Abstract: A Metadata server described herein is configured to generate a metadata table optimized for data durability and recovery. In generating the metadata table, the metadata server associates each possible combination of servers with one of the indices of the table, thereby ensuring that each server participates in recovery in the event of a server failure. In addition, the metadata server may also associate one or more additional servers with each index to provide added data durability. Upon generating the metadata table, the metadata server provides the metadata table to clients or servers. Alternatively, the metadata server may provide rules and parameters to clients to enable those clients to identify servers storing data items. The clients may use these parameters and an index as inputs to the rules to determine the identities of servers storing or designated to store data items corresponding to the index.

Abstract: A method described herein includes acts of executing a cryptographic function over input data utilizing a processor on a computing device and generating a data packet that indicates how the cryptographic function interacts with hardware of the computing device, wherein the hardware of the computing device comprises the processor. The method also includes acts of analyzing the data packet, and generating an indication of security of the cryptographic function with respect to at least one side channel attack based at least in part upon the analyzing of the data packet.

Abstract: A Metadata server described herein is configured to generate a metadata table optimized for data durability and recovery. In generating the metadata table, the metadata server associates each possible combination of servers with one of the indices of the table, thereby ensuring that each server participates in recovery in the event of a server failure. In addition, the metadata server may also associate one or more additional servers with each index to provide added data durability. Upon generating the metadata table, the metadata server provides the metadata table to clients or servers. Alternatively, the metadata server may provide rules and parameters to clients to enable those clients to identify servers storing data items. The clients may use these parameters and an index as inputs to the rules to determine the identities of servers storing or designated to store data items corresponding to the index.

Abstract: Executable instructions designed to provide faster cryptographic processing, fixed-timing memory access, and dedicated memory usage are implementable on an x86 CPU utilizing XMM registers. The instructions can be utilized to implement cryptographic processing in accordance with the Advanced Encryption Standard (AES). To encrypt, a single instruction performs nonlinear transformation, rotation, and linear transformation. Another single instruction used during encryption performs nonlinear transformation and rotation. New instructions also are implemented to perform decryption. The instructions implemented to perform decryption perform the mathematical inverse functions of their counterparts used for encryption.

Abstract: A method described herein includes acts of executing a cryptographic function over input data utilizing a processor on a computing device and generating a data packet that indicates how the cryptographic function interacts with hardware of the computing device, wherein the hardware of the computing device comprises the processor. The method also includes acts of analyzing the data packet, and generating an indication of security of the cryptographic function with respect to at least one side channel attack based at least in part upon the analyzing of the data packet.

Abstract: Methods and apparati are provided for use in cryptographically processing information based on elliptic and other like curves. The methods and apparati allow pairings, such as, for example, Weil pairings, Tate Pairings, Squared Weil pairings, Squared Tate pairings, and/or other like pairings to be determined based on algorithms that utilize a parabola. The methods and apparati represent an improvement over conventional algorithms since they tend to me more computationally efficient.

Abstract: A technology generally related to large-scale computations employed in the fields of cryptography and data security system employing a new and improved variant of the Karatsuba multiplication approach. The variant of the Karatsuba multiplication approach being utilized to minimize the number of coefficient multiplications needed to multiple two polynomials of degree four.

Abstract: A cryptosystem has a secret based on an order of a group of points on a Jacobian of a curve. In certain embodiments, the cryptosystem is used to generate a product identifier corresponding to a particular product. The product identifier is generated by initially receiving a value associated with a copy (or copies) of a product. The received value is padded using a recognizable pattern, and the padded value is converted to a number represented by a particular number of bits. The number is then converted to an element of the Jacobian of the curve, and the element is then raised to a particular power. The result of raising the element to the particular power is then compressed and output as the product identifier. Subsequently, the encryption process can be reversed and the decrypted value used to indicate validity and/or authenticity of the product identifier.

Abstract: Methods and apparati are provided for use in determining “Squared Weil pairings” and/or “Squared Tate Pairing” based on an elliptic curve, for example, and which are then used to support cryptographic processing of selected information. Significant improvements are provided in computing efficiency over the conventional implementation of the Weil and Tate pairings. The resulting Squared Weil and/or Tate pairings can be substituted for conventional Weil or Tate pairings in a variety of applications.

