BITCOIN GENERATOR V 4.5 64 Bitl ~UPD~

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Starting with March 2017 data, Preliminary Monthly Electric Generator Inventory includes a comprehensive list of generators which retired since 2002. The list can be found on the 'Retired' tab of the datafile.

I strongly disagree with saying that AES-128 is broken, in any way, shape or form, and likewise ECC with 256-bit keys. Note that even in this answer by @kelaka regarding AES-128, you would need over 34 million years of the entire bitcoin mining power to carry out a computation of $2^{128}$. This is far from broken. If quantum computers ever happen at scale, it is very very unclear how long it would have to actually run to achieve $2^{64}$ quantum computations for AES-128 (but ECC-256 would be in bigger trouble). Bottom line, these are far from broken. (I don't know what Schneier quote you are referring to, but anyway I completely disagree.)

The Skein Hash Function Family: The Skein Hash Function Family was proposed to NIST in their 2010 hash function competition. Skein is fast due to using just a few simple computational primitives, secure, and very flexible — per the specification, it can be used as a straight-forward hash, MAC, HMAC, digital signature hash, key derivation mechanism, stream cipher, or pseudo-random number generator. Skein supports internal state sizes of 256, 512 and 1024 bits, and arbitrary output lengths.

TESLA requires the sender to generate a chain of authentication keys, where a given key is associated with a single time slot, T. In general, Ti+1 = Ti+Δt. The sender can create as many keys as it wants but might need to limit the length of the chain based upon memory or other constraints. So, suppose the sender wants to create a chain of N keys. The sender will randomly select the N-th key, KN. Then, using a pseudo-random number generator (PRNG) function, P, and the prior key value as the seed, the sender creates the next key in the chain. Thus, KN-1 = P(KN), KN-2 = P(KN-1),..., K0 = P(K1). Each key is assigned to a time interval, so that Ki is associated with Ti. One important feature is that this is a one-way chain; given any key, Ki, all previously used keys can be derived by the receiver (i.e., any Kj can be calculated where ji).

There are a lot of topics that have been discussed above that will be big issues going forward in cryptography. As compute power increases, attackers can go after bigger keys and local devices can process more complex algorithms. Some of these issues include the size of public keys, the ability to forge public key certificates, which hash function(s) to use, and the trust that we will have in random number generators. Interested readers should check out "Recent Parables in Cryptography" (Orman, H., January/February 2014, IEEE Internet Computing, 18(1), 82-86).

Given this need for randomness, how do we ensure that crypto algorithms produce random numbers for high levels of entropy? Computers use random number generators (RNGs) for myriad purposes but computers cannot actually generate truly random sequences but, rather, sequences that have mostly random characteristics. To this end, computers use pseudorandom number generator (PRNG), aka deterministic random number generator, algorithms. NIST has a series of documents (SP 800-90: Random Bit Generators) that address this very issue:

Before thinking that this is too obscure to worry about, let me point out a field of study called kleptography, the "study of stealing information securely and subliminally" (see "The Dark Side of Cryptography: Kleptography in Black-Box Implementations"). Basically, this is a form of attack from within a cryptosystem itself. From that article comes this whimsical example: Imagine a cryptosystem (hardware or software) that generates PKC key pairs. The private key should remain exclusively within the system in order to prevent improper use and duplication. The public key, however, should be able to be freely and widely distributed since the private key cannot be derived from the public key, as described elsewhere in this document. But, now suppose that a cryptographic back door is embedded into the cryptosystem, allowing an attacker to access or derive the private key from the public key — such as weakening the key generation process at its heart by compromising the random number generators essential to creating strong key pairs. The potential negative impact is obvious.

The CipherValue for an RSA-OAEP encrypted key is the base64 [RFC2045] encoding of the octet string computed as per RFC 3447 [PKCS1], section 7.1.1: Encryption operation. As described in the EME-OAEP-ENCODE function RFC 3447 [PKCS1], section 7.1.1, the value input to the key transport function is calculated using the message digest function and string specified in the DigestMethod and OAEPparams elements and using either the mask generator function specified with the xenc11:MGF element or the default MGF1 with SHA1 specified in RFC 3447. The desired output length for EME-OAEP-ENCODE is one byte shorter than the RSA modulus.

As specified in [ESDH], a DH public key consists of up to six quantities, two large primes p and q, a "generator" g, the public key, and validation parameters "seed" and "pgenCounter". These relate as follows: The public key = ( g**x mod p ) where x is the corresponding private key; p = j*q + 1 where j >= 2. "seed" and "pgenCounter" are optional and can be used to determine if the Diffie-Hellman key has been generated in conformance with the algorithm specified in [ESDH]. Because the primes and generator can be safely shared over many DH keys, they may be known from the application environment and are optional. The schema for a DHKeyValue is as follows:

The Diffie-Hellman (DH) key agreement protocol [ESDH] involves the derivation of shared secret information based on compatible DH keys from the sender and recipient. Two DH public keys are compatible if they have the same prime and generator. If, for the second one, Y = g**y mod p, then the two parties can calculate the shared secret ZZ = ( g**(x*y) mod p ) even though each knows only their own private key and the other party's public key. Leading zero bytes MUST be maintained in ZZ so it will be the same length, in bytes, as p. The size of p MUST be at least 512 bits and g at least 160 bits. There are numerous other complex security considerations in the selection of g, p, and a random x as described in [ESDH].

This drastic performance difference is mostly due to different parts of the process being CPU bound to varying degrees, particularly for BIP39 and Electrum seed recovery. As such shifting more processing in to the OpenCL and creating a more efficient seed generator will be future areas of work.

What this means is that in order to fill the maximum workgroup size for the GPU, the seedgenerator needs to pass it a chunk of possible seeds that is many times larger than the max workgroup size. (Eg: for a work group size of 1024, a BIP39 24 word seed will need 262,144 potential seeds) 2b1af7f3a8