Cryptography Protecting democratic elections through secure, verifiable voting |
- Protecting democratic elections through secure, verifiable voting
- Exercise solutions to book :「Cryptography: Theory and Practice by Douglas Stimson. 」
- Corretto - Fast, efficient and bulletproof-friendly cryptographic operations.
- Read the paper that introduced public key cryptography
| Protecting democratic elections through secure, verifiable voting Posted: 06 May 2019 10:49 AM PDT |
| Exercise solutions to book :「Cryptography: Theory and Practice by Douglas Stimson. 」 Posted: 06 May 2019 03:15 PM PDT I've searched the whole internet even in a bilingual way to find the solutions to some specific exercise ( mainly in chapter 6 and 7). But I can't find the one that I need. I heard of this book has been elected as official textbook for many universities worldwide, so why the solutions resource is so few. Does anyone who had an experience on this book and solutions? [link] [comments]  |
| Corretto - Fast, efficient and bulletproof-friendly cryptographic operations. Posted: 06 May 2019 01:59 AM PDT IntroCrypto systems are built on hard problems or one way functions. For example, take a cryptographic hash function y= H(x). Given y it is hard to find the x that gave that specific y value. Although the above is a one way function, it lacks certain properties that make it suitable for general cryptographic protocols, such as public key cryptography and signature protocols. Rivest-Shamir-Adleman (RSA)RSA is based on the assumption that factor two large prime numbers is hard, but multiplying two primes together is easy. In this way, you can think of this as a one way function. Where instead of x, the data being put into the function is two primes and the output is their product. RSA is built on top of these assumptions. Elliptic Curve Cryptography (ECC)Everything in cryptography is based on one way functions or some hard problem. In RSA, it's hard to find the product of two large primes. With elliptic curves, it's hard to find the discrete log of some element. Because it's hard to factor two primes, we use these two primes as our private data and the product of them as our public data/public key. Take 2^x = 8 , in order to find x we take the log of both sides and we can see that x = 3. This is called the continuous log, and is easy. The values of x can be any of the real numbers. If we restrict x to be discrete, meaning x can only be a part of Z_n . Then this problem becomes hard and can act as a one way function. The operation is now called taking the discrete log. Note that in RSA we need two large numbers, while in ECC we have one large number as our secret data. Does this mean that for ECC to be as secure RSA, we need to use bigger numbers? No, it turns out that this is not the case and for comparable security to RSA, ECC can use less data. Ristretto curveRistretto is a technique for constructing prime order elliptic curve groups with non-malleable encodings. The Ristretto protocol arose as an extension of Mike Hamburg's Decaf approach to cofactor elimination, which is applicable to curves of cofactor 4, whereas the Ristretto is designed for non-prime-order curves of cofactor 8 or 4. Embedded curves and CorrettoAn embedded curve A is a curve whose base field is defined by the scalar field of another curve B. In Corretto, B is Ristretto255 and A, the embedded curve is Doppio. Why do we need embedded curves? Can we not use any curve? In short, if you define a rank-1 constraint system over some field Fp, any curve which base field does not match Fp, will need to use binary decomposition in order to operate within that field. Note that the scalar field of Doppio will not equal Fp and so in order to do ScalarMult within the constraint system, you will need binary decomposition. But for point addition this will not be necessary. So we've defined an embedded curve within our constraint system. What now? We can now perform ECC operations within our constraint system. This is powerful because a large proportion of zero knowledge protocols only rely on these operations. One branch of important zero knowledge protocols are those which fall under set inclusion, the most popular one being rangeproofs. With ECC we can prove create a ring signature protocol within our constraint system. The Corretto curve is an elliptic curve developed by Dusk Network based on the Ristretto scalar field. Originally designed to abstract non-prime-order curves into prime-order scalar fields, the Ristretto abstraction would have been far too inefficient to implement for Bulletproofs. Fortunately, our team had designed a brand new curve that enables Dusk Network to utilize the power of the Ristretto scalar field while not indulging in the complex and Bulletproof-unfriendly abstractions that are associated with Ristretto. Corretto opens up new opportunities for the use cases of zero-knowledge proofs inside the Dusk Network protocol as well as making our Bulletproof-integrated ring signature substitute possible. Paper (Github): https://github.com/dusk-network/Corretto/blob/master/docs/Corretto.pdf [link] [comments]  |
| Read the paper that introduced public key cryptography Posted: 06 May 2019 07:27 AM PDT |
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