White-box implementation

A method for computation of an outcome of an exponentiation Cx having a base C and an exponent x by means of a white-box implementation of the exponentiation, the method comprising:

• receiving information indicative of at least a part of a plurality of values ωi and at least a part of information indicative of a plurality of values φi, the plurality of values ωi satisfying ωi=Cλi, the plurality of values φi, satisfying
• x
• =
• ∑
• i
• =
• 1
• r
• 
• λ
• i
• 
• ϕ
• i
• ,
• i=1, 2, . . . , r ;
• and
• encrypting a message to obtain a ciphertext and/or decrypting the ciphertext to obtain the message, by using
• P
• =
• ∏
• i
• =
• 1
• r
• 
• ω
• i
• ϕ
• i
• wherein P=Cx, thereby hiding at least one of the precise value of the base C and exponent x from a white-box attack.

A non-transitory computer readable storage storing a program comprising instructions, which when executed by a processor, causes the processor to perform computation of an outcome of an exponentiation Cx having a base C and an exponent x by means of a white-box implementation of the exponentiation, comprising:

• receiving a device with information indicative of at least a part of a plurality of values ωi and at least a part of information indicative of a plurality of values φi,
• the plurality of values ωi satisfying ωi=Cλi, the plurality of values φi satisfying
• x
• =
• ∑
• i
• =
• 1
• r
• 
• λ
• i
• 
• ϕ
• i
• ,
• i=1, 2, . . . , r;
• and
• encrypting a message m to obtain a ciphertext and/or decrypting the ciphertext to obtain the message m, by using
• P
• =
• ∏
• i
• =
• 1
• r
• 
• ω
• i
• ϕ
• i
• wherein P=Cx, thereby hiding at least one of the precise value of the base C and exponent x from a white-box attack.

A method for computation of an outcome of an exponentiation Cx having a base C and an exponent x by means of a white-box implementation of the exponentiation, the method comprising:

• establishing a plurality of values λi, for i=1, 2, . . . , r,
• establishing a plurality of values ωi for i=1, 2, . . . , r, satisfying ωi=Cλi, C being associated with a key of a cipher,
• establishing a plurality of values φi, for i=1, 2, . . . , r, satisfying
• x
• =
• ∑
• i
• =
• 1
• r
• 
• λ
• i
• 
• ϕ
• i
• ;
• and
• providing a device with information indicative of at least a part of the plurality of values ωi and at least a part of information indicative of the plurality of values φi to calculate
• P
• =
• ∏
• i
• =
• 1
• r
• 
• ω
• i
• ϕ
• i
• wherein P=Cx, thereby hiding at least one of the precise values of the base C and exponent x from a white-box attack.

A non-transitory computer readable storage storing a program comprising instructions, which when executed by a processor, causes the processor to perform computation of an outcome of an exponentiation Cx having a base C and an exponent x by means of a white-box implementation of the exponentiation, comprising:

• establishing a plurality of values λi, for i=1, 2, . . . , r,
• establishing a plurality of values ωi for i=1, 2, . . . , r, satisfying ωi=Cλi, C being associated with a key of a cipher,
• establishing a plurality of values ωi, for i1, 2, . . . , r, satisfying
• x
• =
• ∑
• i
• =
• 1
• r
• 
• λ
• i
• 
• ϕ
• i
• ;
• and
• providing a device with information indicative of at least a part of the plurality of values ωi and at least a part of information indicative of the plurality of values φi to calculate
• P
• =
• ∏
• i
• =
• 1
• r
• 
• ω
• i
• ϕ
• i
• wherein P=Cx, thereby hiding at least one of the precise values of the base C and exponent x from a white-box attack.