One embodiment provides a system that facilitates encryption of manifest content based on permutation. During operation, the system partitions, by a computer system, a collection of data into a first set of content objects, wherein a content object is a chunk comprised of a plurality of bytes. The system performs a first permutation function on the first set of content objects to obtain a first set of permuted content objects. The system creates a manifest based on the permuted content objects, wherein a manifest is a content object which indicates a second set of content objects, wherein a respective content object of the second set is a data object or another manifest. The system encodes the first permutation function and the permuted content objects in the manifest, thereby facilitating an authorized entity that receives the manifest to reassemble the manifest contents based on the permutation function.

A system for parallel combinatorial design includes a processor, an in-memory vector processor and a storage unit. The processor includes a seed generator, a Cspan generator and a rule checker. The seed generator generates at least one seed to generate combinations of length N, defining a space of N choices of which M choices are to be selected. The Cspan generator generates at least one combination from the at least one seed and stores each combination in a separate column of the in-memory vector processor. The rule checker performs a parallel search at least in the in-memory vector processor for combinations which satisfy a rule and the storage unit receives search results of the rule checker from the in-memory vector processor.

A system such as a database management system determines a rule to impose sorted order upon a column without applying a sorting algorithm to the column and stores the rule to be applied to sort the column. In an embodiment, a permutation is the rule. The column, in an embodiment, is a column of a database table. In some cases, the rule is used to efficiently impose a correct sorted order on a subset of unsorted columns without the use of a sorting algorithm. In some cases, the rule is generated based at least in part on another column that is sorted using a sorting algorithm such as quicksort.

A processor-implemented method with homomorphic encryption includes: receiving a first ciphertext corresponding to a first modulus; generating a second ciphertext corresponding to a second modulus by performing modulus raising on the first ciphertext; and performing bootstrapping by encoding the second ciphertext using a commutative property and an associative property of operations included in a rotation operation.

An aggregate order is efficiently obtained while keeping confidentiality. An inverse permutating part (12) generates a share of a vector representing an inversely permutated cross tabulation by applying inverse permutation to a cross tabulation of a table, the inverse permutation being a permutation which moves elements so that, when the table is grouped based on a key attribute, last elements of each group are sequentially arranged from beginning. A partial summing part (13) computes a prefix sum from the inversely permutated cross tabulation. The order computing part (14) generates a share of a vector representing ascending order within a group from a result of the prefix sum.

A secure joining system is a secure joining system including a plurality of secure computing apparatuses. The plurality of secure computing apparatuses include a first vector joining unit, a first permutation calculation unit, a first vector generation unit, a second vector joining unit, a first permutation application unit, a second vector generation unit, a first inverse permutation application unit, a first vector extraction unit, a second permutation application unit, a third vector generation unit, a second inverse permutation application unit, a second vector extraction unit, a modified second table generation unit, a third permutation application unit, a fourth vector generation unit, a shifting unit, a third inverse permutation application unit, a bit inversion unit, a third vector extraction unit, a modified first table generation unit, a first table joining unit, and a first table formatting unit.

To perform permutation processing at high speed. A number-of-elements determination unit (22) calculates the number of elements to be contained in each allocation destination. A start position determination unit (23) calculates a start position corresponding to each allocation destination. An allocation destination determination unit (24) calculates a sequence of values representing allocation destinations in a buffer. A permutation generating unit (25) calculates a sequence of values representing permutation destinations within the respective allocation destination. An initial position setting unit (31) sets the start position into a value indicating a position within processing corresponding to each allocation destination. A rearrangement unit (32) sets the elements of a vector into the respective allocation destinations in the buffer. A permutation execution unit (33) generates an output vector by executing an arbitrary inverse permutation algorithm on the respective allocation destinations.

An aggregate order is efficiently obtained while keeping confidentiality. An inverse permutating part (12) generates a share of a vector representing an inversely permutated cross tabulation by applying inverse permutation to a cross tabulation of a table, the inverse permutation being a permutation which moves elements so that, when the table is grouped based on a key attribute, last elements of each group are sequentially arranged from beginning. A partial summing part (13) computes a prefix sum from the inversely permutated cross tabulation. The order computing part (14) generates a share of a vector representing ascending order within a group from a result of the prefix sum.

A processor-implemented method with homomorphic encryption includes: receiving a first ciphertext corresponding to a first modulus; generating a second ciphertext corresponding to a second modulus by performing modulus raising on the first ciphertext; and performing bootstrapping by encoding the second ciphertext using a commutative property and an associative property of operations included in a rotation operation.

To perform permutation processing at high speed. A number-of-elements determination unit (22) calculates the number of elements to be contained in each allocation destination. A start position determination unit (23) calculates a start position corresponding to each allocation destination. An allocation destination determination unit (24) calculates a sequence of values representing allocation destinations in a buffer. A permutation generating unit (25) calculates a sequence of values representing permutation destinations within the respective allocation to destination. An initial position setting unit (31) sets the start position into a value indicating a position within processing corresponding to each allocation destination. A rearrangement unit (32) sets the elements of a vector into the respective allocation destinations in the buffer. A permutation execution unit (33) generates an output vector by executing an arbitrary inverse permutation algorithm on the respective allocation destinations.