Yao's Garbled Circuit
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Yao's Garbled Circuit
Garbled circuit is a cryptographic protocol that enables two-party secure computation in which two mistrusting parties can jointly evaluate a function over their private inputs without the presence of a trusted third party. In the garbled circuit protocol, the function has to be described as a Boolean circuit. The history of garbled circuits is complicated. The invention of garbled circuit was credited to Andrew Yao, as Yao introduced the idea in the oral presentation of a paper in FOCS'86. This was documented by Oded Goldreich in 2003. The first written document about this technique was by Goldreich, Micali, and Wigderson in STOC'87. The term "garbled circuit" was first used by Beaver, Micali, and Rogaway in STOC'90. Yao's protocol solving Yao's Millionaires' Problem was the beginning example of secure computation, yet it is not directly related to garbled circuits. Background Oblivious transfer In the garbled circuit protocol, we make use of oblivious transfer. In t ...
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Cryptographic Protocol
A cryptographic protocol is an abstract or concrete Communications protocol, protocol that performs a information security, security-related function and applies cryptographic methods, often as sequences of cryptographic primitives. A protocol describes how the algorithms should be used and includes details about data structures and representations, at which point it can be used to implement multiple, interoperable versions of a program. Cryptographic protocols are widely used for secure application-level data transport. A cryptographic protocol usually incorporates at least some of these aspects: * Key agreement or establishment * Entity authentication * Symmetric encryption and message authentication key (cryptography), material construction * Secured application-level data transport * Non-repudiation methods * Secret sharing methods * Secure multi-party computation For example, Transport Layer Security (TLS) is a cryptographic protocol that is used to secure web (HTTPS) conne ...
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Security Parameter
In cryptography, a security parameter is a way of measuring of how "hard" it is for an adversary to break a cryptographic scheme. There are two main types of security parameter: ''computational'' and ''statistical'', often denoted by \kappa and \lambda, respectively. Roughly speaking, the computational security parameter is a measure for the input size of the computational problem on which the cryptographic scheme is based, which determines its computational complexity, whereas the statistical security parameter is a measure of the probability with which an adversary can break the scheme (whatever that means for the protocol). Security parameters are usually expressed in unary representation - i.e. \kappa is expressed as a string of \kappa 1s, \kappa=1\cdots 1, conventionally written as 1^\kappa - so that the time complexity of the cryptographic algorithm is polynomial in the size of the input. Computational security The security of cryptographic primitives relies on the hard ...
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Symmetric Encryption
Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both the encryption of plaintext and the decryption of ciphertext. The keys may be identical, or there may be a simple transformation to go between the two keys. The keys, in practice, represent a shared secret between two or more parties that can be used to maintain a private information link. The requirement that both parties have access to the secret key is one of the main drawbacks of symmetric-key encryption, in comparison to public-key encryption (also known as asymmetric-key encryption). However, symmetric-key encryption algorithms are usually better for bulk encryption. With exception of the one-time pad they have a smaller key size, which means less storage space and faster transmission. Due to this, asymmetric-key encryption is often used to exchange the secret key for symmetric-key encryption. Types Symmetric-key encryption can use either stream ciphers or block ciphers. ...
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Truth Table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid. A truth table has one column for each input variable (for example, A and B), and one final column showing all of the possible results of the logical operation that the table represents (for example, A XOR B). Each row of the truth table contains one possible configuration of the input variables (for instance, A=true, B=false), and the result of the operation for those values. A proposition's truth table is a graphical representation of its truth function. The truth function can be more useful for mathema ...
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Boolean Data Type
In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted ''true'' and ''false'') which is intended to represent the two truth values of logic and Boolean algebra. It is named after George Boole, who first defined an algebraic system of logic in the mid 19th century. The Boolean data type is primarily associated with conditional statements, which allow different actions by changing control flow depending on whether a programmer-specified Boolean ''condition'' evaluates to true or false. It is a special case of a more general ''logical data type—''logic does not always need to be Boolean (see probabilistic logic). Generalities In programming languages with a built-in Boolean data type, such as Pascal, C, Python or Java, the comparison operators such as > and ≠ are usually defined to return a Boolean value. Conditional and iterative commands may be defined to test Boolean-valued expressions. L ...
