Patent Application
20130177155
1. Technical Field
Aspects of this document relate generally to telecommunication systems and techniques for transmitting data across a telecommunication channel.
2. Background Art
In the existing art, normally distributed random variable (RV) samples are generated by first generating a uniform distributed random variable using a Pseudo-Random Number Generator (PRNG) based on well-known techniques using Linear Feedback Shift Registers (LFSR) and then applying one of many available mathematical transforms, such as for example, Box Muller, Central Limit Theorem (Sum-of-Uniforms), Piecewise Linear Approximation using Triangular distribution, Monty Python Method, Recursive Method (Wallace), Ziggurat Method, Inversion Method, etc. to generate the normally distributed RV from the uniform distributed RV. Although there are now many hardware implementations of algorithms that can accurately perform the transformation from a uniform to a normally distributed RV, the accuracy of the normal distribution is still limited by the accuracy of the method for generating the uniformly distributed samples. The traditional method of using LFSR does not produce accurate uniform random variables because of its relatively short periodicity, which limits the accuracy at the tail of the normal distribution. Although techniques have been implemented to mitigate this effect by extending the periodicity of a particular LFSR, these techniques still impose limitations on the accuracy of the normal probability distribution function generated.
As an alternative to digital implementations of uniform distributed random variables, there are also analog methods present in the current art. These analog methods rely on errors in analog components to generate true random numbers, but these methods are sensitive to environmental changes such as temperature, and also cannot support high throughput applications.
Aspects and applications of the disclosure presented here are described below in the drawings and detailed description. Unless specifically noted, it is intended that the words and phrases in the specification and the claims be given their plain, ordinary, and accustomed meaning to those of ordinary skill in the applicable arts. The inventors are fully aware that they can be their own lexicographers if desired. The inventors expressly elect, as their own lexicographers, to use only the plain and ordinary meaning of terms in the specification and claims unless they clearly state otherwise and then further, expressly set forth the “special” definition of that term and explain how it differs from the plain and ordinary meaning Absent such clear statements of intent to apply a “special” definition, it is the inventors' intent and desire that the simple, plain and ordinary meaning to the terms be applied to the interpretation of the specification and claims.
The inventors are also aware of the normal precepts of English grammar. Thus, if a noun, term, or phrase is intended to be further characterized, specified, or narrowed in some way, then such noun, term, or phrase will expressly include additional adjectives, descriptive terms, or other modifiers in accordance with the normal precepts of English grammar. Absent the use of such adjectives, descriptive terms, or modifiers, it is the intent that such nouns, terms, or phrases be given their plain, and ordinary English meaning to those skilled in the applicable arts as set forth above.
Further, the inventors are fully informed of the standards and application of the special provisions of 35 U.S.C. §112, ¶6. Thus, the use of the words “function,” “means” or “step” in the Description , Drawings, or Claims is not intended to somehow indicate a desire to invoke the special provisions of 35 U.S.C. §112, ¶6, to define the invention. To the contrary, if the provisions of 35 U.S.C. §112, ¶6 are sought to be invoked to define the claimed disclosure, the claims will specifically and expressly state the exact phrases “means for” or “step for, and will also recite the word “function” (i.e., will state “means for performing the function of [insert function]”), without also reciting in such phrases any structure, material or act in support of the function. Thus, even when the claims recite a “means for performing the function of . . . ” or “step for performing the function of . . . ,” if the claims also recite any structure, material or acts in support of that means or step, or that perform the recited function, then it is the clear intention of the inventors not to invoke the provisions of 35 U.S.C. §112, ¶6. Moreover, even if the provisions of 35 U.S.C. §112, ¶6 are invoked to define the claimed disclosure, it is intended that the disclosure not be limited only to the specific structure, material or acts that are described in the preferred embodiments, but in addition, include any and all structures, materials or acts that perform the claimed function as described in alternative embodiments or forms of the invention, or that are well known present or later-developed, equivalent structures, material or acts for performing the claimed function.
The foregoing and other aspects, features, and advantages will be apparent to those artisans of ordinary skill in the art from the DESCRIPTION and DRAWINGS, and from the CLAIMS.
Implementations will hereinafter be described in conjunction with the appended drawings, where like designations denote like elements, and:
This disclosure, its aspects and implementations, are not limited to the specific components, encryption types, or methods disclosed herein. Many additional components and assembly procedures known in the art consistent with a method for generating normalized random variables are in use with particular implementations from this disclosure. Accordingly, for example, although particular implementations are disclosed, such implementations and implementing components may comprise any components, models, versions, quantities, and/or the like as is known in the art for such systems and implementing components, consistent with the intended operation.
This disclosure relates generally to a method for generating normally distributed random variables for a communications channel and other application. More specifically, this disclosure relates to a method and system for providing highly accurate normally distributed random variable samples based on the application of one or more cryptographic algorithms. Implementations of the described method and system offer a novel approach for providing high quality and accurate normally distributed random variables. Particular implementations described herein may use but are not limited to using techniques for cryptography and/or digital signal processing (DSP) techniques such as, but not limited to, multiplication, square-root, log, cosine/sine look-up table, encryption/decryption, that may be implemented in devices such as a Field-Programmable Gate Array (FPGA), Programmable Logic Device (PLD), Programmable Integrated Circuit (PIC), Digital Signal Processor (DSP), Application Specific Integrated Circuit (ASIC) or general purpose microprocessors using conventional implementation methods known in the art with knowledge of this disclosure.
