Multiplicador binario paralelo de dos bitstamps
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This project implements the cryptographic primitives used in the Bitcoin system, especially elliptic curve operations and hash functions. It includes a test suite of over a thousand test vectors that cover every feature provided by the library. The library is open-source, and is written by Nayuki from the ground up. It is designed with portability and clarity in mind, and is rigorously verified for correctness and quality.
Browse source files on GitHub: The only libraries used are essentially the cstdint type definitions, memset , memcpy , and strlen. Also all memory used by this library is allocated on the stack, not on the heap. The cryptography code is designed to run efficiently on microprocessors that support bit integer operations and have a hardware multiplier.
The code has been tested on desktop x86, x and embedded bit ARM systems alike. High-performance bit CPUs are supported too, but the code would run faster if specifically rewritten for them by using bit addition, multiplication, etc. In theory it is possible to literally emulate the bit operations with sequences of 8-bit operations, but this is slow and it would be much preferable to design algorithms for native 8-bit processing from the start.
This means when executing x. In particular, the classes Uint, FieldInt, CurvePoint, and Ecdsa are designed with data-independent constant-time execution in mind. This technique thwarts timing attacks, cache-based attacks, and side channel attacks such as power analysis via an oscilloscope.
Here is a simple example:. By applying this masking technique , we can take low-level functions that are known to be constant-time and build them into higher level functions that are still constant-time.
On a desktop PC, it takes about 5 ms. There are two major optimizations implemented: Performing elliptic curve point addition and doubling in projective coordinates, and using Barrett reduction for modular multiplication. Even though both optimizations make the code significantly harder to verify compared to the naive algorithms, the speed gains are well worth it when computing ECDSA signatures on embedded microcontrollers.
Thus the logic will work correctly and identically on bit and bit platforms. In theory it would even work perfectly on 8- and bit platforms if the compiler generated instructions to emulate bit arithmetic. The logic intentionally avoids signed integer overflow a form of undefined behavior ; almost all math is done with unsigned integers. Type punning is never used. The code makes no assumptions on the endianness of the machine, and thus is usable on both big-endian and little-endian processors.
Practically speaking this is fine because within the test cases, the int variables are almost always within the range [0, ], so there is no need to reason about integer widths or overflow. Firstly, my Bitcoin cryptography library has low code complexity. The core implementation excluding tests is only lines of code including blank lines and comments!
This ensures that complete verification of the codebase is tractable for a human reviewer. Every line of source code has been verified carefully on printed paper. Three pieces of tricky code deserve an extra explanation:.
At the end of the process, the numerators are divided by the denominator to get the ordinary affine point. The algebra is explicitly documented in the comments of the CurvePoint class. A Wikibooks page was used for reference, but the math has been independently re-derived and verified by me. I have a full write-up for the Barrett reduction algorithm , where the article carefully justifies the math behind the algorithm and reasons about the bit widths of the intermediate numbers.
With some effort, it is possible to take the binary GCD algorithm and remove the branches and make the outer loop have a constant number of iterations to cover the worst case namely 2 n iterations, where n is the bit width of bigint. No mathematical justifications are given in the code, but the inline comments are helpful to look at if you are re-deriving your own implementation of this constant-time extended GCD concept.
But so far, the code has only been reviewed and tested by Nayuki. Feedback from readers and programmers would be highly appreciated. Libsecpk1 is the code used in the official Bitcoin project for elliptic curve arithmetic and other cryptography such as the SHA hash. In early year , in version 0. Libsecpk1 is the effort of a couple of smart developers for years, and is deployed in live Bitcoin clients processing billions of transactions.
Its core functionality is implemented in about lines of code. However, the requirement to avoid heap allocation makes the Java code fairly ugly. But at least the Java code does achieve its design goals and computes the elliptic curve functions correctly and efficiently.
Bitcoin cryptography library This project implements the cryptographic primitives used in the Bitcoin system, especially elliptic curve operations and hash functions. Source code Browse source files on GitHub: MIT open source Project components: An unsigned bit integer with wrap-around overflow arithmetic. An integer modulo a prime number, in the field used for the elliptic curve. A point on the secpk1 elliptic curve for Bitcoin.
The elliptic curve digital signature algorithm, signing and verification. Constant-time arithmetic operations The entire stack of code for ECDSA signing is implemented using constant-time arithmetic operations. Here is a simple example: Small, rigorously verified code Firstly, my Bitcoin cryptography library has low code complexity. Three pieces of tricky code deserve an extra explanation: Comparison with libsecpk1 Libsecpk1 is the code used in the official Bitcoin project for elliptic curve arithmetic and other cryptography such as the SHA hash.
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