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Carry Flag
In computer processors, the carry flag (usually indicated as the C flag) is a single bit in a system status register A status register, flag register, or condition code register (CCR) is a collection of status Flag (computing), flag bits for a Central processing unit, processor. Examples of such registers include FLAGS register (computing), FLAGS register in the .../flag register used to indicate when an arithmetic carry (arithmetic), carry or borrow has been generated out of the most significant bit, most significant arithmetic logic unit (ALU) bit position. The carry flag enables numbers larger than a single ALU width to be added/subtracted by carrying (adding) a binary digit from a partial addition/subtraction to the least significant bit position of a more significant word. This is typically programmed by the user of the processor on the assembly or machine code level, but can also happen internally in certain processors, via digital logic or microcode, where some processors ...
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Adder–subtractor
In digital circuits, an adder–subtractor is a circuit that is capable of adding or subtracting numbers (in particular, binary). Below is a circuit that adds ''or'' subtracts depending on a control signal. It is also possible to construct a circuit that performs both addition and subtraction at the same time. Construction Having an ''n''-bit adder for ''A'' and ''B'', then . Then, assume the numbers are in two's complement. Then to perform , two's complement theory says to invert each bit of ''A'' with a NOT gate then add one. This yields , which is easy to do with a slightly modified adder. By preceding each ''A'' input bit on the adder with a 2-to-1 multiplexer where: * Input 0 (''I''0) is ''A'' * Input 1 (''I''1) is that has control input ''D'' that is also connected to the initial carry, then the modified adder performs * addition when , or * subtraction when . This works because when the ''A'' input to the adder is really and the carry in is 1. Adding ''B'' to an ...
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Full Adder
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of processors, adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are used to calculate addresses, table indices, increment and decrement operators and similar operations. Although adders can be constructed for many number representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where two's complement or ones' complement is being used to represent negative numbers, it is trivial to modify an adder into an adder–subtractor. Other signed number representations require more logic around the basic adder. History George Stibitz invented the 2-bit binary adder (the Model K) in 1937. Binary adders Half adder The half adder adds two single binary digits A and B. It has two outputs, sum (S) and carry (C). The carry signal represents an overf ...
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Digital Comparator
A digital comparator or magnitude comparator is a Computer hardware, hardware electronic device that takes two numbers as input in Binary numeral system, binary form and determines whether one number is greater than, less than or equal to the other number. Comparators are used in central processing units (CPUs) and microcontrollers (MCUs). Examples of digital comparator include the CMOS 4063 and 4585 and the TTL 7485 and 74682. An XNOR gate is a basic comparator, because its output is "1" only if its two input bits are equal. The analog signal, analog equivalent of digital comparator is the comparator, voltage comparator. Many microcontrollers have analog comparators on some of their inputs that can be read or trigger an interrupt. Implementation Consider two 4-bit binary numbers A and B so A=A_3A_2A_1A_0 B=B_3B_2B_1B_0 Here each subscript represents one of the digits in the numbers. ;Equality The binary numbers A and B will be equal if all the pairs of significant digit ...
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Logic Synthesis
In computer engineering, logic synthesis is a process by which an abstract specification of desired circuit behavior, typically at register transfer level (RTL), is turned into a design implementation in terms of logic gates, typically by a computer program called a ''synthesis tool''. Common examples of this process include synthesis of designs specified in hardware description languages, including VHDL and Verilog. Some synthesis tools generate bitstreams for programmable logic devices such as PALs or FPGAs, while others target the creation of ASICs. Logic synthesis is one step in circuit design in the electronic design automation, the others are place and route and verification and validation. History The roots of logic synthesis can be traced to the treatment of logic by George Boole (1815 to 1864), in what is now termed Boolean algebra. In 1938, Claude Shannon showed that the two-valued Boolean algebra can describe the operation of switching circuits. In the early d ...
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