The described implementations are intended to provide one of ordinary skilled in the art, e.g., a communications software or hardware engineer, and the like to utilize the described methodology without undue experimentation.
In the existing art, digital implementations of systems and methods for generating normally distributed random variables rely on various Linear Feedback Shift Register (LFSR) techniques that produce pseudorandom numbers that do not have the statistical quality of a cryptographic algorithm, such as an Advanced Encryption Standard (AES), and which tend to repeat after a relatively short period. The LFSR based techniques are used to generate uniformly distributed random variables which are then transformed mathematically into normally distributed random variables. A short periodicity, such as that present when using LFSR techniques has a negative impact on the resulting output due to the lack of true randomness. Thus, the quality and accuracy of the normally distributed random variables is limited to the quality of the uniformly distributed random variables which are input into the mathematical transformation. The quality of the normally distributed random variables is evaluated as the probability distribution function quality in the tails as expressed in a maximum attainable multiple of the standard deviation. In implementations of the described method and system, a cryptographic algorithm is used to generate more accurately uniformly distributed random samples rather than those generated through the use of LFSR.
In implementations of the described method and system, higher quality and more accurate normally distributed random variables can be generated by replacing the LFSR with a cryptographic algorithm, such as Advanced Encryption Standard (AES) in Cyclic Block Cipher (CBC) mode. The AES in CBC mode runs freely and generates a stream of pseudorandom numbers having higher entropy and without the relatively short periodicity issue associated with LFSR as used in traditional methodologies. Implementations of the described method can also be efficiently implemented and realized digitally in hardware. This provides for high throughput applications and does not have the instability of analog based implementations.
In implementations of the described method, cryptographic algorithms, such as AES in CBC mode, is used to generate uniform distributed RV with better statistical properties (i.e. higher entropy) and significantly longer period than required for most applications. One of the advantages of using cryptographic algorithms is to remove correlation from a given input data set and generating randomness. Particular modes of operation, such as CBC, allow a cryptographic algorithm to free-run and continuously generate random data even when an input value is held constant by using the cipher output for the previous block and applying the XOR operation with the input In other words, implementations of the disclosed method can continue to generate random samples without the relatively short periodicity limitation associated with LFSR. Thus, implementations of the disclosed methods generate a significantly higher quality random number stream and when combined with a transformation algorithm, such as Box Muller or any other transformation algorithm known to those of ordinary skill in the art, may yield a far more accurate normal distribution of random variable samples that more closely emulate a true normal probability distribution function (PDF). Furthermore, digital implementations of the disclosed method do not suffer from the drawbacks of traditional analog methods such as parameter or component drift, temperature sensitivity or lack of repeatability to name a few examples.
Generation of random variables with a normal probability distribution has utility in many applications. For example, one such application is the implementation of an Additive White Gaussian Noise (AWGN) Generator for simulating a noisy communication channel, such as, for example, in a satellite link. The AWGN is a specific case of a normal distributed random variable with a mean equal to zero and a noise power equal to the variance. Implementations of the described method provide a novel approach for generating normally distributed random variables based on certain advanced cryptographic algorithms, such as for example, Advanced Encryption Standard (AES) in Cyclic Block Cipher (CBC) mode.
Particular implementations of a method for generating accurate normalized random variable samples as disclosed herein may be specifically employed for the application of an Additive White Gaussian Noise (AWGN) generator to simulate communication channels. However, one of ordinary skill in the art will recognize from this disclosure that the principles and aspects disclosed herein may readily be applied any other application that requires accurate normal distributed random variables.
A more specific example of an implementation of the disclosed method in the application of an Additive White Gaussian Noise Generator (AWGN) is provided in
In an implementation of the AWGN generator, using an implementation of the disclosed method, one may digitally tune and control the signal-to-noise level at baseband with a very high resolution and accuracy which provides a significant advantage compared to using methodologies present in the prior art.
As described above, particular implementations of the described methods and systems apply to AWGN generators to simulate a communication channel, but the technology described is not limited to this application. It is also intended that implementations of the described methods may be built into a communication link transmitter in a single hardware device or among a plurality of hardware devices. For example, as shown in
Depending upon the implementation, at least one of a cipher input data, a cipher input key, and/or an initialization vector (IV) may be held at a fixed constant value or may be dynamic and periodically changing.
However, in some applications, it may be advantageous to configure an implementation of the system to create a stand-alone device that creates AWGN or any other form of the normally distributed random variables disclosed herein and receives a data signal and combines the data signal with the AWGN or other noise signal created by the stand-alone device and transmits the combined data and noise signal, as shown in
Furthermore, in some applications, it may be advantageous to configure an implementation of the system to create a stand-alone device that creates AWGN or any other form of the normally distributed random variables disclosed, as shown in
In some implementations, to achieve higher throughput, multiple cryptographic devices or multiple processors within a cryptographic device may be run in parallel.
In places where the description above refers to particular implementations of telecommunication systems and techniques for transmitting data across a telecommunication channel, it should be readily apparent that a number of modifications may be made without departing from the spirit thereof and that these implementations may be applied to other to telecommunication systems and techniques for transmitting data across a telecommunication channel.
This document claims the benefit of the filing date of U.S. Provisional Patent Application No. 61/710,225, entitled “Method and System for Generating Normal Distributed Random Variable Based on Cryptographic Function” to Kasra Akhavan-Toyserkani, et al., which was filed on Oct. 5, 2012,the disclosure of which is hereby incorporated entirely by reference herein.
| Number | Date | Country | |
|---|---|---|---|
| 61710225 | Oct 2012 | US |