Abstract: Techniques are described that facilitate cryptographic operations, such as data encryption, signing and others, encryption using a computerized method for multiplying a scalar by a point. In one implementation, a set of random integers is selected, wherein the set comprises at least one integer selected randomly. A string is configured, based in part on the set of random integers. Output in the form of a product of the scalar and the point is then calculated, based on the string.

Abstract: Techniques are described for generating and validating signatures. In an implementation, a method includes generating a signature by utilizing a plurality of isogenies included on a private key and incorporating the signature and a public key on a product, in which the public key is configured to validate the signature.

Abstract: In at least one implementation, described herein, P and Q1, . . . , Qn are public points on an elliptic curve over a finite field, but the ratios of Qi to P are private. Those ratios are the components (?1, . . . , ?n) of a private key, where Qi=?i P. This implementation generates short digital ciphers (i.e., signatures), at least in part, by mapping a message M to a point T on the elliptic curve and then scaling that point T based upon the private key ? to get S. At least one other implementation, described herein, verifies those ciphers by comparing pairing values of two pairs, where one pair is the public point P and the scaled point S and another pair is public Q and the point T. This implementation tests whether log(Q)/log(P)=log(S)/log(T), without computing any elliptic curve discrete logarithm directly.

Abstract: Systems and methods for providing signatures are described. In an implementation, a system includes a backend configured to generate a plurality of incomplete signatures using an offline portion of an online/offline signature algorithm, storage configured to store the plurality of incomplete signatures and a front end configured to process a plurality of messages using the plurality of incomplete signatures to form a plurality of digital signatures such that each of the messages has a corresponding one of the digital signatures.

Abstract: An architecture and methodology for implementing Montgomery multiplication on a computer system that supports SIMD instructions is described.

Abstract: An implementation of a digital signature technique, described herein, generates, and another implementation of a digital signature technique, also described herein, validates, a hidden plaintext or ciphertext message wherein one or more portions of that message have another ciphertext message implicitly embedded therein. In other implementations, two or more portions of that message have another ciphertext message implicitly embedded therein. This abstract itself is not intended to limit the scope of this patent. The scope of the present invention is pointed out in the appending claims.

Abstract: A cryptosystem based on a Jacobian of a hyperelliptic curve is being used. Various methods and apparati are provided for generating a compressed data format that identifies one or more points—on the Jacobian of the hyperelliptic curve, and for subsequently decompressing the compressed format data.

Abstract: Methods and apparati are provided for determining a “Squared Tate pairing” for hyperelliptic curves and using the results to support at least one cryptographic process. The improved techniques provide increased efficiency and an alternative method to the conventional method of implementing the Tate pairing for Jacobians of hyperelliptic curves. With the Squared Tate pairing for hyperelliptic curves, one may obtain a significant speed-up over a contemporary implementation of the Tate pairing for hyperelliptic curves. The Squared Tate pairing for hyperelliptic curves can be substituted for the Tate pairing for hyperelliptic curves in any applicable cryptographic application.

Abstract: Methods and apparati are provided for use in determining “Squared Weil pairings” and/or “Squared Tate Pairing” based on an elliptic curve, for example, and which are then used to support cryptographic processing of selected information. Significant improvements are provided in computing efficiency over the conventional implementation of the Weil and Tate pairings. The resulting Squared Weil and/or Tate pairings can be substituted for conventional Weil or Tate pairings in a variety of applications.

Abstract: A technology generally related to large-scale computations is described herein. An implementation, described herein, employs a new and improved variant of the Karatsuba multiplication approach.

Abstract: An implementation of a technology, described herein, for facilitating cryptographic systems and techniques. At least one implementation, described herein, maximizes the speed and security of fast exponentiation while minimizing its expense. At least one implementation, described herein, employs elliptic curves with a fast exponentiation technique so that it maximizes speed and security while minimizing expense. At least one implementation, described herein, employs Koblitz exponentiation with “bucketing” techniques to maximize speed and security of cryptosystems while minimizing expense of such techniques. This abstract itself is not intended to limit the scope of this patent. The scope of the present invention is pointed out in the appending claims.