon pe sajaya tumhe, nag mein sagaya tumhe

Paaya maine, paaya tumhe, sab se chupaya tumhe, sapna banaya tumhe, neendhon mein bulaya tumhe

Chahaton ka mazaa, faasalon mein nahin

Aa chupa loon tumhe hauslon mein kahin

Sab se upar likha, hai tere naam ko

Khwaishon se jude silsilon mein kahin

Khwaishein milne ki tumse, khwaishein milne ki tumse

Roz hoti hai nayi

Mere dil ki jeet meri maat ban gayi

Hoo tum jo aaye zindagi mein baat ban gayi

Paaya maine, paaya tumhe, rab ne milaya tumhe, honthon pe sajaya tumhe, nag mein sagaya tumhe

Paaya maine, paaya tumhe, sab se chupaya tumhe, sapna banaya tumhe, neendhon mein bulaya tumhe

Zindagi bewafa hai yeh maana magar

Chod kar raah mein jaoge tum agar

Cheen launga main aasman se tumhe

Soona hoga na yeh, do dilon ka nagar

Raunke hain dil ke dar pe, raunke hain dil ke dar pe

Dhadkane hain surmayi

Meri kismat bhi tumhari, saath ban gayi

Hoo tum jo aaye zindagi mein baat ban gayi

Ishq mazhab, ishq meri zaat ban gayi

Sapne teri chahaton ke, sapne teri chahaton ke

Dekhti hoon ab gayi

Din hai sona aur chaandi raat ban gayi

Hoo tum jo aaye zindagi mein baat ban gayi

http://www.top10bollywood.com/

Paaya maine, paaya tumhe, rab ne milaya tumhe, honthon pe sajaya tumhe, nag mein sagaya tumhe

Paaya maine, paaya tumhe, sab se chupaya tumhe, sapna banaya tumhe, neendhon mein bulaya tumhe

Paaya maine, paaya tumhe, rab ne milaya tumhe, honthon pe sajaya tumhe, nag mein sagaya tumhe

Paaya maine, paaya tumhe, sab se chupaya tumhe, sapna banaya tumhe, neendhon mein bulaya tumhe

majhe tujhyvar khup prem ahe


माझं तुझ्यावर खरचं खुप प्रेम आहे
म्हणूनच तुझ्या सगळयाच गोष्टीवर मी फ़िदा आहे
तु जेव्हा माझ्या बाईकवर बसशील
स्कार्फ़ तू लपेटून घे
नसशील सुंदर तरी चालेल पण पर्स तुझी भरुन घे
मी जेव्हा फ़ोन करीन धावत-धावत भेटायला ये
होत असेल गरम तरीसुध्दा माझ्याबरोबर
टपरीवरचा फ़क्कड चहाच घे
वाढदिवस तुझा असेल तेव्हा माझा गुलाब प्रेमाने घे
फ़ुलामध्येच हिरे मोती सगळं काही तू पाहून घे
असेच प्रेम करु जन्मभर …
पण असेल तुझा लग्नाचा विचार तर खिसा माझा
पाहून नोकरी तू शोधून घे
यामध्ये तुला जे समजायचे ते समजून घे
पण माझ तुझ्यावर खरचं खूप प्रेम आहे
म्हणून तुझ्या सगळ्याच गोष्टीवर मी फ़िदा आहे.

It hurt me so bad when you told me you didn’t care


It hurt me so bad
when you told me you didn’t care
I cannot believe I let one person
make me cry so many tears
I didn’t know how much I loved you
till I realized I had to hate you
now my stomach is in knots
and my heart just hurts
and my head is so confused
because I thought when you said
*I love you*
it meant you really did